brandenburg

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Author name code: brandenburg
ADS astronomy entries on 2022-09-14
author:"Brandenburg, Axel"

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Title: A Comparative Analysis of Machine-learning Models for Solar
Flare Forecasting: Identifying High-performing Active Region Flare
Indicators
Authors: Sinha, Suvadip; Gupta, Om; Singh, Vishal; Lekshmi, B.;
Nandy, Dibyendu; Mitra, Dhrubaditya; Chatterjee, Saikat; Bhattacharya,
Sourangshu; Chatterjee, Saptarshi; Srivastava, Nandita; Brandenburg,
Axel; Pal, Sanchita
2022ApJ...935...45S Altcode: 2022arXiv220405910S
Solar flares create adverse space weather impacting space- and
Earth-based technologies. However, the difficulty of forecasting
flares, and by extension severe space weather, is accentuated by the
lack of any unique flare trigger or a single physical pathway. Studies
indicate that multiple physical properties contribute to active region
flare potential, compounding the challenge. Recent developments in
machine learning (ML) have enabled analysis of higher-dimensional data
leading to increasingly better flare forecasting techniques. However,
consensus on high-performing flare predictors remains elusive. In the
most comprehensive study to date, we conduct a comparative analysis of
four popular ML techniques (k nearest neighbors, logistic regression,
random forest classifier, and support vector machine) by training these
on magnetic parameters obtained from the Helioseismic and Magnetic
Imager on board the Solar Dynamics Observatory for the entirety of solar
cycle 24. We demonstrate that the logistic regression and support vector
machine algorithms perform extremely well in forecasting active region
flaring potential. The logistic regression algorithm returns the highest
true skill score of 0.967 ± 0.018, possibly the highest classification
performance achieved with any strictly parametric study. From a
comparative assessment, we establish that magnetic properties like
total current helicity, total vertical current density, total unsigned
flux, R_VALUE, and total absolute twist are the top-performing flare
indicators. We also introduce and analyze two new performance metrics,
namely, severe and clear space weather indicators. Our analysis
constrains the most successful ML algorithms and identifies physical
parameters that contribute most to active region flare productivity.

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Title: Magnetohydrodynamics predicts heavy-tailed distributions of
axion-photon conversion
Authors: Carenza, Pierluca; Sharma, Ramkishor; Marsh, M. C. David;
Brandenburg, Axel; Müller, Eike
2022arXiv220804333C Altcode:
The conversion of axionlike particles (ALPs) and photons in magnetised
astrophysical environments provides a promising route to search for
ALPs. The strongest limits to date on light ALPs use galaxy clusters
as ALP--photon converters. However, such studies traditionally
rely on simple models of the cluster magnetic fields, with the
state-of-the-art being Gaussian random fields (GRFs). We present the
first systematic study of ALP-photon conversion in more realistic,
turbulent fields from dedicated magnetohydrodynamic (MHD) simulations,
which we compare with GRF models. For GRFs, we analytically derive
the distribution of conversion ratios at fixed energy and find that
it follows an exponential law. We find that the MHD models agree
with the exponential law for typical, small amplitude mixings but
exhibit distinctly heavy tails for rare and large mixings. We explain
how non-Gaussian, local spikes in the MHD magnetic field are mainly
responsible for the heavy tail. Our results indicate that limits placed
on ALPs using GRFs are conservative but that MHD models are necessary
to reach the full potential of these searches.

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Title: Batchelor, Saffman, and Kazantsev spectra in galactic
small-scale dynamos
Authors: Brandenburg, Axel; Zhou, Hongzhe; Sharma, Ramkishor
2022arXiv220709414B Altcode:
The magnetic fields in galaxy clusters and probably also in the
interstellar medium are believed to be generated by a small-scale
dynamo. Theoretically, during its kinematic stage, it is characterized
by a Kazantsev spectrum, which peaks at the resistive scale. It is
only slightly shallower than the Saffman spectrum that is expected for
random and causally connected magnetic fields. Causally disconnected
fields have the even steeper Batchelor spectrum. Here we show that
all three spectra are present in the small-scale dynamo. During the
kinematic stage, the Batchelor spectrum occurs on scales larger than
the energy-carrying scale of the turbulence, and the Kazantsev spectrum
on smaller scales within the inertial range of the turbulence -- even
for a magnetic Prandtl number of unity. In the saturated state, the
dynamo develops a Saffman spectrum on large scales. At large magnetic
Prandtl numbers, elongated structures are seen in the parity-even E
polarization, but not in the parity-odd B polarization. We also observe
a significant excess in the E polarization over the B polarization at
subresistive scales, and a deficiency at larger scales. This finding is
at odds with the observed excess in the Galactic microwave foreground
emission. The E and B polarizations become Gaussian in the saturated
state, but may be highly non-Gaussian and skewed in the kinematic
regime of the dynamo.

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Title: Scaling of the Saffman helicity integral in decaying
magnetically-dominated turbulence
Authors: Zhou, Hongzhe; Sharma, Ramkishor; Brandenburg, Axel
2022arXiv220607513Z Altcode:
The Saffman helicity integral of Hosking and Schekochihin (2021, PRX
11, 041005) has emerged as an important quantity that may govern the
decay properties of magnetically dominated turbulence. Using a range
of different computational methods, we confirm that this quantity is
indeed gauge-invariant and nearly perfectly conserved in the limit of
large Lundquist numbers. For direct numerical simulations with ordinary
viscosity and magnetic diffusivity operators, we find that the solution
develops in a nearly self-similar fashion. In a diagram quantifying the
instantaneous decay coefficients of magnetic energy and integral scale,
we find that the solution evolves along a line that is indeed suggestive
of the governing role of the Saffman helicity integral. The solution
settles near a line in this diagram that is expected for a self-similar
evolution of the magnetic energy spectrum. However, the solution may
settle in a slightly different position when the magnetic diffusivity
decreases with time, which would be compatible with the decay being
governed by the reconnection time scale rather than the Alfvén time.

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Title: Compressible Test-field Method and Its Application to Shear
Dynamos
Authors: Käpylä, Maarit J.; Rheinhardt, Matthias; Brandenburg, Axel
2022ApJ...932....8K Altcode: 2021arXiv210601107K
In this study, we present a compressible test-field method (CTFM)
for computing α-effect and turbulent magnetic diffusivity tensors,
as well as those relevant for the mean ponderomotive force and mass
source, applied to the full MHD equations. We describe the theoretical
background of the method and compare it to the quasi-kinematic
test-field method and to the previously studied variant working in
simplified MHD (SMHD). We present several test cases using velocity
and magnetic fields of the Roberts geometry and also compare with
the imposed-field method. We show that, for moderate imposed-field
strengths, the nonlinear CTFM (nCTFM) gives results in agreement with
the imposed-field method. A comparison of different flavors of the nCTFM
in the shear dynamo case also yields agreement up to equipartition
field strengths. Some deviations between the CTFM and SMHD variants
exist. As a relevant physical application, we study nonhelically forced
shear flows, which exhibit large-scale dynamo action, and present a
reanalysis of low-Reynolds-number, moderate shear systems, where we
previously ignored the pressure gradient in the momentum equation and
found no coherent shear-current effect. Another key difference is that
in the earlier study we used magnetic forcing to mimic small-scale
dynamo action, while here it is self-consistently driven by purely
kinetic forcing. The kinematic CTFM with general validity forms the
core of our analysis. We still find no coherent shear-current effect,
but do recover strong large-scale dynamo action that, according to
our analysis, is driven by incoherent effects.

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Title: Chiral Magnetic Fields and Gravitational Waves
Authors: Stepp, Jonathan; Kahniashvili, Tina; Clarke, Emma;
Brandenburg, Axel
2022AAS...24020202S Altcode:
In the early universe, asymmetry in the number density between right and
left-handed fermions causes chiral magnetic fields to grow exponentially
due to the chiral magnetic effect. Since the total chirality of both
the magnetic field and fermions is conserved, the asymmetry limits the
maximum strength of these magnetic fields due to this effect. Updated
values for effective neutrino count, primordial hydrogen abundance and
baryon-photon ratio allow us to constrain the lepton asymmetry due to
neutrino species and compute new limits on primordial chiral magnetic
fields. We also compute the energy and polarization of gravitational
waves generated by these helical sources and compare them to current
detection prospects.

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Title: Big Bang Nucleosynthesis Limits and Relic Gravitational-Wave
Detection Prospects
Authors: Kahniashvili, Tina; Clarke, Emma; Stepp, Jonathan;
Brandenburg, Axel
2022PhRvL.128v1301K Altcode: 2021arXiv211109541K
We revisit the big bang nucleosynthesis limits on primordial magnetic
fields and/or turbulent motions accounting for the decaying nature
of turbulent sources between the time of generation and big bang
nucleosynthesis. This leads to larger estimates for the gravitational
wave signal than previously expected. We address the detection
prospects through space-based interferometers and pulsar timing arrays
or astrometric missions for gravitational waves generated around the
electroweak and quantum chromodynamics energy scale, respectively.

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Title: Dynamo effect in unstirred self-gravitating turbulence
Authors: Brandenburg, Axel; Ntormousi, Evangelia
2022MNRAS.513.2136B Altcode: 2022MNRAS.tmp..975B; 2021arXiv211203838B
In many astrophysical environments, self-gravity can generate
kinetic energy, which, in principle, is available for driving dynamo
action. Using direct numerical simulations, we show that in unstirred
self-gravitating subsonic turbulence with helicity and a magnetic
Prandtl number of unity, there is a critical magnetic Reynolds
number of about 25 above which the work done against the Lorentz
force exceeds the Ohmic dissipation. The collapse itself drives
predominantly irrotational motions that cannot be responsible for
dynamo action. We find that, with a weak magnetic field, one-third
of the work done by the gravitational force goes into compressional
heating and the remaining two-thirds go first into kinetic energy
of the turbulence before a fraction of it is converted further into
magnetic and finally thermal energies. Close to the collapse, however,
these fractions change toward 1/4 and 3/4 for compressional heating
and kinetic energy, respectively. When the magnetic field is strong,
the compressional heating fraction is unchanged. Out of the remaining
kinetic energy, one quarter goes directly into magnetic energy via work
against the Lorentz force. The fraction of vortical motions diminishes
in favour of compressive motions that are almost exclusively driven by
the Jeans instability. For an initially uniform magnetic field, field
amplification at scales larger than those of the initial turbulence
are driven by tangling.

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Title: Low frequency tail of gravitational wave spectra from
hydromagnetic turbulence
Authors: Sharma, Ramkishor; Brandenburg, Axel
2022arXiv220600055S Altcode:
Hydrodynamic and magnetohydrodynamic (MHD) turbulence in the early
Universe can drive gravitational waves (GWs) and imprint their spectrum
onto that of GWs, which might still be observable today. We study the
production of the GW background from freely decaying MHD turbulence
for helical and nonhelical initial magnetic fields. To understand
the produced GW spectra, we develop a simple model on the basis of
the evolution of the magnetic stress tensor. We find that the GW
spectra obtained in this model reproduce those obtained in numerical
simulations if we consider the time evolution of the low frequency
tail of the stress spectrum from numerical simulations. We also show
that the shapes of the produced GW frequency spectra are different
for helical and nonhelical cases for the same initial magnetic energy
spectra. Such differences can help distinguish helical and nonhelical
initial magnetic fields from a polarized background of GWs -- especially
when the expected circular polarization cannot be detected directly.

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Title: Evolution of Primordial Magnetic Fields during Large-scale
Structure Formation
Authors: Mtchedlidze, Salome; Domínguez-Fernández, Paola; Du,
Xiaolong; Brandenburg, Axel; Kahniashvili, Tina; O'Sullivan, Shane;
Schmidt, Wolfram; Brüggen, Marcus
2022ApJ...929..127M Altcode: 2021arXiv210913520M
Primordial magnetic fields (PMFs) could explain the large-scale magnetic
fields present in the universe. Inflation and phase transitions
in the early universe could give rise to such fields with unique
characteristics. We investigate the magnetohydrodynamic evolution
of these magnetogenesis scenarios with cosmological simulations. We
evolve inflation-generated magnetic fields either as (i) uniform
(homogeneous) or as (ii) scale-invariant stochastic fields, and
phase-transition-generated ones either as (iii) helical or as (iv)
nonhelical fields from the radiation-dominated epoch. We find that
the final distribution of magnetic fields in the simulated cosmic web
shows a dependence on the initial strength and the topology of the
seed field. Thus, the observed field configuration retains information
on the initial conditions at the moment of the field generation. If
detected, PMF observations would open a new window for indirect probes
of the early universe. The differences between the competing models are
revealed on the scale of galaxy clusters, bridges, as well as filaments
and voids. The distinctive spectral evolution of different seed fields
produces imprints on the correlation length today. We discuss how the
differences between rotation measures from highly ionized regions can
potentially be probed with forthcoming surveys.

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Title: Polarization of gravitational waves from helical MHD turbulent
sources
Authors: Roper Pol, Alberto; Mandal, Sayan; Brandenburg, Axel;
Kahniashvili, Tina
2022JCAP...04..019R Altcode: 2021arXiv210705356R
We use direct numerical simulations of decaying primordial hydromagnetic
turbulence with helicity to compute the resulting gravitational wave
(GW) production and its degree of circular polarization. The turbulence
is sourced by magnetic fields that are either initially present
or driven by an electromotive force applied for a short duration,
given as a fraction of one Hubble time. In both types of simulations,
we find a clear dependence of the polarization of the resulting GWs
on the fractional helicity of the turbulent source. We find a low
frequency tail below the spectral peak shallower than the f 3
scaling expected at super-horizon scales, in agreement with similar
recent numerical simulations. This type of spectrum facilitates its
observational detection with the planned Laser Interferometer Space
Antenna (LISA). We show that driven magnetic fields produce GWs
more efficiently than magnetic fields that are initially present,
leading to larger spectral amplitudes, and to modifications of the
spectral shape. In particular, we observe a sharp drop of GW energy
above the spectral peak that is in agreement with the previously
obtained results. The helicity does not have a huge impact on the
maximum spectral amplitude in any of the two types of turbulence
considered. However, the GW spectrum at wave numbers away from the
peak becomes smaller for larger values of the magnetic fractional
helicity. Such variations of the spectrum are most noticeable when
magnetic fields are driven. The degree of circular polarization
approaches zero at frequencies below the peak, and reaches its maximum
at the peak. At higher frequencies, it stays finite if the magnetic
field is initially present, and it approaches zero if it is driven. We
predict that the spectral peak of the GW signal can be detected by LISA
if the turbulent energy density is at least ~3% of the radiation energy
density, and the characteristic scale is a hundredth of the horizon at
the electroweak scale. We show that the resulting GW polarization is
unlikely to be detectable by the anisotropies induced by our proper
motion in the dipole response function of LISA. Such signals can,
however, be detectable by cross-correlating data from the LISA-Taiji
network for turbulent energy densities of ~5%, and fractional helicity
of 0.5 to 1. Second-generation space-base GW detectors, such as BBO
and DECIGO, would allow for the detection of a larger range of the GW
spectrum and smaller amplitudes of the magnetic field.

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Title: Spectral characterisation of inertial particle clustering
in turbulence
Authors: Haugen, Nils E. L.; Brandenburg, Axel; Sandin, Christer;
Mattsson, Lars
2022JFM...934A..37H Altcode: 2021arXiv210501539H
Clustering of inertial particles is important for many types of
astrophysical and geophysical turbulence, but it has been studied
predominately for incompressible flows. Here, we study compressible
flows and compare clustering in both compressively (irrotationally)
and vortically (solenoidally) forced turbulence. Vortically and
compressively forced flows are driven stochastically either by
solenoidal waves or by circular expansion waves, respectively. For
compressively forced flows, the power spectrum of the density of
inertial particles is a useful tool for displaying particle clustering
relative to the fluid density enhancement. Power spectra are shown to
be particularly sensitive for studying large-scale particle clustering,
while conventional tools such as radial distribution functions are more
suitable for studying small-scale clustering. Our primary finding is
that particle clustering through shock interaction is particularly
prominent in turbulence driven by spherical expansion waves. It
manifests itself through a double-peaked distribution of spectral
power as a function of Stokes number. The two peaks are associated
with two distinct clustering mechanisms; shock interaction for smaller
Stokes numbers and the centrifugal sling effect for larger values. The
clustering of inertial particles is associated with the formation
of caustics. Such caustics can only be captured in the Lagrangian
description, which allows us to assess the relative importance
of caustics in vortically and compressively forced turbulence. We
show that the statistical noise resulting from the limited number of
particles in the Lagrangian description can be removed from the particle
power spectra, allowing us a more detailed comparison of the residual
spectra. We focus on the Epstein drag law relevant for rarefied gases,
but show that our findings apply also to the usual Stokes drag.

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Title: Skumanich-55 revisited
Authors: Brandenburg, A.
2022fysr.confE..53B Altcode:
When I started my undergraduate research in Hamburg in 1984, my
professor pointed me to Skumanich-55. It is interesting to review
the thinking at the time. The Vitense-53 paper laid the foundation
for thinking that the Schwarzschild-unstable layer was at least
70 Mm deep, contrary to the earlier picture of the 1930s of less
than 1 Mm. In Skumanich-55, the governing idea is not to postulate
a characteristic size of eddies, but to ask which eddies grow the
fastest. In unstratified Rayleigh-Benard convection, they all grow
at the same rate, but in a polytropic layer, smaller eddies are more
unstable, which led Skumanich to argue that small eddies should be
predominant. This is different from standard mixing length ideas and
perhaps also from some simulations. However, both ignore the phenomenon
of entropy rain and the possibility of the convective flux in the deeper
layers not being carried by a gradient flux, but predominantly by the
Deardorff flux. Although none of this was part of the Skumanich model,
it also suggests a predominance of smaller eddies. In this sense,
his model deserves some renewed attention!

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Title: Dynamo instabilities in plasmas with inhomogeneous chiral
chemical potential
Authors: Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel
2022PhRvD.105d3507S Altcode: 2021arXiv210713028S
We study the dynamics of magnetic fields in chiral magnetohydrodynamics,
which takes into account the effects of an additional electric current
related to the chiral magnetic effect in high-energy plasmas. We perform
direct numerical simulations, considering weak seed magnetic fields and
inhomogeneities of the chiral chemical potential μ5 with a
zero mean. We demonstrate that a small-scale chiral dynamo can occur in
such plasmas if fluctuations of μ5 are correlated on length
scales that are much larger than the scale on which the dynamo growth
rate reaches its maximum. Magnetic fluctuations grow by many orders of
magnitude due to the small-scale chiral dynamo instability. Once the
nonlinear backreaction of the generated magnetic field on fluctuations
of μ5 sets in, the ratio of these scales decreases and
the dynamo saturates. When magnetic fluctuations grow sufficiently to
drive turbulence via the Lorentz force before reaching maximum field
strength, an additional mean-field dynamo phase is identified. The mean
magnetic field grows on a scale that is larger than the integral scale
of turbulence after the amplification of the fluctuating component
saturates. The growth rate of the mean magnetic field is caused by a
magnetic α effect that is proportional to the current helicity. With
the onset of turbulence, the power spectrum of μ5 develops
a universal k-1 scaling independently of its initial shape,
while the magnetic energy spectrum approaches a k-3 scaling.

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Title: Production of a Chiral Magnetic Anomaly with Emerging
Turbulence and Mean-Field Dynamo Action
Authors: Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel
2022PhRvL.128f5002S Altcode: 2021arXiv210712945S
In relativistic magnetized plasmas, asymmetry in the number densities
of left- and right-handed fermions, i.e., a nonzero chiral chemical
potential μ5, leads to an electric current along the
magnetic field. This causes a chiral dynamo instability for a uniform
μ5, but our simulations reveal a dynamo even for fluctuating
μ5 with zero mean. It produces magnetically dominated
turbulence and generates mean magnetic fields via the magnetic
α effect. Eventually, a universal scale-invariant k-1
spectrum of μ5 and a k-3 magnetic spectrum are
formed independently of the initial condition.

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Title: Big Bang Nucleosynthesis Limits and Relic Gravitational Wave
Detection Prospects
Authors: Clarke, Emma; Kahniashvili, Tina; Stepp, Jonathan;
Brandenburg, Axel
2022APS..APRT14003C Altcode:
Big bang nucleosynthesis (BBN) places upper limits on the relativistic
energy density in the early universe, which places bounds on the
strength of primordial magnetic fields and/or turbulent motions in
the early universe and their resulting relic gravitational wave (GW)
signals. Previous studies assumed that velocity and magnetic fields
are “frozen-in” to the primordial plasma and that the ratio between
the turbulent source energy density and thermal energy density remain
unchanged during the radiation-dominated epoch. We revisit the BBN
limits and properly account for the decaying nature of turbulent sources
from their generation until BBN. We find that allowed values for the
magnetic fields at the moment of generation are not constrained by order
of microGauss as was claimed previously based on BBN bounds without
accounting for decaying turbulence. This allows larger estimates for
the initial magnetic field strength and stronger GW signals than were
previously expected. We address the prospects of detecting these GW
signals through space-based interferometers (for GWs generated around
the electroweak scale) and by pulsar timing arrays and astrometric
missions (for GWs generated around the quantum chromodynamics energy
scale).

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Title: Simulations of Helical Inflationary Magnetogenesis and
Gravitational Waves
Authors: Brandenburg, Axel; He, Yutong; Sharma, Ramkishor
2021ApJ...922..192B Altcode: 2021arXiv210712333B
Using numerical simulations of helical inflationary magnetogenesis in
a low reheating temperature scenario, we show that the magnetic energy
spectrum is strongly peaked at a particular wavenumber that depends
on the reheating temperature. Gravitational waves (GWs) are produced
at frequencies between 3 nHz and 50 mHz for reheating temperatures
between 150 MeV and 3 × 105 GeV, respectively. At and
below the peak frequency, the stress spectrum is always found to
be that of white noise. This implies a linear increase of GW energy
per logarithmic wavenumber interval, instead of a cubic one. Both in
the helical and nonhelical cases, the GW spectrum is followed by a
sharp drop for frequencies above the respective peak frequency. In
this magnetogenesis scenario, the presence of a helical term extends
the peak of the GW spectrum and therefore also the position of the
aforementioned drop toward larger frequencies compared to the case
without helicity. This might make a difference in it being detectable
with space interferometers. The efficiency of GW production is found to
be almost the same as in the nonhelical case, and independent of the
reheating temperature, provided the electromagnetic energy at the end
of reheating is fixed to be a certain fraction of the radiation energy
density. Also, contrary to the case without helicity, the electric
energy is now less than the magnetic energy during reheating. The
fractional circular polarization is found to be nearly 100% in a
certain range below the peak frequency range.

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Title: Chirality in Astrophysics
Authors: Brandenburg, Axel
2021arXiv211008117B Altcode:
Chirality, or handedness, enters astrophysics in three distinct
ways. Magnetic field and vortex lines tend to be helical and have a
systematic twist in the northern and southern hemispheres of a star
or a galaxy. Helicity is here driven by external factors. Chirality
can also enter at the microphysical level and can then be traced
back to the parity-breaking weak force. Finally, chirality can
arise spontaneously, but this requires not only the presence of an
instability, but also the action of nonlinearity. Examples can be found
both in magnetohydrodynamics and in astrobiology, where homochirality
among biomolecules probably got established at the origin of life. In
this review, all three types of chirality production will be explored
and compared.

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Title: Leading-order nonlinear gravitational waves from reheating
magnetogeneses
Authors: He, Yutong; Roper Pol, Alberto; Brandenburg, Axel
2021arXiv211014456H Altcode:
We study the leading-order nonlinear gravitational waves
(GWs) produced by an electromagnetic (EM) stress in reheating
magnetogenesis scenarios. Both nonhelical and helical magnetic fields
are considered. By numerically solving the linear and leading-order
nonlinear GW equations, we find that the GW energy from the latter is
usually larger. We compare their differences in terms of the GW spectrum
and parameterize the GW energy difference due to the nonlinear term,
$\Delta\mathcal{E}_{\rm GW}$, in terms of EM energy $\mathcal{E}_{\rm
EM}$ as $\Delta\mathcal{E}_{\rm GW}=(\tilde p\mathcal{E}_{\rm
EM}/k_*)^3$, where $k_*$ is the characteristic wave number, $\tilde
p=0.84$ and $0.88$ are found in the nonhelical and helical cases,
respectively, with reheating around the QCD energy scale, while $\tilde
p=0.45$ is found at the electroweak energy scale. We also compare the
polarization spectrum of the linear and nonlinear cases and find that
adding the nonlinear term usually yields a decrease in the polarization
that is proportional to the EM energy density. We parameterize the
fractional polarization suppression as $|\Delta \mathcal{P}_{\rm
GW}/\mathcal{P}_{\rm GW}|=\tilde r \mathcal{E}_{\rm EM}/k_*$ and
find $\tilde r = 1.2 \times 10^{-1}$, $7.2 \times 10^{-4}$, and $3.2
\times 10^{-2}$ for the helical cases with reheating temperatures
$T_{\rm r} = 300 {\rm TeV}$, $8 {\rm GeV}$, and $120 {\rm MeV}$,
respectively. Prospects of observation by pulsar timing arrays,
space-based interferometers, and other novel detection proposals are
also discussed.

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Title: Simulating Relic Gravitational Waves from Inflationary
Magnetogenesis
Authors: Brandenburg, Axel; Sharma, Ramkishor
2021ApJ...920...26B Altcode: 2021arXiv210603857B
We present three-dimensional direct numerical simulations of the
production of magnetic fields and gravitational waves (GWs) in the early
universe during a low energy scale matter-dominated post-inflationary
reheating era, and during the early subsequent radiative era, which
is strongly turbulent. The parameters of the model are determined
such that it avoids a number of known physical problems and produces
magnetic energy densities between 0.03% and 0.5% of the critical energy
density at the end of reheating. During the subsequent development
of a turbulent magnetohydrodynamic cascade, magnetic fields and GWs
develop a spectrum that extends to higher frequencies in the millihertz
(nanohertz) range for models with reheating temperatures of around 100
GeV (150 MeV) at the beginning of the radiation-dominated era. However,
even though the turbulent cascade is fully developed, the GW spectrum
shows a sharp drop for frequencies above the peak value. This suggests
that the turbulence is less efficient in driving GWs than previously
thought. The peaks of the resulting GW spectra may well be in the
range accessible to space interferometers, pulsar timing arrays,
and other facilities.

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Title: Turbulent radiative diffusion and turbulent Newtonian cooling
Authors: Brandenburg, Axel; Das, Upasana
2021PhFl...33i5125B Altcode: 2020arXiv201007046B
Radiation transport plays an important role in stellar atmospheres,
but the effects of turbulence are being obscured by other effects such
as stratification. Using radiative hydrodynamic simulations of forced
turbulence, we determine the decay rates of sinusoidal large-scale
temperature perturbations of different wavenumbers in the optically
thick and thin regimes. Increasing the wavenumber increases the rate
of decay in both regimes, but this effect is much weaker than for the
usual turbulent diffusion of passive scalars, where the increase is
quadratic for small wavenumbers. The turbulent decay is well described
by an enhanced Newtonian cooling process in the optically thin limit,
which is found to show a weak increase proportional to the square
root of the wavenumber. In the optically thick limit, the increase
in turbulent decay is somewhat steeper for wavenumbers below the
energy-carrying wavenumber of the turbulence, but levels off toward
larger wavenumbers. In the presence of turbulence, the typical cooling
time is comparable to the turbulent turnover time. We observe that
the temperature takes a long time to reach equilibrium in both the
optically thin and thick cases, but in the former, the temperature
retains smaller scale structures for longer.

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Title: Can we observe the QCD phase transition-generated gravitational
waves through pulsar timing arrays?
Authors: Brandenburg, Axel; Clarke, Emma; He, Yutong; Kahniashvili,
Tina
2021PhRvD.104d3513B Altcode: 2021arXiv210212428B
We perform numerical simulations of gravitational waves (GWs)
induced by hydrodynamic and hydromagnetic turbulent sources that
might have been present at cosmological quantum chromodynamic (QCD)
phase transitions. For turbulent energies of about 4% of the radiation
energy density, the typical scale of such motions may have been a
sizable fraction of the Hubble scale at that time. The resulting
GWs are found to have an energy fraction of about 10-9
of the critical energy density in the nHz range today and may already
have been observed by the NANOGrav Collaboration. This is further made
possible by our findings of shallower spectra proportional to the square
root of the frequency for nonhelical hydromagnetic turbulence. This
implies more power at low frequencies than for the steeper spectra
previously anticipated. The behavior toward higher frequencies depends
strongly on the nature of the turbulence. For vortical hydrodynamic
and hydromagnetic turbulence, there is a sharp drop of spectral GW
energy by up to five orders of magnitude in the presence of helicity,
and somewhat less in the absence of helicity. For acoustic hydrodynamic
turbulence, the sharp drop is replaced by a power law decay, albeit
with a rather steep slope. Our study supports earlier findings of a
quadratic scaling of the GW energy with the magnetic energy of the
turbulence and inverse quadratic scaling with the peak frequency,
which leads to larger GW energies under QCD conditions.

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Title: Tensor spectrum of turbulence-sourced gravitational waves as
a constraint on graviton mass
Authors: He, Yutong; Brandenburg, Axel; Sinha, Aditya
2021JCAP...07..015H Altcode: 2021arXiv210403192H; 2021JCAP...08..015H
We consider a generic dispersive massive gravity theory and
numerically study its resulting modified energy and strain spectra
of tensor gravitational waves (GWs) sourced by (i) fully developed
turbulence during the electroweak phase transition (EWPT) and (ii)
forced hydromagnetic turbulence during the QCD phase transition
(QCDPT). The GW spectra are then computed in both spatial and temporal
Fourier domains. We find, from the spatial spectra, that the slope
modifications are weakly dependent on the eddy size at QCDPT, and,
from the temporal spectra, that the modifications are pronounced in
the 1-10 range - the sensitivity range of the North American Nanohertz
Observatory for Gravitational Waves (NANOGrav) - for a graviton mass
in the range 2×10-23 c27×10-22.

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Title: The scalar, vector, and tensor modes in gravitational wave
turbulence simulations
Authors: Brandenburg, Axel; Gogoberidze, Grigol; Kahniashvili, Tina;
Mandal, Sayan; Roper Pol, Alberto; Shenoy, Nakul
2021CQGra..38n5002B Altcode: 2021arXiv210301140B
We study the gravitational wave (GW) signal sourced by primordial
turbulence that is assumed to be present at cosmological phase
transitions like the electroweak and quantum chromodynamics phase
transitions. We consider various models of primordial turbulence, such
as those with and without helicity, purely hydrodynamical turbulence
induced by fluid motions, and magnetohydrodynamic turbulence whose
energy can be dominated either by kinetic or magnetic energy, depending
on the nature of the turbulence. We also study circularly polarized GWs
generated by parity violating sources such as helical turbulence. Our
ultimate goal is to determine the efficiency of GW production through
different classes of turbulence. We find that the GW energy and strain
tend to be large for acoustic or irrotational turbulence, even though
its tensor mode amplitude is relatively small at most wave numbers. Only
at very small wave numbers is the spectral tensor mode significant,
which might explain the efficient GW production in that case.

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Title: Can We Observe QCD Phase Transition-Generated Gravitational
Waves Through Pulsar Timing Arrays?
Authors: Clarke, E.; Brandenburg, A.; He, Y.; Kahniashvili, T.
2021AAS...23823006C Altcode:
The NANOGrav collaboration recently reported evidence of a stochastic
common-spectrum process which might be interpreted as a stochastic
gravitational wave background in the nHz frequency range. One possible
explanation for this signal is gravitational waves (GWs) generated at
quantum chromodynamic (QCD) scales in the early universe. I will discuss
numerical simulations of GWs induced by hydrodynamic and hydromagnetic
turbulent sources that might have been present at cosmological QCD phase
transitions. For turbulent energies of about 4% of the radiation energy
density, the typical scale of such motions may have been a sizable
fraction of the Hubble scale at that time. The resulting GWs are found
to have an energy fraction of about 10-9 of the critical
energy density in the nHz range today. Our finding of shallower GW
spectra proportional to the square root of the frequency for nonhelical
hydromagnetic turbulence implies more power at low frequencies than
for the steeper spectra previously anticipated. The behavior toward
higher frequencies depends strongly on the nature of the turbulence. For
vortical hydrodynamic and hydromagnetic turbulence, there is a sharp
drop of spectral GW energy by up to five orders of magnitude in the
presence of helicity, and somewhat less in the absence of helicity. For
acoustic hydrodynamic turbulence, the sharp drop is replaced by a power
law decay with a rather steep slope. These results support earlier
findings of a quadratic scaling of the GW energy with the magnetic
energy of the turbulence and an inverse quadratic scaling with the
peak frequency, leading to larger GW energies under QCD conditions.

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Title: Relic Gravitational Waves From The Chiral Magnetic Effect
Authors: He, Y.; Brandenburg, A.; Kahniashvili, T.; Rheinhardt, M.;
Schober, J.
2021AAS...23823005H Altcode:
A system of fermions can exhibit chiral asymmetry, which can
be quantified by the chiral chemical potential μ5,
proportional to the number density difference between left- and
right-handed fermions, i.e. μ5 ∝ (nL −
nR). If μ5 is large enough, it can work as a
dynamo effect and exponentially increase a seed magnetic field. This
is known as the chiral magnetic effect (CME). While active, the
CME converts the initial chiral asymmetry μ50 into
magnetic helicity on the order of BrmsξM,
where ξM is the magnetic correlation length. Although
magnetic helicity generated by CME alone is too small compared to the
constraint inferred from the non-observations of GeV-energy halos around
TeV blazars, and the frequency of CME-induced gravitational waves (GWs)
is too high compared to current and future detectors' sensitivity, we
could still treat the CME as a proxy of other sourcing mechanisms for
primordial GWs. In terms of GW production, we identify two regimes of
interest, distinguished by the relative magnitude of two characteristic
velocities vλ = μ50/λ1/2 and
vμ = μ50η, where λ characterises the depletion
of μ5 and η is the magnetic diffusivity. So vλ
characterises the depletion of chiral asymmetry and vμ
characterises the generation of magnetic field. We therefore say
that η k1 &lt; vμ &lt; vλ
is in regime I, and η k1 &lt; vλ &lt;
vμ is in regime II, where k1 is the smallest
wavenumber in the domain and μ50 &gt; k1 is
excitation threshold for CME. In both regimes, we note that there
are two evolutionary phases, where in phase 1) the magnetic field is
CME-driven and reaches maximum, which determines the GW energy, and in
phase 2) the magnetic length scales increase as its energy decreases,
which is probably irrelevant to GW production. In this study, we
performed a series of numerical simulations, where η was varied by
more than 4 orders of magnitude, μ50 and λ1/2
by about 2 orders of magnitude each. We have found that the GW energy
goes as ΩGWsat ∝ vλ5
vμ. Perhaps a counterintuitive finding is that in regime II,
large GW energies can be generated. However, we note that, in general,
the overall conversion from CME-induced magnetic to GW energy is less
efficient than for forced and decaying turbulence due to the small
length scales associated with the CME. References: Brandenburg,
A., He, Y., Kahniashvili, T., Rheinhardt, M. &amp; Schober, J. Relic
gravitational waves from the chiral magnetic effect. ApJ, in press
(2021). 2101.08178.

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Title: Primordial Magnetic Fields through Large Scale Structure
Authors: Mtchedlidze, S.; Domínguez-Fernández, P.; Du, X.;
Brandenburg, A.; Kahniashvili, T.
2021AAS...23810909M Altcode:
The existence of magnetic fields is ubiquitous on astrophysical and
cosmological scales: from planets andstars to galaxies and galaxy
clusters. It is commonly assumed that the observed fields today are
originated from either astrophysical or cosmological magnetic seeds.The
recent observations of blazar spectra by the Fermi Gamma Ray Observatory
provides an intriguing possibility of detecting very weak magnetic
fields in cosmic voids.This poses an exciting avenue for studying the
generation mechanisms and evolution of observed large-scale correlated
magnetic fields. Notably, numerical (cosmological) simulations and
faraday rotation measure maps show the large scale morphology of these
fields, i.e the magnetic correlation lengths extending beyond the
galaxy clusters' scales. This, in principle, is hard to explain by the
astrophysical sources of the field generation and amplification such
as the Biermann battery and dynamo even with the various mechanisms
of magnetic seed transport (in a few Gyr timeframe). On the other
hand, primordial magnetic fields (PMFs), being good candidates for
the seed magnetic fields, might be generated in the early Universe
through different processes such as quantum-mechanical fluctuations
during inflation, bubble collisions during cosmological first order
phase transitions, primordial turbulent motions, etc. Interestingly,
inflationary generated magnetic fields might have unlimited (i.e.not
constrained by the Hubble scale) correlations length scale, while
causally generated magnetic fields (for example during the phase
transitions) are characterized by the correlation length having
an upper limit equal to the Hubble length scale. In our work,
using numerical magnetized cosmological simulations we explore the
evolution of the primordial magnetic fields (assuming various models
of the field generation) during the structure formation (i.e. late
stages). We properly account for the magnetic field dynamics prior
recombination as well as development of turbulent motions. We study
how these seed magnetic fields evolve during structure formation and
what can be the observable traces of such fields. Our findings include:
the distinctive spectral evolution of different seed fields imprinted on
the scale of galaxy clusters, bridges, as well as filaments and voids,
and differences in the rotation measure maps.

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Title: Relic Gravitational Waves from the Chiral Magnetic Effect
Authors: Brandenburg, Axel; He, Yutong; Kahniashvili, Tina; Rheinhardt,
Matthias; Schober, Jennifer
2021ApJ...911..110B Altcode: 2021arXiv210108178B
Relic gravitational waves (GWs) can be produced by primordial magnetic
fields. However, not much is known about the resulting GW amplitudes
and their dependence on the details of the generation mechanism. Here
we treat magnetic field generation through the chiral magnetic effect
(CME) as a generic mechanism and explore its dependence on the speed
of generation (the product of magnetic diffusivity and characteristic
wavenumber) and the speed characterizing the maximum magnetic field
strength expected from the CME. When the latter exceeds the former
(regime I), which is the regime applicable to the early universe, we
obtain an inverse cascade with moderate GW energy that scales with the
third power of the magnetic energy. When the generation speed exceeds
the CME limit (regime II), the GW energy continues to increase without
a corresponding increase of magnetic energy. In the early kinematic
phase, the GW energy spectrum (per linear wavenumber interval) has
opposite slopes in both regimes and is characterized by an inertial
range spectrum in regime I and a white noise spectrum in regime II. The
occurrence of these two slopes is shown to be a generic consequence of
a nearly monochromatic exponential growth of the magnetic field. The
resulting GW energy is found to be proportional to the fifth power of
the limiting CME speed and the first power of the generation speed.

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Title: The effect of a dynamo-generated field on the Parker wind
Authors: Jakab, P.; Brandenburg, A.
2021A&A...647A..18J Altcode: 2020arXiv200602971J
Context. Stellar winds are an integral part of the underlying dynamo,
the motor of stellar activity. The wind controls the star's angular
momentum loss, which depends on the magnetic field geometry which,
in turn, varies significantly in time and latitude. Aims:
Here we study basic properties of a self-consistent model that
includes simple representations of both the global stellar dynamo in
a spherical shell and the exterior in which the wind accelerates
and becomes supersonic. Methods: We numerically solved
an axisymmetric mean-field model for the induction, momentum, and
continuity equations using an isothermal equation of state. The model
allows for the simultaneous generation of a mean magnetic field and
the development of a Parker wind. The resulting flow is transonic
at the critical point, which we arranged to be between the inner
and outer radii of the model. The boundary conditions are assumed to
be such that the magnetic field is antisymmetric about the equator,
that is to say dipolar. Results: At the solar rotation rate,
the dynamo is oscillatory and of α2 type. In most of the
domain, the magnetic field corresponds to that of a split monopole. The
magnetic energy flux is largest between the stellar surface and the
critical point. The angular momentum flux is highly variable in time
and can reach negative values, especially at midlatitudes. At a rapid
rotation of up to 50 times the solar value, most of the magnetic
field is lost along the axis within the inner tangential cylinder of
the model. Conclusions: The model reveals unexpected features
that are not generally anticipated from models that are designed to
reproduce the solar wind: highly variable angular momentum fluxes
even from just an α2 dynamo in the star. A major caveat
of our isothermal models with a magnetic field produced by a dynamo
is the difficulty to reach small enough plasma betas without the
dynamo itself becoming unrealistically strong inside the star. The source code used for the simulations of this study, the PENCIL
CODE (Pencil Code Collaboration 2020), is freely available on <A
href="https://github.com/pencil-code/">https://github.com/pencil-code/</A>.
The DOI of the code is <A
href="https://doi.org/10.5281/zenodo.2315093">https://doi.org/10.5281/zenodo.2315093</A>
(Pencil Code Collaboration 2018). The simulation
setups and corresponding data are freely available on <A
href="https://doi.org/10.5281/zenodo.4284439">https://doi.org/10.5281/zenodo.4284439</A>
(Jakab &amp; Brandenburg 2020).

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Title: Circular polarization of gravitational waves from
early-Universe helical turbulence
Authors: Kahniashvili, Tina; Brandenburg, Axel; Gogoberidze, Grigol;
Mandal, Sayan; Pol, Alberto Roper
2021PhRvR...3a3193K Altcode: 2020arXiv201105556K
We perform direct numerical simulations to compute the net circular
polarization of gravitational waves from helical (chiral) turbulent
sources in the early Universe for a variety of initial conditions,
including driven (stationary) and decaying turbulence. We investigate
the resulting gravitational wave signal assuming different turbulent
geneses such as magnetically or kinetically driven cases. Under
realistic physical conditions in the early Universe we compute
numerically the wave number-dependent polarization degree of the
gravitational waves. We find that the spectral polarization degree
strongly depends on the initial conditions. The peak of the spectral
polarization degree occurs at twice the typical wave number of the
source, as expected, and for fully helical decaying turbulence, it
reaches its maximum of nearly 100% only at the peak. We determine the
temporal evolution of the turbulent sources as well as the resulting
gravitational waves, showing that the dominant contribution to their
spectral energy density happens shortly after the activation of the
source. Only through an artificially prolonged decay of the turbulence
can further increase of the gravitational wave amplitude be achieved. We
estimate the detection prospects for the net polarization, arguing that
its detection contains clean information (including the generation
mechanisms, time, and strength) about the sources of possible parity
violations in the early Universe.

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Title: The Pencil Code, a modular MPI code for partial differential
equations and particles: multipurpose and multiuser-maintained
Authors: Pencil Code Collaboration; Brandenburg, Axel; Johansen,
Anders; Bourdin, Philippe; Dobler, Wolfgang; Lyra, Wladimir;
Rheinhardt, Matthias; Bingert, Sven; Haugen, Nils; Mee, Antony; Gent,
Frederick; Babkovskaia, Natalia; Yang, Chao-Chin; Heinemann, Tobias;
Dintrans, Boris; Mitra, Dhrubaditya; Candelaresi, Simon; Warnecke,
Jörn; Käpylä, Petri; Schreiber, Andreas; Chatterjee, Piyali;
Käpylä, Maarit; Li, Xiang-Yu; Krüger, Jonas; Aarnes, Jørgen;
Sarson, Graeme; Oishi, Jeffrey; Schober, Jennifer; Plasson, Raphaël;
Sandin, Christer; Karchniwy, Ewa; Rodrigues, Luiz; Hubbard, Alexander;
Guerrero, Gustavo; Snodin, Andrew; Losada, Illa; Pekkilä, Johannes;
Qian, Chengeng
2021JOSS....6.2807P Altcode: 2021JOSS....6.2807C; 2020arXiv200908231B
The Pencil Code is a highly modular physics-oriented simulation code
that can be adapted to a wide range of applications. It is primarily
designed to solve partial differential equations (PDEs) of compressible
hydrodynamics and has lots of add-ons ranging from astrophysical
magnetohydrodynamics (MHD) to meteorological cloud microphysics and
engineering applications in combustion. Nevertheless, the framework
is general and can also be applied to situations not related to
hydrodynamics or even PDEs, for example when just the message passing
interface or input/output strategies of the code are to be used. The
code can also evolve Lagrangian (inertial and noninertial) particles,
their coagulation and condensation, as well as their interaction with
the fluid.

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Title: Homochirality: A Prerequisite or Consequence of Life?
Authors: Brandenburg, Axel
2021pcol.book...87B Altcode: 2020arXiv201212850B
Many of the building blocks of life such as amino acids and nucleotides
are chiral, i.e., different from their mirror image. Contemporary life
selects and synthesizes only one of two possible handednesses. In an
abiotic environment, however, there are usually equally many left- and
right-handed molecules. If homochirality was a prerequisite of life,
there must have been physical or chemical circumstances that led to the
selection of a certain preference. Conversely, if it was a consequence
of life, we must identify possible pathways for accomplishing a
transition from a racemic to a homochiral chemistry. After a discussion
of the observational evidence, we review ideas where homochirality of
any handedness could emerge as a consequence of the first polymerization
events of nucleotides in an emerging RNA world. These mechanisms are
not limited to nucleotides, but can also occur for peptides, as a
precursor to the RNA world. The question of homochirality is, in this
sense, intimately tied to the origin of life. Future Mars missions may
be able to detect biomolecules of extant or extinct life. We therefore
also discuss possible experimental setups for determining the chirality
of primitive life forms in situ on Mars.

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Title: Magnetic Helicity: diagnostic signatures and effects
Authors: Brandenburg, A.
2020AGUFMNG011..02B Altcode:
In situ measurements of the solar wind provide us with a unique
opportunity to determine the magnetic helicity and to look for a
systematic hemispheric dependence. Although this has been done, the
results still remain puzzling and point to a reversal of magnetic
helicity some distance above the solar surface. No observational
evidence for an actual reversal exists as yet. This leads us to the
exploration of proxies of helicity, which could be used to verify the
reality of a reversal and to determine its location. Of particular
interest is the technique of decomposing images of linear polarization
into its parity-even and parity-odd constituents, and to associate
the latter with a helicity proxy. In my talk, I will illuminate the
dynamo-theoretical background of helicity, such as what is known as
catastrophic quenching, and will then discuss the status of magnetic
helicity proxies using both observational and numerical results. Many of
these techniques are rather general and can also be applied to intensity
maps, including terrestrial cloud patterns of hurricanes, for example.

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Title: On the Existence of Shear-current Effects in Magnetized
Burgulence
Authors: Käpylä, Maarit J.; Vizoso, Javier Álvarez; Rheinhardt,
Matthias; Brandenburg, Axel; Singh, Nishant K.
2020ApJ...905..179K Altcode: 2020arXiv200605661K
The possibility of explaining shear flow dynamos by a magnetic
shear-current (MSC) effect is examined via numerical simulations. Our
primary diagnostics is the determination of the turbulent magnetic
diffusivity tensor η. In our setup, a negative sign of its component
ηyx is necessary for coherent dynamo action by the SC
effect. To be able to measure turbulent transport coefficients from
systems with magnetic background turbulence, we present an extension of
the test-field method (TFM) applicable to our setup where the pressure
gradient is dropped from the momentum equation: the nonlinear TFM
(NLTFM). Our momentum equation is related to Burgers' equation and
the resulting flows are referred to as magnetized burgulence. We
use both stochastic kinetic and magnetic forcings to mimic cases
without and with simultaneous small-scale dynamo action. When we
force only kinetically, negative ηyx are obtained with
exponential growth in both the radial and azimuthal mean magnetic
field components. Using magnetokinetic forcing, the field growth is
no longer exponential, while NLTFM yields positive ηyx. By
employing an alternative forcing from which wavevectors whose components
correspond to the largest scales are removed, the exponential growth is
recovered, but the NLTFM results do not change significantly. Analyzing
the dynamo excitation conditions for the coherent SC and incoherent
α and SC effects shows that the incoherent effects are the main
drivers of the dynamo in the majority of cases. We find no evidence
for MSC-effect-driven dynamos in our simulations.

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Title: Numerical simulations of gravitational waves from
early-universe turbulence
Authors: Roper Pol, Alberto; Mandal, Sayan; Brandenburg, Axel;
Kahniashvili, Tina; Kosowsky, Arthur
2020PhRvD.102h3512R Altcode: 2019arXiv190308585R
We perform direct numerical simulations of magnetohydrodynamic
turbulence in the early universe and numerically compute the resulting
stochastic background of gravitational waves and relic magnetic
fields. These simulations do not make the simplifying assumptions
of earlier analytic work. If the turbulence is assumed to have
an energy-carrying scale that is about a hundredth of the Hubble
radius at the time of generation, as expected in a first-order phase
transition, the peak of gravitational wave power will be in the mHz
frequency range for a signal produced at the electroweak scale. The
efficiency of gravitational wave (GW) production varies significantly
with how the turbulence is driven. Detectability of turbulence at the
electroweak scale by the planned Laser Interferometer Space Antenna
(LISA) requires anywhere from 0.1% to 10% of the thermal plasma energy
density to be in plasma motions or magnetic fields, depending on the
model of the driving process. Our results predict a new universal form
below the spectral peak frequency that is shallower than previously
thought. This implies larger values of the GW energy spectra in
the low-frequency range. This extends the range where turbulence is
detectable with LISA to lower frequencies, corresponding to higher
energy scales than the assumed energy-carrying scale.

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Title: Helicity proxies from linear polarisation of solar active
regions
Authors: Prabhu, A.; Brandenburg, A.; Käpylä, M. J.; Lagg, A.
2020A&A...641A..46P Altcode: 2020arXiv200110884P
Context. The α effect is believed to play a key role in the
generation of the solar magnetic field. A fundamental test for its
significance in the solar dynamo is to look for magnetic helicity of
opposite signs both between the two hemispheres as well as between
small and large scales. However, measuring magnetic helicity is
compromised by the inability to fully infer the magnetic field vector
from observations of solar spectra, caused by what is known as the
π ambiguity of spectropolarimetric observations. Aims: We
decompose linear polarisation into parity-even and parity-odd E and B
polarisations, which are not affected by the π ambiguity. Furthermore,
we study whether the correlations of spatial Fourier spectra of B and
parity-even quantities such as E or temperature T are a robust proxy for
magnetic helicity of solar magnetic fields. Methods: We analysed
polarisation measurements of active regions observed by the Helioseismic
and Magnetic Imager on board the Solar Dynamics observatory. Theory
predicts the magnetic helicity of active regions to have, statistically,
opposite signs in the two hemispheres. We then computed the parity-odd
EB and TB correlations and tested for a systematic preference of
their sign based on the hemisphere of the active regions. 
Results: We find that: (i) EB and TB correlations are a reliable
proxy for magnetic helicity, when computed from linear polarisation
measurements away from spectral line cores; and (ii) E polarisation
reverses its sign close to the line core. Our analysis reveals that
Faraday rotation does not have a significant influence on the computed
parity-odd correlations. Conclusions: The EB decomposition of
linear polarisation appears to be a good proxy for magnetic helicity
independent of the π ambiguity. This allows us to routinely infer
magnetic helicity directly from polarisation measurements.

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Title: Hall Cascade with Fractional Magnetic Helicity in Neutron
Star Crusts
Authors: Brandenburg, Axel
2020ApJ...901...18B Altcode: 2020arXiv200612984B
The ohmic decay of magnetic fields in the crusts of neutron stars is
generally believed to be governed by Hall drift, which leads to what is
known as a Hall cascade. Here we show that helical and fractionally
helical magnetic fields undergo strong inverse cascading like in
magnetohydrodynamics (MHD), but the magnetic energy decays more slowly
with time t: $\propto \,{t}^{-2/5}$ instead of ∝t-2/3 in
MHD. Even for a nonhelical magnetic field there is a certain degree of
inverse cascading for sufficiently strong magnetic fields. The inertial
range scaling with wavenumber k is compatible with earlier findings
for the forced Hall cascade, i.e., proportional to k-7/3,
but in the decaying cases, the subinertial range spectrum steepens to a
novel k5 slope instead of the k4 slope in MHD. The
energy of the large-scale magnetic field can increase quadratically
in time through inverse cascading. For helical fields, the energy
dissipation is found to be inversely proportional to the large-scale
magnetic field and proportional to the fifth power of the rms magnetic
field. For neutron star conditions with an rms magnetic field of a few
times ${10}^{14}\,{\rm{G}}$ , the large-scale magnetic field might only
be ${10}^{11}\,{\rm{G}}$ , while still producing magnetic dissipation
of ${10}^{33}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ for thousands of years,
which could manifest itself through X-ray emission. Finally, it is
shown that the conclusions from local unstratified models agree rather
well with those from stratified models with boundaries.

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Title: David Moss (1943-2020)
Authors: Shukurov, Anvar; Brandenburg, Axel; Brooke, John; Sokoloff,
Dmitry; Tavakol, Reza
2020A&G....61d4.12S Altcode:
Anvar Shukurov and colleagues remember a theorist known for his work
on stellar and galactic magnetism, who was also a prominent marine
biologist.

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Title: On the Measurement of Handedness in Fermi Large Area Telescope
Data
Authors: Asplund, Julia; Jóhannesson, Guðlaugur.; Brandenburg, Axel
2020ApJ...898..124A Altcode: 2020arXiv200513065A
A handedness in the arrival directions of high-energy photons from
outside our Galaxy can be related to the helicity of an intergalactic
magnetic field. Previous estimates by Tashiro et al. and Chen et
al. showed a hint of a signal present in the photons observed by
the Fermi Large Area Telescope (LAT). An update on the measurement
of handedness in Fermi-LAT data is presented using more than 10 yr of
observations. Simulations are performed to study the uncertainty of the
measurements, taking into account the structure of the exposure caused
by the energy-dependent instrument response and its observing profile,
as well as the background from the interstellar medium. The simulations
are required to accurately estimate the uncertainty and to show that
previously the uncertainty was significantly underestimated. The
apparent signal in the earlier analysis of Fermi-LAT data is rendered
nonsignificant.

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Title: Application of a helicity proxy to edge-on galaxies
Authors: Brandenburg, Axel; Furuya, Ray S.
2020MNRAS.496.4749B Altcode: 2020MNRAS.tmp.1992B; 2020arXiv200307284B
We study the prospects of detecting magnetic helicity in galaxies by
observing the dust polarization of the edge-on galaxy NGC 891. Our
numerical results of mean-field dynamo calculations show that there
should be a large-scale component of the rotationally invariant
parity-odd B polarization that we predict to be negative in the
first and third quadrants, and positive in the second and fourth
quadrants. The large-scale parity-even E polarization is predicted to be
negative near the axis and positive further away in the outskirts. These
properties are shown to be mostly a consequence of the magnetic field
being azimuthal and the polarized intensity being maximum at the centre
of the galaxy and are not a signature of magnetic helicity.

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Title: Scientific usage of the Pencil Code
Authors: Brandenburg, Axel
2020zndo...3466444B Altcode:
A search using ADS https://ui.adsabs.harvard.edu lists the papers in
which the Pencil Code is being quoted. In this document we present
the papers that are making use of the code either for their own
scientific work of those authors, or for code comparison purposes. We
include conference proceedings, which make up 15-20% of all papers. We
classify the references by year and by topic, although the topics are
often overlapping. The primary application of the Pencil Code lies in
astrophysics, in which case we classify the papers mostly by the field
of research. Additional applications can also be found in meteorology
and combustion.

---------------------------------------------------------
Title: Scientific usage of the Pencil Code
Authors: Brandenburg, Axel
2020zndo...3947506B Altcode:
A search using ADS https://ui.adsabs.harvard.edu lists the papers in
which the Pencil Code is being quoted. In this document we present
the papers that are making use of the code either for their own
scientific work of those authors, or for code comparison purposes. We
include conference proceedings, which make up 15-20% of all papers. We
classify the references by year and by topic, although the topics are
often overlapping. The primary application of the Pencil Code lies in
astrophysics, in which case we classify the papers mostly by the field
of research. Additional applications can also be found in meteorology
and combustion.

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Title: Primordial magnetic helicity evolution with a homogeneous
magnetic field from inflation
Authors: Brandenburg, Axel; Durrer, Ruth; Huang, Yiwen; Kahniashvili,
Tina; Mandal, Sayan; Mukohyama, Shinji
2020PhRvD.102b3536B Altcode: 2020arXiv200506449B
Motivated by a scenario of magnetogenesis in which a homogeneous
magnetic field is generated during inflation, we study the
magnetohydrodynamic evolution of the primordial plasma motions for two
kinds of initial conditions—(i) a spatially homogeneous field with
an unlimited correlation length, and (ii) a zero flux scale-invariant
statistically homogeneous magnetic field. In both cases, we apply, for
a short initial time interval, monochromatic forcing at a certain wave
number so that the correlation length is finite, but much smaller than
the typical length scale of turbulence. In particular, we investigate
the decay of nonhelical and helical hydromagnetic turbulence. We show
that, in the presence of a homogeneous magnetic field, the decay of
helical and nonhelical small-scale fields can occur rapidly. This is
a special property of a system with a perfectly homogeneous magnetic
field, which is sometimes considered as a local approximation to a
slowly varying background field. It can never change and acts as an
imposed magnetic field. This is in sharp contrast to the case of a
statistically homogeneous magnetic field, where we recover familiar
decay properties: a much slower decay of magnetic energy and a faster
growth of the correlation length, especially in the case with magnetic
helicity. The result suggests that a homogeneous magnetic field,
if generated during inflation, should persist under the influence of
small-scale fields and could be the origin of the large-scale magnetic
field in the Universe.

---------------------------------------------------------
Title: Dynamo in Weakly Collisional Nonmagnetized Plasmas Impeded
by Landau Damping of Magnetic Fields
Authors: Pusztai, István; Juno, James; Brandenburg, Axel; TenBarge,
Jason M.; Hakim, Ammar; Francisquez, Manaure; Sundström, Andréas
2020PhRvL.124y5102P Altcode: 2020arXiv200111929P
We perform fully kinetic simulations of flows known to produce
dynamo in magnetohydrodynamics (MHD), considering scenarios with
low Reynolds number and high magnetic Prandtl number, relevant for
galaxy cluster scale fluctuation dynamos. We find that Landau damping
on the electrons leads to a rapid decay of magnetic perturbations,
impeding the dynamo. This collisionless damping process operates on
spatial scales where electrons are nonmagnetized, reducing the range
of scales where the magnetic field grows in high magnetic Prandtl
number fluctuation dynamos. When electrons are not magnetized down
to the resistive scale, the magnetic energy spectrum is expected to
be limited by the scale corresponding to magnetic Landau damping or,
if smaller, the electron gyroradius scale, instead of the resistive
scale. In simulations we thus observe decaying magnetic fields where
resistive MHD would predict a dynamo.

---------------------------------------------------------
Title: Hemispheric Handedness in the Galactic Synchrotron Polarization
Foreground
Authors: Brandenburg, Axel; Brüggen, Marcus
2020ApJ...896L..14B Altcode: 2020arXiv200314178B
The large-scale magnetic field of the Milky Way is thought to be
created by an αΩ dynamo, which implies that it should have opposite
handedness north and south of the Galactic midplane. Here we attempt
to detect a variation in handedness using polarization data from
the Wilkinson Microwave Anisotropy Probe. Previous analyzes of the
parity-even and parity-odd parts of linear polarization of the global
dust and synchrotron emission have focused on quadratic correlations
in spectral space of, and between, these two components. Here, by
contrast, we analyze the parity-odd polarization itself and show
that it has, on average, opposite signs in northern and southern
Galactic hemispheres. Comparison with a Galactic mean-field dynamo
model shows broad qualitative agreement and reveals that the sign
of the observed hemispheric dependence of the azimuthally averaged
parity-odd polarization is not determined by the sign of α, but by
the sense of differential rotation.

---------------------------------------------------------
Title: Karl-Heinz Rädler (1935-2020)
Authors: Brandenburg, Axel; Rüdiger, Günther; Ruediger, Guenther;
Ruediger
2020AN....341..365B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Turbulent viscosity and magnetic Prandtl number from
simulations of isotropically forced turbulence
Authors: Käpylä, P. J.; Rheinhardt, M.; Brandenburg, A.; Käpylä,
M. J.
2020A&A...636A..93K Altcode: 2019arXiv190100787K
Context. Turbulent diffusion of large-scale flows and magnetic fields
plays a major role in many astrophysical systems, such as stellar
convection zones and accretion discs. Aims: Our goal is to
compute turbulent viscosity and magnetic diffusivity which are relevant
for diffusing large-scale flows and magnetic fields, respectively. We
also aim to compute their ratio, which is the turbulent magnetic
Prandtl number, Pmt, for isotropically forced homogeneous
turbulence. Methods: We used simulations of forced turbulence
in fully periodic cubes composed of isothermal gas with an imposed
large-scale sinusoidal shear flow. Turbulent viscosity was computed
either from the resulting Reynolds stress or from the decay rate of the
large-scale flow. Turbulent magnetic diffusivity was computed using
the test-field method for a microphysical magnetic Prandtl number of
unity. The scale dependence of the coefficients was studied by varying
the wavenumber of the imposed sinusoidal shear and test fields. 
Results: We find that turbulent viscosity and magnetic diffusivity are
in general of the same order of magnitude. Furthermore, the turbulent
viscosity depends on the fluid Reynolds number (Re) and scale separation
ratio of turbulence. The scale dependence of the turbulent viscosity is
found to be well approximated by a Lorentzian. These results are similar
to those obtained earlier for the turbulent magnetic diffusivity. The
results for the turbulent transport coefficients appear to converge at
sufficiently high values of Re and the scale separation ratio. However,
a weak trend is found even at the largest values of Re, suggesting that
the turbulence is not in the fully developed regime. The turbulent
magnetic Prandtl number converges to a value that is slightly below
unity for large Re. For small Re we find values between 0.5 and 0.6 but
the data are insufficient to draw conclusions regarding asymptotics. We
demonstrate that our results are independent of the correlation
time of the forcing function. Conclusions: The turbulent
magnetic diffusivity is, in general, consistently higher than the
turbulent viscosity, which is in qualitative agreement with analytic
theories. However, the actual value of Pmt found from the
simulations (≈0.9-0.95) at large Re and large scale separation ratio
is higher than any of the analytic predictions (0.4-0.8).

---------------------------------------------------------
Title: The Turbulent Stress Spectrum in the Inertial and Subinertial
Ranges
Authors: Brandenburg, Axel; Boldyrev, Stanislav
2020ApJ...892...80B Altcode: 2019arXiv191207499B
For velocity and magnetic fields, the turbulent pressure and, more
generally, the squared fields such as the components of the turbulent
stress tensor, play important roles in astrophysics. For both one and
three dimensions, we derive the equations relating the energy spectra
of the fields to the spectra of their squares. We solve the resulting
integrals numerically and show that for turbulent energy spectra of
Kolmogorov type, the spectral slope of the stress spectrum is also of
Kolmogorov type. For shallower turbulence spectra, the slope of the
stress spectrum quickly approaches that of white noise, regardless of
how blue the spectrum of the field is. For fully helical fields, the
stress spectrum is elevated by about a factor of two in the subinertial
range, while that in the inertial range remains unchanged. We discuss
possible implications for understanding the spectrum of primordial
gravitational waves from causally generated magnetic fields during
cosmological phase transitions in the early universe. We also discuss
potential diagnostic applications to the interstellar medium, where
polarization and scintillation measurements characterize the square
of the magnetic field.

---------------------------------------------------------
Title: Chiral fermion asymmetry in high-energy plasma simulations
Authors: Schober, J.; Brandenburg, A.; Rogachevskii, I.
2020GApFD.114..106S Altcode:
The chiral magnetic effect (CME) is a quantum relativistic effect
that describes the appearance of an additional electric current along
a magnetic field. It is caused by an asymmetry between the number
densities of left- and right-handed fermions, which can be maintained
at high energies when the chirality flipping rate can be neglected,
for example in the early Universe. The inclusion of the CME in the
Maxwell equations leads to a modified set of magnetohydrodynamical
(MHD) equations. The CME is studied here in numerical simulations
with the PENCIL CODE. We discuss how the CME is implemented in
the code and how the time step and the spatial resolution of a
simulation need to be adjusted in presence of a chiral asymmetry. The
CME plays a key role in the evolution of magnetic fields, since it
results in a dynamo effect associated with an additional term in the
induction equation. This term is formally similar to the α effect
in classical mean-field MHD. However, the chiral dynamo can operate
without turbulence and is associated with small spatial scales that
can be, in the case of the early Universe, orders of magnitude below
the Hubble radius. A chiral ? effect has also been identified in
mean-field theory. It occurs in the presence of turbulence, but is
not related to kinetic helicity. Depending on the plasma parameters,
chiral dynamo instabilities can amplify magnetic fields over many
orders of magnitude. These instabilities can potentially affect the
propagation of MHD waves. Our numerical simulations demonstrate strong
modifications of the dispersion relation for MHD waves for large
chiral asymmetry. We also study the coupling between the evolution
of the chiral chemical potential and the ordinary chemical potential,
which is proportional to the sum of the number densities of left- and
right-handed fermions. An important consequence of this coupling is
the emergence of chiral magnetic waves (CMWs). We confirm numerically
that linear CMWs and MHD waves are not interacting. Our simulations
suggest that the chemical potential has only a minor effect on the
non-linear evolution of the chiral dynamo.

---------------------------------------------------------
Title: The timestep constraint in solving the gravitational wave
equations sourced by hydromagnetic turbulence
Authors: Roper Pol, Alberto; Brandenburg, Axel; Kahniashvili, Tina;
Kosowsky, Arthur; Mandal, Sayan
2020GApFD.114..130R Altcode: 2018arXiv180705479R
Hydromagnetic turbulence produced during phase transitions in the
early universe can be a powerful source of stochastic gravitational
waves (GWs). GWs can be modelled by the linearised spatial part of the
Einstein equations sourced by the Reynolds and Maxwell stresses. We
have implemented two different GW solvers into the Pencil Code -
a code which uses a third order timestep and sixth order finite
differences. Using direct numerical integration of the GW equations,
we study the appearance of a numerical degradation of the GW amplitude
at the highest wavenumbers, which depends on the length of the timestep
- even when the Courant-Friedrichs-Lewy condition is ten times below
the stability limit. This degradation leads to a numerical error,
which is found to scale with the third power of the timestep. A similar
degradation is not seen in the magnetic and velocity fields. To mitigate
numerical degradation effects, we alternatively use the exact solution
of the GW equations under the assumption that the source is constant
between subsequent timesteps. This allows us to use a much longer
timestep, which cuts the computational cost by a factor of about ten.

---------------------------------------------------------
Title: The time step constraint in radiation hydrodynamics
Authors: Brandenburg, Axel; Das, Upasana
2020GApFD.114..162B Altcode: 2019arXiv190106385B
Explicit radiation hydrodynamic simulations of the atmospheres of
massive stars and of convection in accretion discs around white dwarfs
suffer from prohibitively short time steps due to radiation. This
constraint is related to the cooling time rather than the radiative
pressure, which also becomes important in hot stars and discs. We show
that the radiative time step constraint is governed by the minimum
of the sum of the optically thick and thin contributions rather than
the smaller one of the two. In simulations with the PENCIL CODE,
their weighting fractions are found empirically. In three-dimensional
convective accretion disc simulations, the Deardorff term is found to be
the main contributor to the enthalpy flux rather than the superadiabatic
gradient. We conclude with a discussion of how the radiative time step
problem could be mitigated in certain types of investigations.

---------------------------------------------------------
Title: Convergence properties of detonation simulations
Authors: Qian, Chengeng; Wang, Cheng; Liu, JianNan; Brandenburg,
Axel; Haugen, Nils E. L.; Liberman, Mikhael A.
2020GApFD.114...58Q Altcode: 2019arXiv190203816Q
We present a high-resolution convergence study of detonation initiated
by a temperature gradient in a stoichiometric hydrogen-oxygen mixture
using the PENCIL CODE and compare with a code that employs a fifth
order weighted essentially non-oscillating (WENO) scheme. With Mach
numbers reaching 10-30, a certain amount of shock viscosity is needed
in the PENCIL CODE to remove or reduce numerical pressure oscillations
on the grid scale at the position of the shock. Detonation is found
to occur for intermediate values of the shock viscosity parameter. At
fixed values of this parameter, the numerical error associated with
those small wiggles in the pressure profile is found to decrease
with decreasing mesh width ? like ? down to ?. With the WENO scheme,
solutions are smooth at ?, but no detonation is obtained for ?. This
is argued to be an artifact of a decoupling between pressure and
reaction fronts.

---------------------------------------------------------
Title: Sensitivity to luminosity, centrifugal force, and boundary
conditions in spherical shell convection
Authors: Käpylä, P. J.; Gent, F. A.; Olspert, N.; Käpylä, M. J.;
Brandenburg, A.
2020GApFD.114....8K Altcode: 2018arXiv180709309K
We test the sensitivity of hydrodynamic and magnetohydrodynamic
turbulent convection simulations with respect to Mach number, thermal
and magnetic boundary conditions, and the centrifugal force. We find
that varying the luminosity, which also controls the Mach number, has
only a minor effect on the large-scale dynamics. A similar conclusion
can also be drawn from the comparison of two formulations of the lower
magnetic boundary condition with either vanishing electric field or
current density. The centrifugal force has an effect on the solutions,
but only if its magnitude with respect to acceleration due to gravity
is by two orders of magnitude greater than in the Sun. Finally, we find
that the parameterisation of the photospheric physics, either by an
explicit cooling term or enhanced radiative diffusion, is more important
than the thermal boundary condition. In particular, runs with cooling
tend to lead to more anisotropic convection and stronger deviations
from the Taylor-Proudman state. In summary, the fully compressible
approach taken here with the Pencil Code is found to be valid, while
still allowing the disparate timescales to be taken into account.

---------------------------------------------------------
Title: Magnetism in the Early Universe
Authors: Kahniashvili, Tina; Brandenburg, Axel; Kosowsky, Arthur;
Mandal, Sayan; Roper Pol, Alberto
2020IAUGA..30..295K Altcode: 2018arXiv181011876K
Blazar observations point toward the possible presence of magnetic
fields over intergalactic scales of the order of up to ~1 Mpc,
with strengths of at least ~10-16 G. Understanding the
origin of these large-scale magnetic fields is a challenge for modern
astrophysics. Here we discuss the cosmological scenario, focussing
on the following questions: (i) How and when was this magnetic
field generated? (ii) How does it evolve during the expansion of
the universe? (iii) Are the amplitude and statistical properties of
this field such that they can explain the strengths and correlation
lengths of observed magnetic fields? We also discuss the possibility of
observing primordial turbulence through direct detection of stochastic
gravitational waves in the mHz range accessible to LISA.

---------------------------------------------------------
Title: Introduction
Authors: Brandenburg, A.; Candelaresi, S.; Gent, F. A.
2020GApFD.114....1B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: f-mode strengthening from a localised bipolar subsurface
magnetic field
Authors: Singh, Nishant K.; Raichur, Harsha; Käpylä, Maarit J.;
Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J.
2020GApFD.114..196S Altcode:
Recent numerical work in helioseismology has shown that a periodically
varying subsurface magnetic field leads to a fanning of the f-mode,
which emerges from a density jump at the surface. In an attempt to model
a more realistic situation, we now modulate this periodic variation with
an envelope, giving thus more emphasis on localised bipolar magnetic
structures in the middle of the domain. Some notable findings are: (i)
compared to the purely hydrodynamic case, the strength of the f-mode is
significantly larger at high horizontal wavenumbers k, but the fanning
is weaker for the localised subsurface magnetic field concentrations
investigated here than the periodic ones studied earlier; (ii) when
the strength of the magnetic field is enhanced at a fixed depth below
the surface, the fanning of the f-mode in the ? diagram increases
proportionally in such a way that the normalised f-mode strengths remain
nearly the same in different such cases; (iii) the unstable Bloch modes
reported previously in case of harmonically varying magnetic fields
are now completely absent when more realistic localised magnetic field
concentrations are imposed beneath the surface, thus suggesting that
the Bloch modes are unlikely to be supported during most phases of the
solar cycle; (iv) the f-mode strength appears to depend also on the
depth of magnetic field concentrations such that it shows a relative
decrement when the maximum of the magnetic field is moved to a deeper
layer. We argue that detections of f-mode perturbations such as those
being explored here could be effective tracers of solar magnetic fields
below the photosphere before these are directly detectable as visible
manifestations in terms of active regions or sunspots.

---------------------------------------------------------
Title: The nature of mean-field generation in three classes of
optimal dynamos
Authors: Brandenburg, Axel; Chen, Long
2020JPlPh..86a9010B Altcode: 2019arXiv191101712B
In recent years, several optimal dynamos have been discovered. They
minimize the magnetic energy dissipation or, equivalently, maximize
the growth rate at a fixed magnetic Reynolds number. In the optimal
dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we
find mean-field dynamo action for planar averages. One component
of the magnetic field grows exponentially while the other decays
in an oscillatory fashion near onset. This behaviour is different
from that of an α2 dynamo, where the two non-vanishing
components of the planar averages are coupled and have the same
growth rate. For the Willis dynamo, we find that the mean field is
excited by a negative turbulent magnetic diffusivity, which has a
non-uniform spatial profile near onset. The temporal oscillations in
the decaying component are caused by the corresponding component of the
diffusivity tensor being complex when the mean field is decaying and,
in this way, time dependent. The growing mean field can be modelled
by a negative magnetic diffusivity combined with a positive magnetic
hyperdiffusivity. In two other classes of optimal dynamos of Chen
et al. (J. Fluid Mech., vol. 783, 2015, pp. 23-45), we find, to some
extent, similar mean-field dynamo actions. When the magnetic boundary
conditions are mixed, the two components of the planar averaged field
grow at different rates when the dynamo is 15 % supercritical. When
the mean magnetic field satisfies homogeneous boundary conditions
(where the magnetic field is tangential to the boundary), mean-field
dynamo action is found for one-dimensional averages, but not for planar
averages. Despite having different spatial profiles, both dynamos show
negative turbulent magnetic diffusivities. Our finding suggests that
negative turbulent magnetic diffusivities may support a broader class of
dynamos than previously thought, including these three optimal dynamos.

---------------------------------------------------------
Title: Landau damping of magnetic fluctuations inhibit the dynamo
in weakly collisional nonmagnetized plasmas
Authors: Pusztai, Istvan; Juno, James; Brandenburg, Axel; Tenbarge,
Jason M.; Hakim, Ammar; Francisquez, Manaure; Sundström, Andréas
2020APS..DPPJ03001P Altcode:
We perform fully kinetic simulations of flows known to produce
dynamo in magnetohydrodynamics (MHD), considering scenarios with low
Reynolds number and high magnetic Prandtl number, with relevance to
fluctuation dynamos in galaxy clusters. We find that Landau damping
on the electrons leads to a rapid decay of magnetic perturbations
(apart from those corresponding to a current caused by the forcing of
the flows), impeding the dynamo. The effect of the magnetic Landau
damping is similar to that of a magnetic diffusivity that scales
with the wave number of the perturbation. This collisionless damping
process operates on spatial scales where electrons are nonmagnetized,
reducing the range of scales where the magnetic field grows in high
magnetic Prandtl number fluctuation dynamos. When electrons are not
magnetized down to the resistive scale, such as galaxy clusters at
typical Biermann battery seed fields, the magnetic energy spectrum is
expected to be limited by the scale corresponding to magnetic Landau
damping or, if smaller, the electron gyroradius scale, instead of the
resistive scale, potentially reducing the total energy in magnetic
fluctuations. In simulations we thus observe decaying magnetic fields
where resistive MHD predicts a dynamo.

---------------------------------------------------------
Title: Magnetic field evolution in solar-type stars
Authors: Brandenburg, Axel
2020IAUS..354..169B Altcode: 2020arXiv200400439B
We discuss selected aspects regarding the magnetic field evolution of
solar-type stars. Most of the stars with activity cycles are in the
range where the normalized chromospheric Calcium emission increases
linearly with the inverse Rossby number. For Rossby numbers below about
a quarter of the solar value, the activity saturates and no cycles have
been found. For Rossby numbers above the solar value, again no activity
cycles have been found, but now the activity goes up again for a major
fraction of the stars. Rapidly rotating stars show nonaxisymmetric
large-scale magnetic fields, but there is disagreement between models
and observations regarding the actual value of the Rossby number where
this happens. We also discuss the prospects of detecting the sign of
magnetic helicity using various linear polarization techniques both
at the stellar surface using the parity-odd contribution to linear
polarization and above the surface using Faraday rotation.

---------------------------------------------------------
Title: Magnetic Helicity Dissipation and Production in an Ideal
MHD Code
Authors: Brandenburg, Axel; Scannapieco, Evan
2020ApJ...889...55B Altcode: 2019arXiv191006074B
We study a turbulent helical dynamo in a periodic domain by solving the
ideal magnetohydrodynamic (MHD) equations with the FLASH code using
the divergence-cleaning eight-wave method and compare our results
with direct numerical simulations (DNS) using the Pencil Code. At
low resolution, FLASH reproduces the DNS results qualitatively by
developing the large-scale magnetic field expected from DNS, but
at higher resolution, no large-scale magnetic field is obtained. In
all those cases in which a large-scale magnetic field is generated,
the ideal MHD results yield too little power at small scales. As a
consequence, the small-scale current helicity is too small compared
with that of the DNS. The resulting net current helicity has then always
the wrong sign, and its statistical average also does not approach zero
at late times, as expected from the DNS. Our results have implications
for astrophysical dynamo simulations of stellar and galactic magnetism
using ideal MHD codes.

---------------------------------------------------------
Title: A Global Two-scale Helicity Proxy from π-ambiguous Solar
Magnetic Fields
Authors: Brandenburg, Axel
2019ApJ...883..119B Altcode: 2019arXiv190603877B
If the α effect plays a role in the generation of the Sun’s magnetic
field, the field should show evidence of magnetic helicity of opposite
signs at large and small length scales. Measuring this faces two
challenges: (i) in weak-field regions, horizontal field measurements
are unreliable because of the π ambiguity, and (ii) one needs a truly
global approach to computing helicity spectra in the case where one
expects a sign reversal across the equator at all wavenumbers. Here we
develop such a method using spin-2 spherical harmonics to decompose the
linear polarization in terms of the parity-even and parity-odd E and
B polarizations, respectively. Using simple one- and two-dimensional
models, we show that the product of the spectral decompositions of E
and B, taken at spherical harmonic degrees that are shifted by one,
can act as a proxy of the global magnetic helicity with a sign that
represents that in the northern hemisphere. We then apply this method
to the analysis of solar synoptic vector magnetograms, from which we
extract a pseudo-polarization corresponding to a “π-ambiguated”
magnetic field, i.e., a magnetic field vector that has no arrow. We find
a negative sign of the global EB helicity proxy at spherical harmonic
degrees of around 6. This could indicate a positive magnetic helicity at
large length scales, but the spectrum fails to capture clear evidence of
the well-known negative magnetic helicity at smaller scales. This method
might also be applicable to stellar and Galactic polarization data.

---------------------------------------------------------
Title: Spectral Magnetic Helicity of Solar Active Regions between
2006 and 2017
Authors: Gosain, Sanjay; Brandenburg, Axel
2019ApJ...882...80G Altcode: 2019arXiv190211273G
We compute magnetic helicity and energy spectra from about 2485 patches
of about 100 Mm side length on the solar surface using data from
Hinode during 2006-2017. An extensive database is assembled where we
list the magnetic energy and helicity, large- and small-scale magnetic
helicity, mean current helicity density, fractional magnetic helicity,
and correlation length along with the Hinode map identification number
(MapID), as well as the Carrington latitude and longitude for each
MapID. While there are departures from the hemispheric sign rule
for magnetic and current helicities, the weak trend reported here
is in agreement with the previous results. This is argued to be a
physical effect associated with the dominance of individual active
regions that contribute more strongly in the better-resolved Hinode
maps. In comparison with earlier work, the typical correlation length
is found to be 6-8 {Mm}, while the length scale relating the magnetic
and current helicities to each other is around 1.4 {Mm}.

---------------------------------------------------------
Title: Ambipolar diffusion in large Prandtl number turbulence
Authors: Brandenburg, Axel
2019MNRAS.487.2673B Altcode: 2019arXiv190308976B; 2019MNRAS.tmp.1443B
We study the effects of ambipolar diffusion (AD) on hydromagnetic
turbulence. We consider the regime of large magnetic Prandtl number,
relevant to the interstellar medium. In most of the cases, we use the
single-fluid approximation where the drift velocity between charged and
neutral particles is proportional to the Lorentz force. In two cases we
also compare with the corresponding two-fluid model, where ionization
and recombination are included in the continuity and momentum equations
for the neutral and charged species. The magnetic field properties
are found to be well represented by the single-fluid approximation. We
quantify the effects of AD on total and spectral kinetic and magnetic
energies, the ohmic and AD dissipation rates, the statistics of the
magnetic field, the current density, and the linear polarization as
measured by the rotationally invariant E and B mode polarizations. We
show that the kurtosis of the magnetic field decreases with increasing
AD. The E mode polarization changes its skewness from positive values
for small AD to negative ones for large AD. Even when AD is weak,
changes in AD have a marked effect on the skewness and kurtosis
of E, and only a weak effect on those of B. These results open the
possibility of employing E and B mode polarizations as diagnostic tools
for characterizing turbulent properties of the interstellar medium.

---------------------------------------------------------
Title: Reversed Dynamo at Small Scales and Large Magnetic Prandtl
Number
Authors: Brandenburg, Axel; Rempel, Matthias
2019ApJ...879...57B Altcode: 2019arXiv190311869B
We show that at large magnetic Prandtl numbers, the Lorentz force does
work on the flow at small scales and drives fluid motions, whose energy
is dissipated viscously. This situation is the opposite of that in a
normal dynamo, where the flow does work against the Lorentz force. We
compute the spectral conversion rates between kinetic and magnetic
energies for several magnetic Prandtl numbers and show that normal
(forward) dynamo action occurs on large scales over a progressively
narrower range of wavenumbers as the magnetic Prandtl number is
increased. At higher wavenumbers, reversed dynamo action occurs,
i.e., magnetic energy is converted back into kinetic energy at small
scales. We demonstrate this in both direct numerical simulations
forced by volume stirring and in large eddy simulations (LESs) of solar
convectively driven small-scale dynamos. Low-density plasmas such as
stellar coronae tend to have large magnetic Prandtl numbers, i.e., the
viscosity is large compared with the magnetic diffusivity. The regime
in which viscous dissipation dominates over resistive dissipation for
large magnetic Prandtl numbers was also previously found in LESs of the
solar corona, i.e., our findings are a more fundamental property of MHD
that is not just restricted to dynamos. Viscous energy dissipation is a
consequence of positive Lorentz force work, which may partly correspond
to particle acceleration in close-to-collisionless plasmas. This is,
however, not modeled in the MHD approximation employed. By contrast,
resistive energy dissipation on current sheets is expected to be
unimportant in stellar coronae.

---------------------------------------------------------
Title: The Limited Roles of Autocatalysis and Enantiomeric
Cross-Inhibition in Achieving Homochirality in Dilute Systems
Authors: Brandenburg, Axel
2019OLEB...49...49B Altcode: 2019arXiv190307855B; 2019OLEB..tmp...17B
To understand the effects of fluctuations on achieving homochirality,
we employ a Monte-Carlo method where autocatalysis and enantiomeric
cross-inhibition, as well as racemization and deracemization reactions
are included. The results of earlier work either without autocatalysis
or without cross-inhibition are reproduced. Bifurcation diagrams
and the dependencies of the number of reaction steps on parameters
are studied. In systems with 30,000 molecules, for example, up to a
billion reaction steps may be needed to achieve homochirality without
autocatalysis.

---------------------------------------------------------
Title: Learning about solar/stellar dynamo physics from the
variability
Authors: Brandenburg, Axel
2019shin.confE.220B Altcode:
I will highlight three reasons where current simulations fail to
reproduce the Sun, but I will also highlight three robust results,
and finally, I will highlight three striking differences between
simulations and observations. (A) Realistic solar/stellar convectively
driven dynamo simulations suffer from three principle difficulties:
(i) the tremendous stratification, the range of time and length scales,
and the lack of realistic surface physics (radiation); (ii) a barely
resolved near-surface shear layer, especially at higher latitudes;
(iii) angular velocity contours that are still not as spoke-like
as suggested by helioseismology; (B) Nevertheless, several robust
results have emerged from such simulations: (i) at some rotation rate
(Rossby number close to the solar value), there is a transition from
solar-like to antisolar-like differential rotation for slower rotation;
(ii) at a very similar rotation rate, there is another transition from
axisymmetric to nonaxisymmetric (m=1) large-scale magnetic fields; (iii)
the rotation to cycle period ratio decreases with increasing stellar
activity or decreasing Rossby number. (C) Conflicts between observations
and simulations include: (i) the presence of an intermediate solar-like
branch where the period frequency ratio increases with increasing
stellar activity. The transition to nonaxisymmetric large-scale magnetic
fields would be to the right of this branch (larger activity), and
the transition to anti solar differential rotation would be to the
left, but in simulations the two transitions are found to appear at
the same rotation rate, so this intermediate solar-like branch has
disappeared. (ii) Both simulations and observations can show evidence
for multiple periods. If this is real, it is unclear how the surface
appearance of the magnetic field changes. Also, while some observational
work has associated the longer periods with dynamo activity closer
to the surface, different models show instead that longer periods may
originate from deeper down in the convection zone. (iii) Variability
in the sunspot data shows relatively nice cycles with a single grand
minimum. Stellar cycles are never that clean, and simulations show
surface patterns with additional significant variation away from the
sunspot belts. Can these discrepancies simply be explained by sunspots
being a threshold phenomenon, or is there more behind this difference.

---------------------------------------------------------
Title: Efficient quasi-kinematic large-scale dynamo as the small-scale
dynamo saturates
Authors: Bhat, Pallavi; Subramanian, Kandaswamy; Brandenburg, Axel
2019arXiv190508278B Altcode:
Large-scale magnetic fields in stars and galaxies are thought to arise
by mean-field dynamo action due to the combined influence of both
helical turbulence and shear. Those systems are also highly conducting
and the turbulence therein leads to a fluctuation (or small-scale)
dynamo which more rapidly amplifies magnetic field fluctuations on the
eddy scales and smaller. Will this then interfere with and suppress the
mean (or large-scale) field growth? Using direct numerical simulations
of helical turbulence (with and without shear), we identify a novel
quasi-kinematic large-scale dynamo which operates as the small-scale
dynamo saturates. Thus both dynamos operate efficiently, one after
the other, and lead to the generation of significant large-scale fields.

---------------------------------------------------------
Title: Effects of a subadiabatic layer on convection and dynamos in
spherical wedge simulations
Authors: Käpylä, P. J.; Viviani, M.; Käpylä, M. J.; Brandenburg,
A.; Spada, F.
2019GApFD.113..149K Altcode: 2018arXiv180305898K
We consider the effect of a subadiabatic layer at the base of the
convection zone on convection itself and the associated large-scale
dynamos in spherical wedge geometry. We use a heat conduction
prescription based on the Kramers opacity law which allows the depth
of the convection zone to dynamically adapt to changes in the physical
characteristics such as rotation rate and magnetic fields. We find
that the convective heat transport is strongly concentrated towards
the equatorial and polar regions in the cases without a substantial
radiative layer below the convection zone. The presence of a stable
layer below the convection zone significantly reduces the anisotropy
of radial enthalpy transport. Furthermore, the dynamo solutions are
sensitive to subtle changes in the convection zone structure. We find
that the kinetic helicity changes sign in the deeper parts of the
convection zone at high latitudes in all runs. This region expands
progressively towards the equator in runs with a thicker stably
stratified layer.

---------------------------------------------------------
Title: Energetics of turbulence generated by chiral MHD dynamos
Authors: Schober, J.; Brandenburg, A.; Rogachevskii, I.; Kleeorin, N.
2019GApFD.113..107S Altcode: 2018arXiv180306350S
An asymmetry in the number density of left- and right-handed fermions
is known to give rise to a new term in the induction equation that can
result in a dynamo instability. At high temperatures, when a chiral
asymmetry can survive for long enough, this chiral dynamo instability
can amplify magnetic fields efficiently, which in turn drive turbulence
via the Lorentz force. While it has been demonstrated in numerical
simulations that this chiral magnetically driven turbulence exists and
strongly affects the dynamics of the magnetic field, the details of
this process remain unclear. The goal of this paper is to analyse the
energetics of chiral magnetically driven turbulence and its effect on
the generation and dynamics of the magnetic field using direct numerical
simulations. We study these effects for different initial conditions,
including a variation of the initial chiral chemical potential and
the magnetic Prandtl number, ? . In particular, we determine the
ratio of kinetic to magnetic energy, ? , in chiral magnetically driven
turbulence. Within the parameter space explored in this study, ? reaches
a value of approximately 0.064-0.074-independently of the initial
chiral asymmetry and for ? . Our simulations suggest, that ? decreases
as a power law when increasing ? by decreasing the viscosity. While the
exact scaling depends on the details of the fitting criteria and the
Reynolds number regime, an approximate result of ? is reported. Using
the findings from our numerical simulations, we analyse the energetics
of chiral magnetically driven turbulence in the early Universe.

---------------------------------------------------------
Title: Dynamo effect in decaying helical turbulence
Authors: Brandenburg, Axel; Kahniashvili, Tina; Mandal, Sayan; Pol,
Alberto Roper; Tevzadze, Alexander G.; Vachaspati, Tanmay
2019PhRvF...4b4608B Altcode: 2017arXiv171001628B
We show that in decaying hydromagnetic turbulence with initial
kinetic helicity, a weak magnetic field eventually becomes fully
helical. The sign of magnetic helicity is opposite to that of the
kinetic helicity—regardless of whether the initial magnetic field
was helical. The magnetic field undergoes inverse cascading with the
magnetic energy decaying approximately like t−1 /2. This
is even slower than in the fully helical case, where it decays like
t−2 /3. In this parameter range, the product of magnetic
energy and correlation length raised to a certain power slightly larger
than unity is approximately constant. This scaling of magnetic energy
persists over long timescales. At very late times and for domain sizes
large enough to accommodate the growing spatial scales, we expect a
crossover to the t−2 /3 decay law that is commonly observed
for fully helical magnetic fields. Regardless of the presence or absence
of initial kinetic helicity, the magnetic field experiences exponential
growth during the first few turnover times, which is suggestive of
small-scale dynamo action. Our results have applications to a wide
range of experimental dynamos and astrophysical time-dependent plasmas,
including primordial turbulence in the early universe.

---------------------------------------------------------
Title: Magnetic bipoles in rotating turbulence with coronal envelope
Authors: Losada, I. R.; Warnecke, J.; Brandenburg, A.; Kleeorin, N.;
Rogachevskii, I.
2019A&A...621A..61L Altcode: 2018arXiv180304446L
Context. The formation mechanism of sunspots and starspots is not yet
fully understood. It is a major open problem in astrophysics. 
Aims: Magnetic flux concentrations can be produced by the negative
effective magnetic pressure instability (NEMPI). This instability
is strongly suppressed by rotation. However, the presence of an
outer coronal envelope was previously found to strengthen the flux
concentrations and make them more prominent. It also allows for the
formation of bipolar regions (BRs). We aim to understand the important
issue of whether the presence of an outer coronal envelope also changes
the excitation conditions and the rotational dependence of NEMPI. Methods: We have used direct numerical simulations and mean-field
simulations. We adopted a simple two-layer model of turbulence that
mimics the jump between the convective turbulent and coronal layers
below and above the surface of a star, respectively. The computational
domain is Cartesian and located at a certain latitude of a rotating
sphere. We investigated the effects of rotation on NEMPI by changing the
Coriolis number, the latitude, the strengths of the imposed magnetic
field, and the box resolution. Results: Rotation has a strong
impact on the process of BR formation. Even rather slow rotation is
found to suppress BR formation. However, increasing the imposed magnetic
field strength also makes the structures stronger and alleviates the
rotational suppression somewhat. The presence of a coronal layer itself
does not significantly reduce the effects of rotational suppression.

---------------------------------------------------------
Title: E and B Polarizations from Inhomogeneous and Solar Surface
Turbulence
Authors: Brandenburg, Axel; Bracco, Andrea; Kahniashvili, Tina; Mandal,
Sayan; Roper Pol, Alberto; Petrie, Gordon J. D.; Singh, Nishant K.
2019ApJ...870...87B Altcode: 2018arXiv180711457B
Gradient- and curl-type or E- and B-type polarizations have been
routinely analyzed to study the physics contributing to the cosmic
microwave background polarization and galactic foregrounds. They
characterize the parity-even and parity-odd properties of the underlying
physical mechanisms, such as, for example, hydromagnetic turbulence
in the case of dust polarization. Here, we study spectral correlation
functions characterizing the parity-even and parity-odd parts of
linear polarization for homogeneous and inhomogeneous turbulence
to show that only the inhomogeneous helical case can give rise to a
parity-odd polarization signal. We also study nonhelical turbulence and
suggest that a strong non-vanishing (here negative) skewness of the E
polarization is responsible for an enhanced ratio of the EE to the BB
(quadratic) correlation in both the helical and nonhelical cases. This
could explain the enhanced EE/BB ratio observed recently for dust
polarization. We close with a preliminary assessment of using the
linear polarization of the Sun to characterize its helical turbulence
without being subjected to the π ambiguity that magnetic inversion
techniques have to address.

---------------------------------------------------------
Title: Is there a left-handed magnetic field in the solar
neighborhood?. Exploring helical magnetic fields in the interstellar
medium through dust polarization power spectra
Authors: Bracco, A.; Candelaresi, S.; Del Sordo, F.; Brandenburg, A.
2019A&A...621A..97B Altcode: 2018arXiv180710188B
Context. The analysis of the full-sky Planck polarization data at 850
μm revealed unexpected properties of the E- and B-mode power spectra
of dust emission in the interstellar medium (ISM). The positive
cross-correlations over a wide range of angular scales between the
total dust intensity, T, and both E and (most of all) B modes has
raised new questions about the physical mechanisms that affect dust
polarization, such as the Galactic magnetic field structure. This
is key both to better understanding ISM dynamics and to accurately
describing Galactic foregrounds to the polarization of the cosmic
microwave background (CMB). In particular, in the quest to find
primordial B modes of the CMB, the observed positive cross-correlation
between T and B for interstellar dust requires further investigation
towards parity-violating processes in the ISM. Aims: In this
theoretical paper we investigate the possibility that the observed
cross-correlations in the dust polarization power spectra, and
specifically the one between T and B, can be related to a parity-odd
quantity in the ISM such as the magnetic helicity. Methods: We
produce synthetic dust polarization data, derived from 3D analytical
toy models of density structures and helical magnetic fields, to
compare with the E and B modes of observations. We present several
models. The first is an ideal fully helical isotropic case, such as the
Arnold-Beltrami-Childress field. Second, following the nowadays favored
interpretation of the T-E signal in terms of the observed alignment
between the magnetic field morphology and the filamentary density
structure of the diffuse ISM, we design models for helical magnetic
fields wrapped around cylindrical interstellar filaments. Lastly,
focusing on the observed T-B correlation, we propose a new line of
interpretation of the Planck observations advocating the presence
of a large-scale helical component of the Galactic magnetic field
in the solar neighborhood. Results: Our analysis shows that:
I) the sign of magnetic helicity does not affect E and B modes for
isotropic magnetic-field configurations; II) helical magnetic fields
threading interstellar filaments cannot reproduce the Planck results;
and III) a weak helical left-handed magnetic field structure in the
solar neighborhood may explain the T-B correlation seen in the Planck
data. Such a magnetic-field configuration would also account for
the observed large-scale T-E correlation. Conclusions: This
work suggests a new perspective for the interpretation of the dust
polarization power spectra that supports the imprint of a large-scale
structure of the Galactic magnetic field in the solar neighborhood.

---------------------------------------------------------
Title: Magnetic helicity and fluxes in an inhomogeneous alpha
squared dynamo
Authors: Brandenburg, A.
2019arXiv190107552B Altcode:
Much work on turbulent three-dimensional dynamos has been done using
triply periodic domains, in which there are no magnetic helicity
fluxes. Here we present simulations where the turbulent intensity is
still nearly homogeneous, but now there is a perfect conductor boundary
condition on one end and a vertical field or pseudo-vacuum condition on
the other. This leads to migratory dynamo waves. Good agreement with a
corresponding analytically solvable alpha^2 dynamo is found. Magnetic
helicity fluxes are studied in both types of models. It is found that
at moderate magnetic Reynolds numbers, most of the magnetic helicity
losses occur at large scales. Whether this changes at even larger
magnetic Reynolds numbers, as required for alleviating the catastrophic
dynamo quenching problem, remains still unclear.

---------------------------------------------------------
Title: Pencil Code
Authors: Brandenburg, Axel
2018zndo...2315093B Altcode:
This is the current version; see the "Scientific Usage of the
Pencil Code" under http://pencil-code.nordita.org/highlights/ for
the currently over 400 publications using the code. The code has
received 29,502 commits since 2001. The latest version is available
under https://github.com/pencil-code

---------------------------------------------------------
Title: Magnetic Helicity from Multipolar Regions on the Solar Surface
Authors: Bourdin, Philippe-A.; Brandenburg, Axel
2018ApJ...869....3B Altcode: 2018arXiv180404160B
The emergence of dipolar magnetic features on the solar surface
is an idealization. Most of the magnetic flux emergence occurs in
complex multipolar regions. Here, we show that the surface pattern of
magnetic structures alone can reveal the sign of the underlying magnetic
helicity in the nearly force-free coronal regions above. The sign of
the magnetic helicity can be predicted to good accuracy by considering
the three-dimensional position vectors of three spots on the sphere
ordered by their relative strengths at the surface and compute from
them the skew product. This product, which is a pseudoscalar, is shown
to be a good proxy for the sign of the coronal magnetic helicity.

---------------------------------------------------------
Title: Magnetic Helicity Reversal in the Corona at Small Plasma Beta
Authors: Bourdin, Philippe; Singh, Nishant K.; Brandenburg, Axel
2018ApJ...869....2B Altcode: 2018arXiv180404153B
Solar and stellar dynamos shed small-scale and large-scale magnetic
helicity of opposite signs. However, solar wind observations and
simulations have shown that some distance above the dynamo both
the small-scale and large-scale magnetic helicities have reversed
signs. With realistic simulations of the solar corona above an active
region now being available, we have access to the magnetic field and
current density along coronal loops. We show that a sign reversal in
the horizontal averages of the magnetic helicity occurs when the local
maximum of the plasma beta drops below unity and the field becomes
nearly fully force free. Hence, this reversal is expected to occur well
within the solar corona and would not directly be accessible to in situ
measurements with the Parker Solar Probe or SolarOrbiter. We also show
that the reversal is associated with subtle changes in the relative
dominance of structures with positive and negative magnetic helicity.

---------------------------------------------------------
Title: Cross-helically forced and decaying hydromagnetic turbulence
Authors: Brandenburg, A.; Oughton, S.
2018AN....339..641B Altcode: 2019arXiv190105875B
We study the evolution of kinetic and magnetic energy spectra in
magnetohydrodynamic flows in the presence of strong cross helicity. For
forced turbulence, we find a weak inverse transfer of kinetic energy
toward the smallest wavenumber. This is plausibly explained by the
finiteness of scale separation between the injection wavenumber and the
smallest wavenumber of the domain, which here is a factor of 15. In the
decaying case, there is a slight increase at the smallest wavenumber,
which is probably explained by the dominance of kinetic energy
over magnetic energy at the smallest wavenumbers. Within a range of
wavenumbers covering almost an order of magnitude, the decay is purely
exponential, which is argued to be a consequence of a suppression of
nonlinearity due to the presence of strong cross helicity.

---------------------------------------------------------
Title: Magnetic helicity and fluxes in an inhomogeneous α2
dynamo
Authors: Brandenburg, A.
2018AN....339..631B Altcode:
Much work on turbulent three-dimensional dynamos has been done using
triply periodic domains, in which there are no magnetic helicity
fluxes. Here, we present simulations where the turbulent intensity
is still nearly homogeneous, but now there is a perfect conductor
boundary condition on one end and a vertical field or pseudovacuum
conditions on the other. This leads to migratory dynamo waves. Good
agreement with a corresponding analytically solvable α2
dynamo is found. Magnetic helicity fluxes are studied in both types of
models. It is found that at moderate magnetic Reynolds numbers, most of
the magnetic helicity losses occur on large scales. Whether this changes
at even larger magnetic Reynolds numbers, as required for alleviating
the catastrophic dynamo quenching problem, remains stillunclear.

---------------------------------------------------------
Title: Compressibility in turbulent magnetohydrodynamics and passive
scalar transport: mean-field theory
Authors: Rogachevskii, I.; Kleeorin, N.; Brandenburg, A.
2018JPlPh..84e7302R Altcode: 2018arXiv180101804R
We develop a mean-field theory of compressibility effects in turbulent
magnetohydrodynamics and passive scalar transport using the quasi-linear
approximation and the spectral τ-approach. We find that compressibility
decreases the α effect and the turbulent magnetic diffusivity both at
small and large magnetic Reynolds numbers, Rm. Similarly,
compressibility decreases the turbulent diffusivity for passive scalars
both at small and large Péclet numbers, Pe. On the other
hand, compressibility does not affect the effective pumping velocity
of the magnetic field for large Rm, but it decreases it
for small Rm. Density stratification causes turbulent
pumping of passive scalars, but it is found to become weaker with
increasing compressibility. No such pumping effect exists for magnetic
fields. However, compressibility results in a new passive scalar
pumping effect from regions of low to high turbulent intensity both for
small and large Péclet numbers. It can be interpreted as compressible
turbophoresis of non-inertial particles and gaseous admixtures, while
the classical turbophoresis effect exists only for inertial particles
and causes them to be pumped to regions with lower turbulent intensity.

---------------------------------------------------------
Title: Varying the forcing scale in low Prandtl number dynamos
Authors: Brandenburg, A.; Haugen, N. E. L.; Li, Xiang-Yu; Subramanian,
K.
2018MNRAS.479.2827B Altcode: 2018arXiv180501249B; 2018MNRAS.tmp.1491B
Small-scale dynamos are expected to operate in all astrophysical
fluids that are turbulent and electrically conducting, for example
the interstellar medium, stellar interiors, and accretion discs,
where they may also be affected by or competing with large-scale
dynamos. However, the possibility of small-scale dynamos being excited
at small and intermediate ratios of viscosity to magnetic diffusivity
(the magnetic Prandtl number) has been debated, and the possibility
of them depending on the large-scale forcing wavenumber has been
raised. Here, we show, using four values of the forcing wavenumber,
that the small-scale dynamo does not depend on the scale separation
between the size of the simulation domain and the integral scale of the
turbulence, i.e. the forcing scale. Moreover, the spectral bottleneck in
turbulence, which has been implied as being responsible for raising the
excitation conditions of small-scale dynamos, is found to be invariant
under changing the forcing wavenumber. However, when forcing at the
lowest few wavenumbers, the effective forcing wavenumber that enters
in the definition of the magnetic Reynolds number is found to be about
twice the minimum wavenumber of the domain. Our work is relevant to
future studies of small-scale dynamos, of which several applications
are being discussed.

---------------------------------------------------------
Title: Statistical properties of scale-invariant helical magnetic
fields and applications to cosmology
Authors: Brandenburg, Axel; Durrer, Ruth; Kahniashvili, Tina; Mandal,
Sayan; Yin, Weichen Winston
2018JCAP...08..034B Altcode: 2018arXiv180401177B
We investigate the statistical properties of isotropic, stochastic,
Gaussian distributed, helical magnetic fields characterized by
different shapes of the energy spectra at large length scales and
study the associated realizability condition. We discuss smoothed
magnetic fields that are commonly used when the primordial magnetic
field is constrained by observational data. We are particularly
interested in scale-invariant magnetic fields that can be generated
during the inflationary stage by quantum fluctuations. We determine
the correlation length of such magnetic fields and relate it to the
infrared cutoff of perturbations produced during inflation. We show that
this scale determines the observational signatures of the inflationary
magnetic fields on the cosmic microwave background. At smaller scales,
the scale-invariant spectrum changes with time. It becomes a steeper
weak-turbulence spectrum at progressively larger scales. We show
numerically that the critical length scale where this happens is the
turbulent-diffusive scale, which increases with the square root of time.

---------------------------------------------------------
Title: Solar Kinetic Energy and Cross Helicity Spectra
Authors: Zhang, Hongqi; Brandenburg, Axel
2018ApJ...862L..17Z Altcode: 2018arXiv180410321Z
We develop a formalism that treats the calculation of solar kinetic
energy and cross helicity spectra in an equal manner to that of magnetic
energy and helicity spectra. The magnetic helicity spectrum is shown
to be equal to the vertical part of the current helicity spectrum
divided by the square of the wavenumber. For the cross helicity,
we apply the recently developed two-scale approach globally over an
entire active region to account for the sign change between the two
polarities. Using vector magnetograms and Dopplergrams of NOAA 11158
and 12266, we show that kinetic and magnetic energy spectra have
similar slopes at intermediate wavenumbers, where the contribution
from the granulation velocity has been removed. At wavenumbers around
0.3 {Mm}}-1, the magnetic helicity is found to be close to
its maximal value. The cross helicity spectra are found to be within
about 10% of the maximum possible value. Using the two-scale method
for NOAA 12266, the global cross helicity spectrum is found to be
particularly steep, similarly to what has previously been found in
theoretical models of spot generation. In the quiet Sun, by comparison,
the cross helicity spectrum is found to be small.

---------------------------------------------------------
Title: Chiral fermion asymmetry in high-energy plasma simulations
Authors: Schober, Jennifer; Brandenburg, Axel; Rogachevskii, Igor
2018arXiv180806624S Altcode:
The chiral magnetic effect (CME) is a quantum relativistic effect
that describes the appearance of an additional electric current
along a magnetic field. It is caused by an asymmetry between the
number densities of left- and right-handed fermions, which can be
maintained at high energies when the chirality flipping rate can be
neglected, for example in the early Universe. The inclusion of the CME
in the Maxwell equations leads to a modified set of MHD equations. We
discuss how the CME is implemented in the PENCIL CODE. The CME plays
a key role in the evolution of magnetic fields since it results in
a dynamo effect associated with an additional term in the induction
equation. This term is formally similar to the $\alpha$ effect
in classical mean-field MHD. However, the chiral dynamo can operate
without turbulence and is associated with small spatial scales that can
be, in the case of the early Universe, orders of magnitude below the
Hubble radius. A chiral $\alpha_\mu$ effect has also been identified
in mean-field theory. It occurs in the presence of turbulence but is
not related to kinetic helicity. Depending on the plasma parameters,
chiral dynamo instabilities can amplify magnetic fields over many
orders of magnitude. These instabilities can affect the propagation
of MHD waves, which is demonstrated by our DNS. We also study the
coupling between the evolution of the chiral chemical potential and
the ordinary chemical potential, which is proportional to the sum of
the number densities of left- and right-handed fermions. An important
consequence of this coupling is the emergence of chiral magnetic waves
(CMWs). We confirm numerically that linear CMWs and MHD waves are not
interacting. Our simulations suggest that the chemical potential has
only a minor effect on the non-linear evolution of the chiral dynamo.

---------------------------------------------------------
Title: Advances in mean-field dynamo theory and applications to
astrophysical turbulence
Authors: Brandenburg, Axel
2018JPlPh..84d7304B Altcode: 2018arXiv180105384B
Recent advances in mean-field theory are reviewed and applications
to the Sun, late-type stars, accretion disks, galaxies and the
early Universe are discussed. We focus particularly on aspects of
spatio-temporal non-locality, which provided some of the main new
qualitative and quantitative insights that emerged from applying the
test-field method to magnetic fields of different length and time
scales. We also review the status of nonlinear quenching and the
relation to magnetic helicity, which is an important observational
diagnostic of modern solar dynamo theory. Both solar and some stellar
dynamos seem to operate in an intermediate regime that has not
yet been possible to model successfully. This regime is bracketed
by antisolar-like differential rotation on one end and stellar
activity cycles belonging to the superactive stars on the other. The
difficulty in modelling this regime may be related to shortcomings
in simulating solar/stellar convection. On galactic and extragalactic
length scales, the observational constraints on dynamo theory are still
less stringent and more uncertain, but recent advances both in theory
and observations suggest that more conclusive comparisons may soon be
possible also here. The possibility of inversely cascading magnetic
helicity in the early Universe is particularly exciting in explaining
the recently observed lower limits of magnetic fields on cosmological
length scales. Such magnetic fields may be helical with the same sign
of magnetic helicity throughout the entire Universe. This would be a
manifestation of parity breaking.

---------------------------------------------------------
Title: $f$-mode strengthening from a localized bipolar subsurface
magnetic field
Authors: Singh, Nishant K.; Raichur, Harsha; Käpylä, Maarit J.;
Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J.
2018arXiv180808904S Altcode:
Recent numerical work in helioseismology has shown that a periodically
varying subsurface magnetic field leads to a fanning of the $f$-mode,
which emerges from the density jump at the surface. In an attempt
to model a more realistic situation, we now modulate this periodic
variation with an envelope, giving thus more emphasis on localized
bipolar magnetic structures in the middle of the domain. Some notable
findings are: (i) compared to the purely hydrodynamic case, the strength
of the $f$-mode is significantly larger at high horizontal wavenumbers
$k$, but the fanning is weaker for the localized subsurface magnetic
field concentrations investigated here than the periodic ones studied
earlier; (ii) when the strength of the magnetic field is enhanced at
a fixed depth below the surface, the fanning of the $f$-mode in the
$k\omega$ diagram increases proportionally in such a way that the
normalized $f$-mode strengths remain nearly the same in different
such cases; (iii) the unstable Bloch modes reported previously in
case of harmonically varying magnetic fields are now completely
absent when more realistic localized magnetic field concentrations
are imposed beneath the surface, thus suggesting that the Bloch modes
are unlikely to be supported during most phases of the solar cycle;
(iv) the $f$-mode strength appears to depend also on the depth of
magnetic field concentrations such that it shows a relative decrement
when the maximum of the magnetic field is moved to a deeper layer. We
argue that detections of $f$-mode perturbations such as those being
explored here could be effective tracers of solar magnetic fields
below the photosphere before these are directly detectable as visible
manifestations in terms of active regions or sunspots.

---------------------------------------------------------
Title: Transition from axi- to nonaxisymmetric dynamo modes in
spherical convection models of solar-like stars
Authors: Viviani, M.; Warnecke, J.; Käpylä, M. J.; Käpylä, P. J.;
Olspert, N.; Cole-Kodikara, E. M.; Lehtinen, J. J.; Brandenburg, A.
2018A&A...616A.160V Altcode: 2017arXiv171010222V
Context. Both dynamo theory and observations of stellar large-scale
magnetic fields suggest a change from nearly axisymmetric configurations
at solar rotation rates to nonaxisymmetric configurations for rapid
rotation. Aims: We seek to understand this transition using
numerical simulations. Methods: We use three-dimensional
simulations of turbulent magnetohydrodynamic convection in spherical
shell wedges and considered rotation rates between 1 and 31 times
the solar value. Results: We find a transition from axi-
to nonaxisymmetric solutions at around 1.8 times the solar rotation
rate. This transition coincides with a change in the rotation profile
from antisolar- to solar-like differential rotation with a faster
equator and slow poles. In the solar-like rotation regime, the
field configuration consists of an axisymmetric oscillatory field
accompanied by an m = 1 azimuthal mode (two active longitudes),
which also shows temporal variability. At slow (rapid) rotation,
the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric
mode produces latitudinal dynamo waves with polarity reversals, while
the nonaxisymmetric mode often exhibits a slow drift in the rotating
reference frame and the strength of the active longitudes changes
cyclically over time between the different hemispheres. In the majority
of cases we find retrograde waves, while prograde waves are more often
found from observations. Most of the obtained dynamo solutions exhibit
cyclic variability either caused by latitudinal or azimuthal dynamo
waves. In an activity-period diagram, the cycle lengths normalized
by the rotation period form two different populations as a function
of rotation rate or magnetic activity level. The slowly rotating
axisymmetric population lies close to what in observations is called
the inactive branch, where the stars are believed to have solar-like
differential rotation, while the rapidly rotating models are close to
the superactive branch with a declining cycle to rotation frequency
ratio and an increasing rotation rate. Conclusions: We can
successfully reproduce the transition from axi- to nonaxisymmetric
dynamo solutions for high rotation rates, but high-resolution
simulations are required to limit the effect of rotational quenching
of convection at rotation rates above 20 times the solar value.

---------------------------------------------------------
Title: Bihelical Spectrum of Solar Magnetic Helicity and Its Evolution
Authors: Singh, Nishant K.; Käpylä, Maarit J.; Brandenburg, Axel;
Käpylä, Petri J.; Lagg, Andreas; Virtanen, Ilpo
2018ApJ...863..182S Altcode: 2018arXiv180404994S
Using a recently developed two-scale formalism to determine the
magnetic helicity spectrum, we analyze synoptic vector magnetograms
built with data from the Vector Spectromagnetograph instrument on the
Synoptic Optical Long-term Investigations of the Sun telescope during
2010 January-2016 July. In contrast to an earlier study using only
three Carrington rotations (CRs), our analysis includes 74 synoptic
CR maps. We recover here bihelical spectra at different phases of
solar cycle 24, where the net magnetic helicity in the majority of the
data is consistent with a large-scale dynamo with helical turbulence
operating in the Sun. More than 20% of the analyzed maps, however,
show violations of the expected sign rule.

---------------------------------------------------------
Title: Large-scale dynamos in rapidly rotating plane layer convection
Authors: Bushby, P. J.; Käpylä, P. J.; Masada, Y.; Brandenburg,
A.; Favier, B.; Guervilly, C.; Käpylä, M. J.
2018A&A...612A..97B Altcode: 2017arXiv171003174B
Context. Convectively driven flows play a crucial role in the dynamo
processes that are responsible for producing magnetic activity in stars
and planets. It is still not fully understood why many astrophysical
magnetic fields have a significant large-scale component. 
Aims: Our aim is to investigate the dynamo properties of compressible
convection in a rapidly rotating Cartesian domain, focusing upon a
parameter regime in which the underlying hydrodynamic flow is known to
be unstable to a large-scale vortex instability. Methods: The
governing equations of three-dimensional non-linear magnetohydrodynamics
(MHD) are solved numerically. Different numerical schemes are compared
and we propose a possible benchmark case for other similar codes. Results: In keeping with previous related studies, we find that
convection in this parameter regime can drive a large-scale dynamo. The
components of the mean horizontal magnetic field oscillate, leading to
a continuous overall rotation of the mean field. Whilst the large-scale
vortex instability dominates the early evolution of the system, the
large-scale vortex is suppressed by the magnetic field and makes
a negligible contribution to the mean electromotive force that is
responsible for driving the large-scale dynamo. The cycle period of
the dynamo is comparable to the ohmic decay time, with longer cycles
for dynamos in convective systems that are closer to onset. In these
particular simulations, large-scale dynamo action is found only when
vertical magnetic field boundary conditions are adopted at the upper
and lower boundaries. Strongly modulated large-scale dynamos are
found at higher Rayleigh numbers, with periods of reduced activity
(grand minima-like events) occurring during transient phases in which
the large-scale vortex temporarily re-establishes itself, before being
suppressed again by the magnetic field.

---------------------------------------------------------
Title: Laminar and Turbulent Dynamos in Chiral
Magnetohydrodynamics. II. Simulations
Authors: Schober, Jennifer; Rogachevskii, Igor; Brandenburg, Axel;
Boyarsky, Alexey; Fröhlich, Jürg; Ruchayskiy, Oleg; Kleeorin, Nathan
2018ApJ...858..124S Altcode: 2017arXiv171109733S
Using direct numerical simulations (DNS), we study laminar and
turbulent dynamos in chiral magnetohydrodynamics with an extended
set of equations that accounts for an additional contribution to the
electric current due to the chiral magnetic effect (CME). This quantum
phenomenon originates from an asymmetry between left- and right-handed
relativistic fermions in the presence of a magnetic field and gives
rise to a chiral dynamo. We show that the magnetic field evolution
proceeds in three stages: (1) a small-scale chiral dynamo instability,
(2) production of chiral magnetically driven turbulence and excitation
of a large-scale dynamo instability due to a new chiral effect (α
 μ effect), and (3) saturation of magnetic helicity and
magnetic field growth controlled by a conservation law for the total
chirality. The α μ effect becomes dominant at large
fluid and magnetic Reynolds numbers and is not related to kinetic
helicity. The growth rate of the large-scale magnetic field and its
characteristic scale measured in the numerical simulations agree well
with theoretical predictions based on mean-field theory. The previously
discussed two-stage chiral magnetic scenario did not include stage (2),
during which the characteristic scale of magnetic field variations
can increase by many orders of magnitude. Based on the findings
from numerical simulations, the relevance of the CME and the chiral
effects revealed in the relativistic plasma of the early universe and
of proto-neutron stars are discussed.

---------------------------------------------------------
Title: Enhanced Stellar Activity for Slow Antisolar Differential
Rotation?
Authors: Brandenburg, Axel; Giampapa, Mark S.
2018ApJ...855L..22B Altcode: 2018arXiv180208689B
High-precision photometry of solar-like members of the open cluster M67
with Kepler/K2 data has recently revealed enhanced activity for stars
with a large Rossby number, which is the ratio of rotation period
to the convective turnover time. Contrary to the well established
behavior for shorter rotation periods and smaller Rossby numbers,
the chromospheric activity of the more slowly rotating stars of M67
was found to increase with increasing Rossby number. Such behavior has
never been reported before, although it was theoretically predicted
to emerge as a consequence of antisolar differential rotation (DR)
for stars with Rossby numbers larger than that of the Sun, because in
those models the absolute value of the DR was found to exceed that for
solar-like DR. Using gyrochronological relations and an approximate
age of 4 Gyr for the members of M67, we compare with computed rotation
rates using just the B - V color. The resulting rotation-activity
relation is found to be compatible with that obtained by employing
the measured rotation rate. This provides additional support for the
unconventional enhancement of activity at comparatively low rotation
rates and the possible presence of antisolar differential rotation.

---------------------------------------------------------
Title: Small-scale dynamos in simulations of stratified turbulent
convection
Authors: Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.
2018AN....339..127K Altcode: 2018arXiv180209607K
Small-scale dynamo action is often held responsible for the
generation of quiet Sun magnetic fields. We aim to determine the
excitation conditions and saturation level of small-scale dynamos in
nonrotating turbulent convection at low magnetic Prandtl numbers. We
use high-resolution direct numerical simulations of weakly stratified
turbulent convection. We find that the critical magnetic Reynolds
number for dynamo excitation increases as the magnetic Prandtl number
is decreased, which might suggest that small-scale dynamo action is not
automatically evident in bodies with small magnetic Prandtl numbers,
such as the Sun. As a function of the magnetic Reynolds number (Rm),
the growth rate of the dynamo is consistent with an Rm1/2
scaling. No evidence for a logarithmic increase of the growth rate
with Rm is found.

---------------------------------------------------------
Title: Strong nonlocality variations in a spherical mean‑field
dynamo
Authors: Brandenburg, Axel; Chatterjee, Piyali
2018AN....339..118B Altcode: 2018arXiv180204231B
To explain the large-scale magnetic field of the Sun and other
bodies, mean-field dynamo theory is commonly applied where one
solves the averaged equations for the mean magnetic field. However,
the standard approach breaks down when the scale of the turbulent
eddies becomes comparable to the scale of the variations of the mean
magnetic field. Models showing sharp magnetic field structures have
therefore been regarded as unreliable. Our aim is to look for new
effects that occur when we relax the restrictions of the standard
approach, which becomes particularly important at the bottom of the
convection zone where the size of the turbulent eddies is comparable
to the depth of the convection zone itself. We approximate the
underlying integro-differential equation by a partial differential
equation corresponding to a reaction-diffusion type equation for the
mean electromotive force, making an approach that is nonlocal in
space and time feasible under conditions where spherical geometry
and nonlinearity are included. In agreement with earlier findings,
spatio-temporal nonlocality lowers the excitation conditions of the
dynamo. Sharp structures are now found to be absent. However, in the
surface layers the field remains similar to before.

---------------------------------------------------------
Title: Turbulent transport coefficients in spherical wedge dynamo
simulations of solar-like stars
Authors: Warnecke, J.; Rheinhardt, M.; Tuomisto, S.; Käpylä, P. J.;
Käpylä, M. J.; Brandenburg, A.
2018A&A...609A..51W Altcode: 2016arXiv160103730W
 Aims: We investigate dynamo action in global compressible
solar-like convective dynamos in the framework of mean-field
theory. Methods: We simulate a solar-type star in a wedge-shaped
spherical shell, where the interplay between convection and rotation
self-consistently drives a large-scale dynamo. To analyze the dynamo
mechanism we apply the test-field method for azimuthally (φ) averaged
fields to determine the 27 turbulent transport coefficients of the
electromotive force, of which six are related to the α tensor. This
method has previously been used either in simulations in Cartesian
coordinates or in the geodynamo context and is applied here for the
first time to fully compressible simulations of solar-like dynamos. Results: We find that the φφ-component of the α tensor does
not follow the profile expected from that of kinetic helicity. The
turbulent pumping velocities significantly alter the effective mean
flows acting on the magnetic field and therefore challenge the flux
transport dynamo concept. All coefficients are significantly affected by
dynamically important magnetic fields. Quenching as well as enhancement
are being observed. This leads to a modulation of the coefficients with
the activity cycle. The temporal variations are found to be comparable
to the time-averaged values and seem to be responsible for a nonlinear
feedback on the magnetic field generation. Furthermore, we quantify the
validity of the Parker-Yoshimura rule for the equatorward propagation
of the mean magnetic field in the present case.

---------------------------------------------------------
Title: The Global Solar Dynamo
Authors: Cameron, R. H.; Dikpati, M.; Brandenburg, A.
2018smf..book..367C Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Spontaneous flux concentrations from the negative effective
magnetic pressure instability beneath a radiative stellar surface
Authors: Perri, B.; Brandenburg, A.
2018A&A...609A..99P Altcode: 2017arXiv170103018P
Context. The formation of sunspots requires the concentration of
magnetic flux near the surface. The negative effective magnetic
pressure instability (NEMPI) might be a possible mechanism for
accomplishing this, but it has mainly been studied in simple
systems using an isothermal equation of state without a natural
free surface. Aims: We study NEMPI in a stratified Cartesian
mean-field model where turbulence effects are parameterized. We use
an ideal equation of state and include radiation transport, which
establishes selfconsistently a free surface. Methods: We use
a Kramers-type opacity with adjustable exponents chosen such that the
deeper layers are approximately isentropic. No convection is therefore
possible in this model, allowing us to study NEMPI with radiation
in isolation. We restrict ourselves to two-dimensional models. We
use artificially enhanced mean-field coefficients to allow NEMPI to
develop, thereby making it possible to study the reason why it is
much harder to excite in the presence of radiation. Results:
NEMPI yields moderately strong magnetic flux concentrations a certain
distance beneath the surface where the optical depth is unity. The
instability is oscillatory and in the form of upward traveling
waves. This seems to be a new effect that has not been found in
earlier models without radiative transport. The horizontal wavelength
is about ten times smaller than what has previously been found in more
idealized isothermal models. Conclusions: In our models, NEMPI
saturates at field strengths too low to explain sunspots. Furthermore,
the structures appear too narrow and too far beneath the surface to
cause significant brightness variations at the radiative surface. We
speculate that the failure to reproduce effects resembling sunspots
may be related to the neglect of convection.

---------------------------------------------------------
Title: Evolution of hydromagnetic turbulence from the electroweak
phase transition
Authors: Brandenburg, Axel; Kahniashvili, Tina; Mandal, Sayan; Pol,
Alberto Roper; Tevzadze, Alexander G.; Vachaspati, Tanmay
2017PhRvD..96l3528B Altcode: 2017arXiv171103804B
We present new simulations of decaying hydromagnetic turbulence for
a relativistic equation of state relevant to the early Universe. We
compare helical and nonhelical cases either with kinetically or
magnetically dominated initial fields. Both kinetic and magnetic initial
helicities lead to maximally helical magnetic fields after some time,
but with different temporal decay laws. Both are relevant to the
early Universe, although no mechanisms have yet been identified that
produce magnetic helicity with strengths comparable to the big bang
nucleosynthesis limit at scales comparable to the Hubble horizon at the
electroweak phase transition. Nonhelical magnetically dominated fields
could still produce picoGauss magnetic fields under most optimistic
conditions. Only helical magnetic fields can potentially have nanoGauss
strengths at scales up to 30 kpc today.

---------------------------------------------------------
Title: Scale-invariant helical magnetic field evolution and the
duration of inflation
Authors: Kahniashvili, Tina; Brandenburg, Axel; Durrer, Ruth; Tevzadze,
Alexander G.; Yin, Winston
2017JCAP...12..002K Altcode: 2016arXiv161003139K
We consider a scale-invariant helical magnetic field generated during
inflation. We show that, if the mean magnetic helicity density of
such a field is measured, it can be used to determine a lower bound
on the duration of inflation. Even if we just have upper bounds on
the helicity, these can be used to derive constraints on the minimal
duration if one assumes that the magnetic field generated during
inflation is helical. Using three-dimensional simulations, we show
that an initially scale-invariant field develops, which is similar both
with and without magnetic helicity. In the fully helical case, however,
the magnetic field appears to have a more pronounced folded structure.

---------------------------------------------------------
Title: Enhancement of Small-scale Turbulent Dynamo by Large-scale
Shear
Authors: Singh, Nishant K.; Rogachevskii, Igor; Brandenburg, Axel
2017ApJ...850L...8S Altcode: 2016arXiv161007215S
Small-scale dynamos (SSDs) are ubiquitous in a broad range of
turbulent flows with large-scale shear, ranging from solar and
galactic magnetism to accretion disks, cosmology, and structure
formation. Using high-resolution direct numerical simulations, we show
that in non-helically forced turbulence with zero mean magnetic field,
large-scale shear supports SSD action, I.e., the dynamo growth rate
increases with shear and shear enhances or even produces turbulence,
which, in turn, further increases the growth rate. When the production
rates of turbulent kinetic energy due to shear and forcing are
comparable, we find scalings for the growth rate γ of the SSD and
the turbulent rms velocity {u}{rms} with shear rate S
that are independent of the magnetic Prandtl number: γ \propto | S|
and {u}{rms}\propto | S{| }2/3. For large fluid
and magnetic Reynolds numbers, γ, normalized by its shear-free value,
depends only on shear. Having compensated for shear-induced effects on
turbulent velocity, we find that the normalized growth rate of the SSD
exhibits the scaling, \widetilde{γ }\propto | S{| }2/3,
arising solely from the induction equation for a given velocity field.

---------------------------------------------------------
Title: A new look at sunspot formation using theory and observations
Authors: Losada, I. R.; Warnecke, J.; Glogowski, K.; Roth, M.;
Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2017IAUS..327...46L Altcode: 2017arXiv170404062L
Sunspots are of basic interest in the study of the Sun. Their
relevance ranges from them being an activity indicator of magnetic
fields to being the place where coronal mass ejections and flares
erupt. They are therefore also an important ingredient of space
weather. Their formation, however, is still an unresolved problem in
solar physics. Observations utilize just 2D surface information near the
spot, but it is debatable how to infer deep structures and properties
from local helioseismology. For a long time, it was believed that flux
tubes rising from the bottom of the convection zone are the origin of
the bipolar sunspot structure seen on the solar surface. However,
this theory has been challenged, in particular recently by new
surface observation, helioseismic inversions, and numerical models
of convective dynamos. In this article we discuss another theoretical
approach to the formation of sunspots: the negative effective magnetic
pressure instability. This is a large-scale instability, in which the
total (kinetic plus magnetic) turbulent pressure can be suppressed
in the presence of a weak large-scale magnetic field, leading to a
converging downflow, which eventually concentrates the magnetic field
within it. Numerical simulations of forced stratified turbulence have
been able to produce strong super-equipartition flux concentrations,
similar to sunspots at the solar surface. In this framework, sunspots
would only form close to the surface due to the instability constraints
on stratification and rotation. Additionally, we present some ideas
from local helioseismology, where we plan to use the Hankel analysis
to study the pre-emergence phase of a sunspot and to constrain its
deep structure and formation mechanism.

---------------------------------------------------------
Title: The Global Solar Dynamo
Authors: Cameron, R. H.; Dikpati, M.; Brandenburg, A.
2017SSRv..210..367C Altcode: 2016arXiv160201754C; 2016SSRv..tmp....5C
A brief summary of the various observations and constraints
that underlie solar dynamo research are presented. The arguments
that indicate that the solar dynamo is an alpha-omega dynamo of
the Babcock-Leighton type are then shortly reviewed. The main open
questions that remain are concerned with the subsurface dynamics,
including why sunspots emerge at preferred latitudes as seen in
the familiar butterfly wings, why the cycle is about 11 years long,
and why the sunspot groups emerge tilted with respect to the equator
(Joy's law). Next, we turn to magnetic helicity, whose conservation
property has been identified with the decline of large-scale magnetic
fields found in direct numerical simulations at large magnetic Reynolds
numbers. However, magnetic helicity fluxes through the solar surface
can alleviate this problem and connect theory with observations,
as will be discussed.

---------------------------------------------------------
Title: Laminar and Turbulent Dynamos in Chiral
Magnetohydrodynamics. I. Theory
Authors: Rogachevskii, Igor; Ruchayskiy, Oleg; Boyarsky, Alexey;
Fröhlich, Jürg; Kleeorin, Nathan; Brandenburg, Axel; Schober,
Jennifer
2017ApJ...846..153R Altcode: 2017arXiv170500378R
The magnetohydrodynamic (MHD) description of plasmas with relativistic
particles necessarily includes an additional new field, the chiral
chemical potential associated with the axial charge (I.e., the number
difference between right- and left-handed relativistic fermions). This
chiral chemical potential gives rise to a contribution to the electric
current density of the plasma (chiral magnetic effect). We present a
self-consistent treatment of the chiral MHD equations, which include
the back-reaction of the magnetic field on a chiral chemical potential
and its interaction with the plasma velocity field. A number of novel
phenomena are exhibited. First, we show that the chiral magnetic
effect decreases the frequency of the Alfvén wave for incompressible
flows, increases the frequencies of the Alfvén wave and of the fast
magnetosonic wave for compressible flows, and decreases the frequency
of the slow magnetosonic wave. Second, we show that, in addition to
the well-known laminar chiral dynamo effect, which is not related to
fluid motions, there is a dynamo caused by the joint action of velocity
shear and chiral magnetic effect. In the presence of turbulence with
vanishing mean kinetic helicity, the derived mean-field chiral MHD
equations describe turbulent large-scale dynamos caused by the chiral
alpha effect, which is dominant for large fluid and magnetic Reynolds
numbers. The chiral alpha effect is due to an interaction of the chiral
magnetic effect and fluctuations of the small-scale current produced by
tangling magnetic fluctuations (which are generated by tangling of the
large-scale magnetic field by sheared velocity fluctuations). These
dynamo effects may have interesting consequences in the dynamics of
the early universe, neutron stars, and the quark-gluon plasma.

---------------------------------------------------------
Title: Extended Subadiabatic Layer in Simulations of Overshooting
Convection
Authors: Käpylä, Petri J.; Rheinhardt, Matthias; Brandenburg, Axel;
Arlt, Rainer; Käpylä, Maarit J.; Lagg, Andreas; Olspert, Nigul;
Warnecke, Jörn
2017ApJ...845L..23K Altcode: 2017arXiv170306845K
We present numerical simulations of hydrodynamic overshooting convection
in local Cartesian domains. We find that a substantial fraction
of the lower part of the convection zone (CZ) is stably stratified
according to the Schwarzschild criterion while the enthalpy flux is
outward directed. This occurs when the heat conduction profile at the
bottom of the CZ is smoothly varying, based either on a Kramers-like
opacity prescription as a function of temperature and density or a
static profile of a similar shape. We show that the subadiabatic layer
arises due to nonlocal energy transport by buoyantly driven downflows
in the upper parts of the CZ. Analysis of the force balance of the
upflows and downflows confirms that convection is driven by cooling
at the surface. We find that the commonly used prescription for the
convective enthalpy flux being proportional to the negative entropy
gradient does not hold in the stably stratified layers where the flux is
positive. We demonstrate the existence of a non-gradient contribution
to the enthalpy flux, which is estimated to be important throughout
the convective layer. A quantitative analysis of downflows indicates
a transition from a tree-like structure where smaller downdrafts merge
into larger ones in the upper parts to a structure in the deeper parts
where a height-independent number of strong downdrafts persist. This
change of flow topology occurs when a substantial subadiabatic layer
is present in the lower part of the CZ.

---------------------------------------------------------
Title: The Turbulent Chiral Magnetic Cascade in the Early Universe
Authors: Brandenburg, Axel; Schober, Jennifer; Rogachevskii, Igor;
Kahniashvili, Tina; Boyarsky, Alexey; Fröhlich, Jürg; Ruchayskiy,
Oleg; Kleeorin, Nathan
2017ApJ...845L..21B Altcode: 2017arXiv170703385B
The presence of asymmetry between fermions of opposite handedness in
plasmas of relativistic particles can lead to exponential growth of
a helical magnetic field via a small-scale chiral dynamo instability
known as the chiral magnetic effect. Here, we show, using dimensional
arguments and numerical simulations, that this process produces
through the Lorentz force chiral magnetically driven turbulence. A
{k}-2 magnetic energy spectrum emerges via inverse transfer
over a certain range of wavenumbers k. The total chirality (magnetic
helicity plus normalized chiral chemical potential) is conserved in
this system. Therefore, as the helical magnetic field grows, most of
the total chirality gets transferred into magnetic helicity until the
chiral magnetic effect terminates. Quantitative results for height,
slope, and extent of the spectrum are obtained. Consequences of this
effect for cosmic magnetic fields are discussed.

---------------------------------------------------------
Title: Compensating Faraday Depolarization by Magnetic Helicity in
the Solar Corona
Authors: Brandenburg, Axel; Ashurova, Mohira B.; Jabbari, Sarah
2017ApJ...845L..15B Altcode: 2017arXiv170609540B
A turbulent dynamo in spherical geometry with an outer corona is
simulated to study the sign of magnetic helicity in the outer parts. In
agreement with earlier studies, the sign in the outer corona is found
to be opposite to that inside the dynamo. Line-of-sight observations
of polarized emission are synthesized to explore the feasibility of
using the local reduction of Faraday depolarization to infer the sign
of helicity of magnetic fields in the solar corona. This approach was
previously identified as an observational diagnostic in the context
of galactic magnetic fields. Based on our simulations, we show that
this method can be successful in the solar context if sufficient
statistics are gathered by using averages over ring segments in the
corona separately for the regions north and south of the solar equator.

---------------------------------------------------------
Title: Evolution of Co-existing Long and Short Period Stellar
Activity Cycles
Authors: Brandenburg, Axel; Mathur, Savita; Metcalfe, Travis S.
2017ApJ...845...79B Altcode: 2017arXiv170409009B
The magnetic activity of the Sun becomes stronger and weaker over
roughly an 11 year cycle, modulating the radiation and charged particle
environment experienced by the Earth as “space weather.” Decades
of observations from the Mount Wilson Observatory have revealed that
other stars also show regular activity cycles in their Ca II H+K line
emission, and identified two different relationships between the length
of the cycle and the rotation rate of the star. Recent observations
at higher cadence have allowed the discovery of shorter cycles with
periods between 1{--}3 {years}. Some of these shorter cycles coexist
with longer cycle periods, suggesting that two underlying dynamos
can operate simultaneously. We combine these new observations with
previous data, and show that the longer and shorter cycle periods agree
remarkably well with those expected from an earlier analysis based on
the mean activity level and the rotation period. The relative turbulent
length scales associated with the two branches of cyclic behavior
suggest that a near-surface dynamo may be the dominant mechanism
that drives cycles in more active stars, whereas a dynamo operating
in deeper layers may dominate in less active stars. However, several
examples of equally prominent long and short cycles have been found
at all levels of activity of stars younger than 2.3 Gyr. Deviations
from the expected cycle periods show no dependence on the depth of
the convection zone or on the metallicity. For some stars that exhibit
longer cycles, we compute the periods of shorter cycles that might be
detected with future high-cadence observations.

---------------------------------------------------------
Title: The contribution of kinetic helicity to turbulent magnetic
diffusivity
Authors: Brandenburg, A.; Schober, J.; Rogachevskii, I.
2017AN....338..790B Altcode: 2017arXiv170603421B
Using numerical simulations of forced turbulence with and without mean
kinetic helicity, we show that for magnetic Reynolds numbers larger than
unity, that is, beyond the regime of quasilinear theory, the turbulent
magnetic diffusivity attains an additional negative contribution
that is quadratic in the kinetic helicity. In particular, for large
magnetic Reynolds numbers, the turbulent magnetic diffusivity without
helicity is about twice the value with helicity. Such a contribution
was not previously anticipated, but, as we discuss, it turns out to be
important when accurate estimates of the turbulent magnetic diffusivity
are needed.

---------------------------------------------------------
Title: Sharp magnetic structures from dynamos with density
stratification
Authors: Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan;
Rogachevskii, Igor
2017MNRAS.467.2753J Altcode: 2017MNRAS.467.1507J; 2017MNRAS.tmp..163J; 2016arXiv160708897J
Recent direct numerical simulations (DNS) of large-scale turbulent
dynamos in strongly stratified layers have resulted in surprisingly
sharp bipolar structures at the surface. Here, we present new DNS of
helically and non-helically forced turbulence with and without rotation
and compare with corresponding mean-field simulations (MFS) to show that
these structures are a generic outcome of a broader class of dynamos in
density-stratified layers. The MFS agree qualitatively with the DNS,
but the period of oscillations tends to be longer in the DNS. In both
DNS and MFS, the sharp structures are produced by converging flows
at the surface and might be driven in non-linear stage of evolution
by the Lorentz force associated with the large-scale dynamo-driven
magnetic field if the dynamo number is at least 2.5 times supercritical.

---------------------------------------------------------
Title: Convection-driven spherical shell dynamos at varying Prandtl
numbers
Authors: Käpylä, P. J.; Käpylä, M. J.; Olspert, N.; Warnecke,
J.; Brandenburg, A.
2017A&A...599A...4K Altcode: 2016arXiv160505885K
Context. Stellar convection zones are characterized by vigorous
high-Reynolds number turbulence at low Prandtl numbers. Aims:
We study the dynamo and differential rotation regimes at varying
levels of viscous, thermal, and magnetic diffusion. Methods: We
perform three-dimensional simulations of stratified fully compressible
magnetohydrodynamic convection in rotating spherical wedges at various
thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25
to 5, respectively). Differential rotation and large-scale magnetic
fields are produced self-consistently. Results: We find that for
high thermal diffusivity, the rotation profiles show a monotonically
increasing angular velocity from the bottom of the convection zone to
the top and from the poles toward the equator. For sufficiently rapid
rotation, a region of negative radial shear develops at mid-latitudes
as the thermal diffusivity is decreased, corresponding to an increase
of the Prandtl number. This coincides with and results in a change of
the dynamo mode from poleward propagating activity belts to equatorward
propagating ones. Furthermore, the clearly cyclic solutions disappear
at the highest magnetic Reynolds numbers and give way to irregular sign
changes or quasi-stationary states. The total (mean and fluctuating)
magnetic energy increases as a function of the magnetic Reynolds
number in the range studied here (5-151), but the energies of the
mean magnetic fields level off at high magnetic Reynolds numbers. The
differential rotation is strongly affected by the magnetic fields and
almost vanishes at the highest magnetic Reynolds numbers. In some
of our most turbulent cases, however, we find that two regimes are
possible, where either differential rotation is strong and mean magnetic
fields are relatively weak, or vice versa. Conclusions: Our
simulations indicate a strong nonlinear feedback of magnetic fields on
differential rotation, leading to qualitative changes in the behaviors
of large-scale dynamos at high magnetic Reynolds numbers. Furthermore,
we do not find indications of the simulations approaching an asymptotic
regime where the results would be independent of diffusion coefficients
in the parameter range studied here.

---------------------------------------------------------
Title: Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay
Authors: Brandenburg, Axel; Kahniashvili, Tina
2017PhRvL.118e5102B Altcode: 2016arXiv160701360B
We perform numerical simulations of decaying hydrodynamic and
magnetohydrodynamic turbulence. We classify our time-dependent solutions
by their evolutionary tracks in parametric plots between instantaneous
scaling exponents. We find distinct classes of solutions evolving
along specific trajectories toward points on a line of self-similar
solutions. These trajectories are determined by the underlying physics
governing individual cases, while the infrared slope of the initial
conditions plays only a limited role. In the helical case, even for
a scale-invariant initial spectrum (inversely proportional to wave
number k ), the solution evolves along the same trajectory as for a
Batchelor spectrum (proportional to k4).

---------------------------------------------------------
Title: Two-scale Analysis of Solar Magnetic Helicity
Authors: Brandenburg, Axel; Petrie, Gordon J. D.; Singh, Nishant K.
2017ApJ...836...21B Altcode: 2016arXiv161005410B
We develop a two-scale formalism to determine global magnetic helicity
spectra in systems where the local magnetic helicity has opposite
signs on both sides of the equator, giving rise to cancellation with
conventional methods. We verify this approach using first a synthetic
one-dimensional magnetic field and then two-dimensional slices from
a three-dimensional α effect-type dynamo-generated magnetic field,
with forced turbulence of opposite helicity above and below the
midplane of the domain. We then apply this formalism to global solar
synoptic vector magnetograms. To improve the statistics, data from three
consecutive Carrington rotations (2161-2163) are combined into a single
map. We find that the spectral magnetic helicity representative of the
northern hemisphere is negative at all wavenumbers and peaks at ≈ 0.06
{{Mm}}-1 (scales around 100 {Mm}). There is no evidence of
bihelical magnetic fields that are found in three-dimensional turbulence
simulations of helicity-driven α effect-type dynamos.

---------------------------------------------------------
Title: Analytic solution of an oscillatory migratory α2
stellar dynamo
Authors: Brandenburg, A.
2017A&A...598A.117B Altcode: 2016arXiv161102671B
Context. Analytic solutions of the mean-field induction equation
predict a nonoscillatory dynamo for homogeneous helical turbulence
or constant α effect in unbounded or periodic domains. Oscillatory
dynamos are generally thought impossible for constant α. Aims:
We present an analytic solution for a one-dimensional bounded domain
resulting in oscillatory solutions for constant α, but different
(Dirichlet and von Neumann or perfect conductor and vacuum) boundary
conditions on the two boundaries. Methods: We solve a second
order complex equation and superimpose two independent solutions
to obey both boundary conditions. Results: The solution has
time-independent energy density. On one end where the function value
vanishes, the second derivative is finite, which would not be correctly
reproduced with sine-like expansion functions where a node coincides
with an inflection point. The field always migrates away from the
perfect conductor boundary toward the vacuum boundary, independently
of the sign of α. Conclusions: The obtained solution may serve
as a benchmark for numerical dynamo experiments and as a pedagogical
illustration that oscillatory migratory dynamos are possible with
constant α.

---------------------------------------------------------
Title: High-wavenumber Solar f-mode Strengthening Prior to Active
Region Formation
Authors: Singh, Nishant K.; Raichur, Harsha; Brandenburg, Axel
2016ApJ...832..120S Altcode: 2016arXiv160100629S
We report a systematic strengthening of the local solar surface or
fundamental f-mode one to two days prior to the emergence of an active
region (AR) in the same (corotating) location. Except for a possibly
related increase in the kurtosis of the magnetic field, no indication
can be seen in the magnetograms at that time. Our study is motivated
by earlier numerical findings of Singh et al., which showed that,
in the presence of a nonuniform magnetic field that is concentrated
a few scale heights below the surface, the f-mode fans out in the
diagnostic kω diagram at high wavenumbers. Here we explore this
possibility using data from the Helioseismic and Magnetic Imager on
board the Solar Dynamics Observatory and show for six isolated ARs,
11130, 11158, 11242, 11105, 11072, and 11768, that at large latitudinal
wavenumbers (corresponding to horizontal scales of around 3000 {km}),
the f-mode displays strengthening about two days prior to AR formation
and thus provides a new precursor for AR formation. Furthermore, we
study two ARs, 12051 and 11678, apart from a magnetically quiet patch
lying next to AR 12529, to demonstrate the challenges in extracting
such a precursor signal when a newly forming AR emerges in a patch that
lies in close proximity to one or several already existing ARs, which
are expected to pollute neighboring patches. We then discuss plausible
procedures for extracting precursor signals from regions with crowded
environments. The idea that the f-mode is perturbed days before any
visible magnetic activity occurs at the surface can be important in
constraining dynamo models aimed at understanding the global magnetic
activity of the Sun.

---------------------------------------------------------
Title: Magnetic concentrations in stratified turbulence: the negative
effective magnetic pressure instability
Authors: Brandenburg, Axel; Rogachevskii, Igor; Kleeorin, Nathan
2016NJPh...18l5011B Altcode: 2016arXiv161003459B
In the presence of strong density stratification, hydromagnetic
turbulence attains qualitatively new properties: the formation
of magnetic flux concentrations. We review here the theoretical
foundations of this mechanism in terms of what is now called the
negative effective magnetic pressure instability. We also present
direct numerical simulations of forced turbulence in strongly stratified
layers and discuss the qualitative and quantitative similarities with
corresponding mean-field simulations. Finally, the relevance to sunspot
formation is discussed.

---------------------------------------------------------
Title: Influence of a coronal envelope as a free boundary to global
convective dynamo simulations
Authors: Warnecke, J.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg,
A.
2016A&A...596A.115W Altcode: 2015arXiv150305251W
 Aims: We explore the effects of an outer stably stratified
coronal envelope on rotating turbulent convection, differential
rotation, and large-scale dynamo action in spherical wedge models of
the Sun. Methods: We solve the compressible magnetohydrodynamic
equations in a two-layer model with unstable stratification below the
surface, representing the convection zone, and a stably stratified
coronal envelope above. The interface represents a free surface. We
compare our model to models that have no coronal envelope. 
Results: The presence of a coronal envelope is found to modify
the Reynolds stress and the Λ effect resulting in a weaker and
non-cylindrical differential rotation. This is related to the reduced
latitudinal temperature variations that are caused by and dependent
on the angular velocity. Some simulations develop a near-surface
shear layer that we can relate to a sign change in the meridional
Reynolds stress term in the thermal wind balance equation. Furthermore,
the presence of a free surface changes the magnetic field evolution
since the toroidal field is concentrated closer to the surface. In all
simulations, however, the migration direction of the mean magnetic field
can be explained by the Parker-Yoshimura rule, which is consistent
with earlier findings. Conclusions: A realistic treatment of
the upper boundary in spherical dynamo simulations is crucial for the
dynamics of the flow and magnetic field evolution.

---------------------------------------------------------
Title: Stellar Mixing Length Theory with Entropy Rain
Authors: Brandenburg, Axel
2016ApJ...832....6B Altcode: 2015arXiv150403189B
The effects of a non-gradient flux term originating from the motion
of convective elements with entropy perturbations of either sign are
investigated and incorporated into a modified version of stellar mixing
length theory (MLT). Such a term, first studied by Deardorff in the
meteorological context, might represent the effects of cold intense
downdrafts caused by the rapid cooling in the granulation layer at
the top of the convection zone of late-type stars. These intense
downdrafts were first seen in the strongly stratified simulations of
Stein &amp; Nordlund in the late 1980s. These downdrafts transport
heat nonlocally, a phenomenon referred to as entropy rain. Moreover,
the Deardorff term can cause upward enthalpy transport even in a weakly
Schwarzschild-stably stratified layer. In that case, no giant cell
convection would be excited. This is interesting in view of recent
observations, which could be explained if the dominant flow structures
were of small scale even at larger depths. To study this possibility,
three distinct flow structures are examined: one in which convective
structures have similar size and mutual separation at all depths,
one in which the separation increases with depth, but their size is
still unchanged, and one in which both size and separation increase
with depth, which is the standard flow structure. It is concluded
that the third possibility with fewer and thicker downdrafts in deeper
layers remains the most plausible, but it may be unable to explain the
suspected absence of large-scale flows with speeds and scales expected
from MLT.

---------------------------------------------------------
Title: Robustness of oscillatory α2 dynamos in spherical
wedges
Authors: Cole, E.; Brandenburg, A.; Käpylä, P. J.; Käpylä, M. J.
2016A&A...593A.134C Altcode: 2016arXiv160105246C
Context. Large-scale dynamo simulations are sometimes confined to
spherical wedge geometries by imposing artificial boundary conditions
at high latitudes. This may lead to spatio-temporal behaviours that
are not representative of those in full spherical shells. Aims:
We study the connection between spherical wedge and full spherical
shell geometries using simple mean-field dynamos. Methods: We
solve the equations for one-dimensional time-dependent α2
and α2Ω mean-field dynamos with only latitudinal extent to
examine the effects of varying the polar angle θ0 between
the latitudinal boundaries and the poles in spherical coordinates. Results: In the case of constant α and ηt profiles,
we find oscillatory solutions only with the commonly used perfect
conductor boundary condition in a wedge geometry, while for full spheres
all boundary conditions produce stationary solutions, indicating that
perfect conductor conditions lead to unphysical solutions in such a
wedge setup. To search for configurations in which this problem can be
alleviated we choose a profile of the turbulent magnetic diffusivity
that decreases toward the poles, corresponding to high conductivity
there. Oscillatory solutions are now achieved with models extending to
the poles, but the magnetic field is strongly concentrated near the
poles and the oscillation period is very long. By changing both the
turbulent magnetic diffusivity and α profiles so that both effects are
more concentrated toward the equator, we see oscillatory dynamos with
equatorward drift, shorter cycles, and magnetic fields distributed over
a wider range of latitudes. Those profiles thus remove the sensitive and
unphysical dependence on θ0. When introducing radial shear,
we again see oscillatory dynamos, and the direction of drift follows
the Parker-Yoshimura rule. Conclusions: A reduced α effect near
the poles with a turbulent diffusivity concentrated toward the equator
yields oscillatory dynamos with equatorward migration and reproduces
best the solutions in spherical wedges. For weak shear, oscillatory
solutions are obtained only for perfect conductor field conditions and
negative shear. Oscillatory solutions become preferred at sufficiently
strong shear. Recent three-dimensional dynamo simulations producing
solar-like magnetic activity are expected to lie in this range.

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Title: Two-scale Analysis of Solar Magnetic Helicity
Authors: Brandenburg, Axel; Petrie, Gordon; Singh, Nishant
2016usc..confE.110B Altcode:
The solar magnetic helicity has opposite signs not only in the two
hemispheres, but also at large and small length scales. The latter
can be detected by computing magnetic helicity spectra, but this must
be done separately in each hemisphere. Here we utilize a two-scale
method from mean-field dynamo theory that allows us to compute
magnetic helicity spectra as a function of two different wavenumbers:
one corresponding to rapidly varying scale and one corresponding to a
slowly varying one. We generalize this method to spherical harmonics and
compute in that way global magnetic helicity spectra for that part of
the field that shows a global dipolar symmetry. We present results from
simple one-dimensional model calculations, three-dimensional dynamo
simulations, and the two-dimensional magnetic field from synaptic
vector magnetograms.

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Title: The evolution of primordial magnetic fields since their
generation
Authors: Kahniashvili, Tina; Brandenburg, Axel; Tevzadze, Alexander G.
2016PhyS...91j4008K Altcode: 2015arXiv150700510K
We study the evolution of primordial magnetic fields in an expanding
cosmic plasma. For this purpose we present a comprehensive theoretical
model to consider the evolution of MHD turbulence that can be used
over a wide range of physical conditions, including cosmological and
astrophysical applications. We model different types of decaying
cosmic MHD turbulence in the expanding Universe and characterize
the large-scale magnetic fields in such a medium. Direct numerical
simulations of freely decaying MHD turbulence are performed for
different magnetogenesis scenarios: magnetic fields generated during
cosmic inflation as well as electroweak and QCD phase transitions in
the early Universe. Magnetic fields and fluid motions are strongly
coupled due to the high Reynolds number in the early Universe. Hence,
we abandon the simple adiabatic dilution model to estimate magnetic
field amplitudes in the expanding Universe and include turbulent
mixing effects on the large-scale magnetic field evolution. Numerical
simulations have been carried out for non-helical and helical magnetic
field configurations. The numerical results show the possibility of
inverse transfer of energy in magnetically dominated non-helical MHD
turbulence. On the other hand, decay properties of helical turbulence
depend on whether the turbulent magnetic field is in a weakly or a fully
helical state. Our results show that primordial magnetic fields can
be considered as a seed for the observed large-scale magnetic fields
in galaxies and clusters. Bounds on the magnetic field strength are
obtained and are consistent with the upper and lower limits set by
observations of extragalactic magnetic fields.

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Title: A unified large/small-scale dynamo in helical turbulence
Authors: Bhat, Pallavi; Subramanian, Kandaswamy; Brandenburg, Axel
2016MNRAS.461..240B Altcode: 2015arXiv150802706B
We use high resolution direct numerical simulations (DNS) to show
that helical turbulence can generate significant large-scale fields
even in the presence of strong small-scale dynamo action. During the
kinematic stage, the unified large/small-scale dynamo grows fields
with a shape-invariant eigenfunction, with most power peaked at small
scales or large k, as in Subramanian &amp; Brandenburg. Nevertheless,
the large-scale field can be clearly detected as an excess power
at small k in the negatively polarized component of the energy
spectrum for a forcing with positively polarized waves. Its strength
overline{B}, relative to the total rms field Brms, decreases
with increasing magnetic Reynolds number, ReM. However,
as the Lorentz force becomes important, the field generated by the
unified dynamo orders itself by saturating on successively larger
scales. The magnetic integral scale for the positively polarized waves,
characterizing the small-scale field, increases significantly from the
kinematic stage to saturation. This implies that the small-scale field
becomes as coherent as possible for a given forcing scale, which averts
the ReM-dependent quenching of overline{B}/B_rms. These
results are obtained for 10243 DNS with magnetic Prandtl
numbers of PrM = 0.1 and 10. For PrM = 0.1,
overline{B}/B_rms grows from about 0.04 to about 0.4 at saturation,
aided in the final stages by helicity dissipation. For PrM
= 10, overline{B}/B_rms grows from much less than 0.01 to values
of the order the 0.2. Our results confirm that there is a unified
large/small-scale dynamo in helical turbulence.

---------------------------------------------------------
Title: Turbulent reconnection of magnetic bipoles in stratified
turbulence
Authors: Jabbari, S.; Brandenburg, A.; Mitra, Dhrubaditya; Kleeorin,
N.; Rogachevskii, I.
2016MNRAS.459.4046J Altcode: 2016MNRAS.tmp..680J; 2016arXiv160108167J
We consider strongly stratified forced turbulence in a plane-parallel
layer with helicity and corresponding large-scale dynamo action in
the lower part and non-helical turbulence in the upper. The magnetic
field is found to develop strongly concentrated bipolar structures
near the surface. They form elongated bands with a sharp interface
between opposite polarities. Unlike earlier experiments with imposed
magnetic field, the inclusion of rotation does not strongly suppress the
formation of these structures. We perform a systematic numerical study
of this phenomenon by varying magnetic Reynolds number, scale-separation
ratio, and Coriolis number. We focus on the formation of a current sheet
between bipolar regions where reconnection of oppositely oriented field
lines occurs. We determine the reconnection rate by measuring either the
inflow velocity in the vicinity of the current sheet or by measuring
the electric field in the reconnection region. We demonstrate that
for large Lundquist numbers, S &gt; 103, the reconnection
rate is nearly independent of S in agreement with results of recent
numerical simulations performed by other groups in simpler settings.

---------------------------------------------------------
Title: High-wavenumber solar f-mode strengthening prior to active
region formation
Authors: Singh, Nishant; Raichur, Harsha; Brandenburg, Axel
2016SPD....47.0711S Altcode:
We report a systematic strengthening of the local solar surface mode,
i.e. the f-mode, 1-2 days prior to the emergence of an active region
(AR) in the same (corotating) location while no indication can yet be
seen in the magnetograms. Our study is motivated by earlier numerical
findings of Singh et al. (2014) which showed that, in the presence of
a nonuniform magnetic field that is concentrated a few scale heights
below the surface, the f-mode fans out in the diagnostic kΩ diagram
at high wavenumbers. Here we explore this possibility using data from
the Helioseismic and Magnetic Imager on board the Solar Dynamics
Observatory, and show for four ARs 11130, 11158, 11768, and 12051,
that at large latitudinal wavenumbers (corresponding to horizontal
scales of around 3000 km), the f-mode displays strengthening about
two days prior to AR formation and thus provides a new precursor for
AR formation. The idea that the f-mode is perturbed days before any
visible magnetic activity occurs on the surface can be important in
constraining dynamo models aimed at understanding the global magnetic
activity of the Sun.

---------------------------------------------------------
Title: The magnetic helicity spectrum from solar vector magnetograms
Authors: Brandenburg, Axel; Zhang, Hongqi; Sokoloff, Dmitry
2016SPD....4720103B Altcode:
The gauge-invariant (or relative) magnetic helicity is often
measured to characterize the degree of magnetic complexity of active
regions. However, magnetic helicity is expected to have different
signs on different length scales that can be identified with the
large- and small-scale fields used in dynamo theory. To address this,
it is important to determine magnetic helicity spectra as functions of
wavenumber. These spectra are defined such that the integral over all
wavenumbers gives the usual magnetic helicity density in a particular
patch of interest. Using vector magnetograms from the Helioseismic
and Magnetic Imager on board the Solar Dynamics Observatory for
active region NOAA 11515, which was on the southern hemisphere, we
show that the magnetic helicity spectrum has positive sign on scales
below 30 Mm, but negative sign on larger scales. This active region
was rather complex and its magnetic helicity was within 26% of its
theoretical maximum value. This is much more than that of NOAA 11158,
which was also rather complex, but only within 5% of its theoretical
maximum value. Since the contribution of larger length scales turned
out to be important in the case of NOAA 11515, its total magnetic
helicity is dominated by the negative values from large length scales,
which explains the unusual sign for the southern hemisphere. Measuring
magnetic helicity spectra with DKIST may become an important tool to
learn about the workings of the underlying dynamo.

---------------------------------------------------------
Title: Bipolar region formation in stratified two-layer turbulence
Authors: Warnecke, J.; Losada, I. R.; Brandenburg, A.; Kleeorin, N.;
Rogachevskii, I.
2016A&A...589A.125W Altcode: 2015arXiv150203799W
 Aims: This work presents an extensive study of the previously
discovered formation of bipolar flux concentrations in a two-layer
model. We interpret the formation process in terms of negative
effective magnetic pressure instability (NEMPI), which is a possible
mechanism to explain the origin of sunspots. Methods: In our
simulations, we use a Cartesian domain of isothermal stratified gas that
is divided into two layers. In the lower layer, turbulence is forced
with transverse nonhelical random waves, whereas in the upper layer no
flow is induced. A weak uniform magnetic field is imposed in the entire
domain at all times. In most cases, it is horizontal, but a vertical
and an inclined field are also considered. In this study we vary the
stratification by changing the gravitational acceleration, magnetic
Reynolds number, strength of the imposed magnetic field, and size of
the domain to investigate their influence on the formation process. Results: Bipolar magnetic structure formation takes place over
a large range of parameters. The magnetic structures become more
intense for higher stratification until the density contrast becomes
around 100 across the turbulent layer. For the fluid Reynolds numbers
considered, magnetic flux concentrations are generated at magnetic
Prandtl number between 0.1 and 1. The magnetic field in bipolar regions
increases with higher imposed field strength until the field becomes
comparable to the equipartition field strength of the turbulence. A
larger horizontal extent enables the flux concentrations to become
stronger and more coherent. The size of the bipolar structures turns
out to be independent of the domain size. A small imposed horizontal
field component is necessary to generate bipolar structures. In the
case of bipolar region formation, we find an exponential growth of
the large-scale magnetic field, which is indicative of a hydromagnetic
instability. Additionally, the flux concentrations are correlated with
strong large-scale downward and converging flows. These findings imply
that NEMPI is responsible for magnetic flux concentrations.

---------------------------------------------------------
Title: The structure and evolution of boundary layers in stratified
convection
Authors: Anders, Evan H.; Brown, Benjamin; Brandenburg, Axel;
Rast, Mark
2016SPD....47.0712A Altcode:
Solar convection is highly stratified, and the density in the Sun
increases by many orders of magnitude from the photosphere to the
base of the convection zone. The photosphere is an important boundary
layer, and interactions between the surface convection and deep
convection may lie at the root of the solar convection conundrum,
where observed large-scale velocities are much lower than predicted
by full numerical simulations. Here, we study the structure and time
evolution of boundary layers in numerical stratified convection. We
study fully compressible convection within plane-parallel layers using
the Dedalus pseudospectral framework. Within the context of polytropic
stratification, we study flows from low (1e-3) to moderately high (0.1)
Mach number, and at moderate to high Rayleigh number to study both
laminar and turbulent convective transport. We aim to characterize
the thickness and time variation of velocity and thermal (entropy)
boundary layers at the top and bottom boundaries of the domain.

---------------------------------------------------------
Title: Multiple dynamo modes as a mechanism for long-term solar
activity variations
Authors: Käpylä, M. J.; Käpylä, P. J.; Olspert, N.; Brandenburg,
A.; Warnecke, J.; Karak, B. B.; Pelt, J.
2016A&A...589A..56K Altcode: 2015arXiv150705417K
Context. Solar magnetic activity shows both smooth secular changes,
such as the modern Grand Maximum, and quite abrupt drops that
are denoted as grand minima, such as the Maunder Minimum. Direct
numerical simulations (DNS) of convection-driven dynamos offer one
way of examining the mechanisms behind these events. Aims:
In this work, we analyze a solution of a solar-like DNS that was
evolved for roughly 80 magnetic cycles of 4.9 years and where epochs
of irregular behavior are detected. The emphasis of our analysis is
to find physical causes for such behavior. Methods: The DNS
employed is a semi-global (wedge-shaped) magnetoconvection model. For
the data analysis tasks we use Ensemble Empirical Mode Decomposition
and phase dispersion methods, as they are well suited for analyzing
cyclic (non-periodic) signals. Results: A special property
of the DNS is the existence of multiple dynamo modes at different
depths and latitudes. The dominant mode is solar-like (equatorward
migration at low latitudes and poleward at high latitudes). This mode
is accompanied by a higher frequency mode near the surface and at low
latitudes, showing poleward migration, and a low-frequency mode at the
bottom of the convection zone. The low-frequency mode is almost purely
antisymmetric with respect to the equator, while the dominant mode has
strongly fluctuating mixed parity. The overall behavior of the dynamo
solution is extremely complex, exhibiting variable cycle lengths, epochs
of disturbed and even ceased surface activity, and strong short-term
hemispherical asymmetries. Surprisingly, the most prominent suppressed
surface activity epoch is actually a global magnetic energy maximum;
during this epoch the bottom toroidal magnetic field obtains a maximum,
demonstrating that the interpretation of grand minima-type events
is non-trivial. The hemispherical asymmetries are seen only in the
magnetic field, while the velocity field exhibits considerably weaker
asymmetry. Conclusions: We interpret the overall irregular
behavior as being due to the interplay of the different dynamo modes
showing different equatorial symmetries, especially the smoother part
of the irregular variations being related to the variations of the
mode strengths, evolving with different and variable cycle lengths. The
abrupt low-activity epoch in the dominant dynamo mode near the surface
is related to a strong maximum of the bottom toroidal field strength,
which causes abrupt disturbances especially in the differential rotation
profile via the suppression of the Reynolds stresses.

---------------------------------------------------------
Title: Magnetic flux concentrations from turbulent stratified
convection
Authors: Käpylä, P. J.; Brandenburg, A.; Kleeorin, N.; Käpylä,
M. J.; Rogachevskii, I.
2016A&A...588A.150K Altcode: 2015arXiv151103718K
Context. The formation of magnetic flux concentrations within the solar
convection zone leading to sunspot formation is unexplained. Aims: We study the self-organization of initially uniform
sub-equipartition magnetic fields by highly stratified turbulent
convection. Methods: We perform simulations of magnetoconvection
in Cartesian domains representing the uppermost 8.5-24 Mm of the solar
convection zone with the horizontal size of the domain varying between
34 and 96 Mm. The density contrast in the 24 Mm deep models is more than
3 × 103 or eight density scale heights, corresponding to a
little over 12 pressure scale heights. We impose either a vertical or
a horizontal uniform magnetic field in a convection-driven turbulent
flow in set-ups where no small-scale dynamos are present. In the most
highly stratified cases we employ the reduced sound speed method to
relax the time step constraint arising from the high sound speed in
the deep layers. We model radiation via the diffusion approximation
and neglect detailed radiative transfer in order to concentrate on
purely magnetohydrodynamic effects. Results: We find that
super-equipartition magnetic flux concentrations are formed near
the surface in cases with moderate and high density stratification,
corresponding to domain depths of 12.5 and 24 Mm. The size of the
concentrations increases as the box size increases and the largest
structures (20 Mm horizontally near the surface) are obtained in the
models that are 24 Mm deep. The field strength in the concentrations
is in the range of 3-5 kG, almost independent of the magnitude of the
imposed field. The amplitude of the concentrations grows approximately
linearly in time. The effective magnetic pressure measured in the
simulations is positive near the surface and negative in the bulk of the
convection zone. Its derivative with respect to the mean magnetic field,
however, is positive in most of the domain, which is unfavourable for
the operation of the negative effective magnetic pressure instability
(NEMPI). Simulations in which a passive vector field is evolved do not
show a noticeable difference from magnetohydrodynamic runs in terms
of the growth of the structures. Furthermore, we find that magnetic
flux is concentrated in regions of converging flow corresponding to
large-scale supergranulation convection pattern. Conclusions:
The linear growth of large-scale flux concentrations implies that
their dominant formation process is a tangling of the large-scale
field rather than an instability. One plausible mechanism that
can explain both the linear growth and the concentration of the
flux in the regions of converging flow pattern is flux expulsion. A
possible reason for the absence of NEMPI is that the derivative of the
effective magnetic pressure with respect to the mean magnetic field
has an unfavourable sign. Furthermore, there may not be sufficient
scale separation, which is required for NEMPI to work. Movies
associated to Figs. 4 and 5 are available in electronic form at <A
href="http://www.aanda.org/10.1051/0004-6361/201527731/olm">http://www.aanda.org</A>

---------------------------------------------------------
Title: Commission 12: Solar Radiation and Structure
Authors: Cauzzi, Gianna; Shchukina, Nataliya; Kosovichev, Alexander;
Bianda, Michele; Brandenburg, Axel; Chou, Dean-Yi; Dasso, Sergio; Ding,
Ming-De; Jefferies, Stuart; Krivova, Natalie; Kuznetsov, Vladimir D.;
Moreno-Insertis, Fernando
2016IAUTA..29..278C Altcode:
Commission 12 of the International Astronomical Union encompasses
investigations of the internal structure and dynamics of the Sun,
the quiet solar atmosphere, solar radiation and its variability, and
the nature of relatively stable magnetic structures like sunspots,
faculae and the magnetic network. The Commission sees participation
of over 300 scientists worldwide.

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Title: Evolution of Magnetic Helicity and Energy Spectra of Solar
Active Regions
Authors: Zhang, Hongqi; Brandenburg, Axel; Sokoloff, D. D.
2016ApJ...819..146Z Altcode: 2015arXiv150300846Z
We adopt an isotropic representation of the Fourier-transformed
two-point correlation tensor of the magnetic field to estimate the
magnetic energy and helicity spectra as well as current helicity
spectra of two individual active regions (NOAA 11158 and NOAA 11515)
and the change of the spectral indices during their development as
well as during the solar cycle. The departure of the spectral indices
of magnetic energy and current helicity from 5/3 are analyzed, and
it is found that it is lower than the spectral index of the magnetic
energy spectrum. Furthermore, the fractional magnetic helicity tends
to increase when the scale of the energy-carrying magnetic structures
increases. The magnetic helicity of NOAA 11515 violates the expected
hemispheric sign rule, which is interpreted as an effect of enhanced
field strengths at scales larger than 30-60 Mm with opposite signs
of helicity. This is consistent with the general cycle dependence,
which shows that around the solar maximum the magnetic energy and
helicity spectra are steeper, emphasizing the large-scale field.

---------------------------------------------------------
Title: Large-scale flow generation by inhomogeneous helicity
Authors: Yokoi, N.; Brandenburg, A.
2016PhRvE..93c3125Y Altcode: 2015arXiv151108983Y
The effect of kinetic helicity (velocity-vorticity correlation) on
turbulent momentum transport is investigated. The turbulent kinetic
helicity (pseudoscalar) enters the Reynolds stress (mirror-symmetric
tensor) expression in the form of a helicity gradient as the coupling
coefficient for the mean vorticity and/or the angular velocity (axial
vector), which suggests the possibility of mean-flow generation in
the presence of inhomogeneous helicity. This inhomogeneous helicity
effect, which was previously confirmed at the level of a turbulence-
or closure-model simulation, is examined with the aid of direct
numerical simulations of rotating turbulence with nonuniform helicity
sustained by an external forcing. The numerical simulations show
that the spatial distribution of the Reynolds stress is in agreement
with the helicity-related term coupled with the angular velocity,
and that a large-scale flow is generated in the direction of angular
velocity. Such a large-scale flow is not induced in the case of
homogeneous turbulent helicity. This result confirms the validity
of the inhomogeneous helicity effect in large-scale flow generation
and suggests that a vortex dynamo is possible even in incompressible
turbulence where there is no baroclinicity effect.

---------------------------------------------------------
Title: Hydraulic effects in a radiative atmosphere with ionization
Authors: Bhat, P.; Brandenburg, A.
2016A&A...587A..90B Altcode: 2014arXiv1411.6610B
Context. In his 1978 paper, Eugene Parker postulated the need for
hydraulic downward motion to explain magnetic flux concentrations at
the solar surface. A similar process has also recently been seen in
simplified (e.g., isothermal) models of flux concentrations from the
negative effective magnetic pressure instability (NEMPI). Aims:
We study the effects of partial ionization near the radiative surface
on the formation of these magnetic flux concentrations. Methods:
We first obtain one-dimensional (1D) equilibrium solutions using either
a Kramers-like opacity or the H- opacity. The resulting
atmospheres are then used as initial conditions in two-dimensional
(2D) models where flows are driven by an imposed gradient force
that resembles a localized negative pressure in the form of a
blob. To isolate the effects of partial ionization and radiation, we
ignore turbulence and convection. Results: Because of partial
ionization, an unstable stratification always forms near the surface. We
show that the extrema in the specific entropy profiles correspond to
the extrema in the degree of ionization. In the 2D models without
partial ionization, strong flux concentrations form just above the
height where the blob is placed. Interestingly, in models with partial
ionization, such flux concentrations always form at the surface well
above the blob. This is due to the corresponding negative gradient in
specific entropy. Owing to the absence of turbulence, the downflows
reach transonic speeds. Conclusions: We demonstrate that,
together with density stratification, the imposed source of negative
pressure drives the formation of flux concentrations. We find that
the inclusion of partial ionization affects the entropy profile
dramatically, causing strong flux concentrations to form closer to the
surface. We speculate that turbulence effects are needed to limit the
strength of flux concentrations and homogenize the specific entropy
to a stratification that is close to marginal.

---------------------------------------------------------
Title: A New Twist in Simulating Solar Flares
Authors: Brandenburg, Axel
2016PhyOJ...9...26B Altcode: 2016arXiv160301917B
Simulations show for the first time how the magnetic fields that
produce solar flares can extend out of the Sun by acquiring a twist.

---------------------------------------------------------
Title: Is the Small-scale Magnetic Field Correlated with the Dynamo
Cycle?
Authors: Karak, Bidya Binay; Brandenburg, Axel
2016ApJ...816...28K Altcode: 2015arXiv150506632K
The small-scale magnetic field is ubiquitous at the solar surface—even
at high latitudes. From observations we know that this field is
uncorrelated (or perhaps even weakly anticorrelated) with the global
sunspot cycle. Our aim is to explore the origin, and particularly
the cycle dependence, of such a phenomenon using three-dimensional
dynamo simulations. We adopt a simple model of a turbulent dynamo in
a shearing box driven by helically forced turbulence. Depending on the
dynamo parameters, large-scale (global) and small-scale (local) dynamos
can be excited independently in this model. Based on simulations in
different parameter regimes, we find that, when only the large-scale
dynamo is operating in the system, the small-scale magnetic field
generated through shredding and tangling of the large-scale magnetic
field is positively correlated with the global magnetic cycle. However,
when both dynamos are operating, the small-scale field is produced
from both the small-scale dynamo and the tangling of the large-scale
field. In this situation, when the large-scale field is weaker than the
equipartition value of the turbulence, the small-scale field is almost
uncorrelated with the large-scale magnetic cycle. On the other hand,
when the large-scale field is stronger than the equipartition value,
we observe an anticorrelation between the small-scale field and the
large-scale magnetic cycle. This anticorrelation can be interpreted
as a suppression of the small-scale dynamo. Based on our studies
we conclude that the observed small-scale magnetic field in the Sun
is generated by the combined mechanisms of a small-scale dynamo and
tangling of the large-scale field.

---------------------------------------------------------
Title: Large-Eddy Simulations of Magnetohydrodynamic Turbulence in
Heliophysics and Astrophysics
Authors: Miesch, Mark; Matthaeus, William; Brandenburg, Axel;
Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank;
Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli,
Marco
2015SSRv..194...97M Altcode: 2015arXiv150501808M; 2015SSRv..tmp...83M
We live in an age in which high-performance computing is transforming
the way we do science. Previously intractable problems are now becoming
accessible by means of increasingly realistic numerical simulations. One
of the most enduring and most challenging of these problems is
turbulence. Yet, despite these advances, the extreme parameter regimes
encountered in space physics and astrophysics (as in atmospheric and
oceanic physics) still preclude direct numerical simulation. Numerical
models must take a Large Eddy Simulation (LES) approach, explicitly
computing only a fraction of the active dynamical scales. The success
of such an approach hinges on how well the model can represent the
subgrid-scales (SGS) that are not explicitly resolved. In addition
to the parameter regime, heliophysical and astrophysical applications
must also face an equally daunting challenge: magnetism. The presence
of magnetic fields in a turbulent, electrically conducting fluid flow
can dramatically alter the coupling between large and small scales,
with potentially profound implications for LES/SGS modeling. In this
review article, we summarize the state of the art in LES modeling of
turbulent magnetohydrodynamic (MHD) flows. After discussing the nature
of MHD turbulence and the small-scale processes that give rise to energy
dissipation, plasma heating, and magnetic reconnection, we consider how
these processes may best be captured within an LES/SGS framework. We
then consider several specific applications in heliophysics and
astrophysics, assessing triumphs, challenges, and future directions.

---------------------------------------------------------
Title: Magnetohydrodynamics of the Sun
Authors: Brandenburg, Axel
2015GApFD.109..615B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Negative Magnetic Eddy Diffusivities from the Test-field
Method and Multiscale Stability Theory
Authors: Andrievsky, Alexander; Brandenburg, Axel; Noullez, Alain;
Zheligovsky, Vladislav
2015ApJ...811..135A Altcode: 2015arXiv150104465A
The generation of a large-scale magnetic field in the kinematic
regime in the absence of an α-effect is investigated by following two
different approaches: the test-field method and the multiscale stability
theory relying on the homogenization technique. Our computations of
the magnetic eddy diffusivity tensor of the parity-invariant flow
IV of G. O. Roberts and the modified Taylor-Green flow confirm the
findings of previous studies and also explain some of their apparent
contradictions. The two flows have large symmetry groups; this is
used to considerably simplify the eddy diffusivity tensor. Finally,
a new analytic result is presented: upon expressing the eddy
diffusivity tensor in terms of solutions to auxiliary problems for
the adjoint operator, we derive relations between the magnetic eddy
diffusivity tensors that arise for mutually reverse small-scale flows
{\boldsymbol{v}}(x) and -{\boldsymbol{v}}(x).

---------------------------------------------------------
Title: Division II: Commission 12: Solar Radiation and Structure
Authors: Kosovichev, Alexander; Cauzzi, Gianna; Martinez Pillet,
Valentin; Asplund, Martin; Brandenburg, Axel; Chou, Dean-Yi;
Christensen-Dalsgaard, Jorgen; Gan, Weiqun; Kuznetsov, Vladimir D.;
Rovira, Marta G.; Shchukina, Nataliya; Venkatakrishnan, P.
2015IAUTB..28..109K Altcode:
The President of C12, Alexander Kosovichev, presented the status of
the Commission and its working Group(s). Primary activities included
organization of international meetings (IAU Symposia, Special Sessions
and Joint Discussion); review and support of proposals for IAU sponsored
meetings; organization of working groups on the Commission topics
to promote the international cooperation; preparation of triennial
report on the organizational and science activities of Commission
members. Commission 12 broadly encompasses topics of solar research
which include studies of the Sun's internal structure, composition,
dynamics and magnetism (through helioseismology and other techniques),
studies of the quiet photosphere, chromosphere and corona, and also
research of the mechanisms of solar radiation, and its variability on
various time scales. Some overlap with topics covered by Commission
10 Solar Activity is unavoidable, and many activities are sponsored
jointly by these two commissions. The Commission website can be found
at http://sun.stanford.edu/IAU-Com12/, with information about related
IAU Symposiums and activities, and links to appropriate web sites.

---------------------------------------------------------
Title: Posters: Dust from impacts on exoplanets
Authors: Cataldi, G.; Brandeker, A.; Thebault, P.; Singer, K.; Ahmed,
E.; Brandenburg, A.; Olofsson, G.; de Vries, B.
2015pthp.confE..49C Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Bipolar Magnetic Spots from Dynamos in Stratified Spherical
Shell Turbulence
Authors: Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Mitra,
Dhrubaditya; Rogachevskii, Igor
2015ApJ...805..166J Altcode: 2014arXiv1411.4912J
Recent work by Mitra et al. (2014) has shown that in strongly stratified
forced two-layer turbulence with helicity and corresponding large-scale
dynamo action in the lower layer, and nonhelical turbulence in the
upper, a magnetic field occurs in the upper layer in the form of
sharply bounded bipolar magnetic spots. Here we extend this model to
spherical wedge geometry covering the northern hemisphere up to 75°
latitude and an azimuthal extent of 180°. The kinetic helicity and
therefore also the large-scale magnetic field are strongest at low
latitudes. For moderately strong stratification, several bipolar
spots form that eventually fill the full longitudinal extent. At
early times, the polarity of spots reflects the orientation of the
underlying azimuthal field, as expected from Parker’s Ω-shaped flux
loops. At late times their tilt changes such that there is a radial
field of opposite orientation at different latitudes separated by about
10°. Our model demonstrates the spontaneous formation of spots of sizes
much larger than the pressure scale height. Their tendency to produce
filling factors close to unity is argued to be reminiscent of highly
active stars. We confirm that strong stratification and strong scale
separation are essential ingredients behind magnetic spot formation,
which appears to be associated with downflows at larger depths.

---------------------------------------------------------
Title: Hysteresis between Distinct Modes of Turbulent Dynamos
Authors: Karak, Bidya Binay; Kitchatinov, Leonid L.; Brandenburg, Axel
2015ApJ...803...95K Altcode: 2014arXiv1411.0485K
Nonlinear mean-field models of the solar dynamo show long-term
variability, which may be relevant to different states of activity
inferred from long-term radiocarbon data. This paper is aimed at
probing the dynamo hysteresis predicted by the recent mean-field models
of Kitchatinov &amp; Olemskoy with direct numerical simulations. We
perform three-dimensional (3D) simulations of large-scale dynamos in a
shearing box with helically forced turbulence. As an initial condition,
we either take a weak random magnetic field or we start from a snapshot
of an earlier simulation. Two quasi-stable states are found to coexist
in a certain range of parameters close to the onset of the large-scale
dynamo. The simulations converge to one of these states depending on
the initial conditions. When either the fractional helicity or the
magnetic Prandtl number is increased between successive runs above the
critical value for onset of the dynamo, the field strength jumps to
a finite value. However, when the fractional helicity or the magnetic
Prandtl number is then decreased again, the field strength stays at a
similar value (strong field branch) even below the original onset. We
also observe intermittent decaying phases away from the strong field
branch close to the point where large-scale dynamo action is just
possible. The dynamo hysteresis seen previously in mean-field models
is thus reproduced by 3D simulations. Its possible relation to distinct
modes of solar activity such as grand minima is discussed.

---------------------------------------------------------
Title: Magnetically controlled stellar differential rotation near
the transition from solar to anti-solar profiles
Authors: Karak, B. B.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg,
A.; Olspert, N.; Pelt, J.
2015A&A...576A..26K Altcode: 2014arXiv1407.0984K
Context. Late-type stars rotate differentially owing to anisotropic
turbulence in their outer convection zones. The rotation is called
solar-like (SL) when the equator rotates fastest and anti-solar (AS)
otherwise. Hydrodynamic simulations show a transition from SL to AS
rotation as the influence of rotation on convection is reduced, but
the opposite transition occurs at a different point in the parameter
space. The system is bistable, i.e., SL and AS rotation profiles can
both be stable. Aims: We study the effect of a dynamo-generated
magnetic field on the large-scale flows, particularly on the possibility
of bistable behaviour of differential rotation. Methods: We
solve the hydromagnetic equations numerically in a rotating spherical
shell that typically covers ± 75° latitude (wedge geometry) for a
set of different radiative conductivities controlling the relative
importance of convection. We analyse the resulting differential
rotation, meridional circulation, and magnetic field and compare the
corresponding modifications of the Reynolds and Maxwell stresses. Results: In agreement with earlier findings, our models display SL
rotation profiles when the rotational influence on convection is strong
and a transition to AS when the rotational influence decreases. We find
that dynamo-generated magnetic fields help to produce SL differential
rotation compared to the hydrodynamic simulations. We do not observe
any bistable states of differential rotation. In the AS cases we find
coherent single-cell meridional circulation, whereas in SL cases
we find multi-cellular patterns. In both cases, we obtain poleward
circulation near the surface with a magnitude close to that observed
in the Sun. In the slowly rotating cases, we find activity cycles,
but no clear polarity reversals, whereas in the more rapidly rotating
cases irregular variations are obtained. Moreover, both differential
rotation and meridional circulation have significant temporal variations
that are similar in strength to those of the Sun. Conclusions:
Purely hydrodynamic simulations of differential rotation and meridional
circulation are shown to be of limited relevance as magnetic fields,
self-consistently generated by dynamo action, significantly affect
the flows.

---------------------------------------------------------
Title: Properties of p and f modes in hydromagnetic turbulence
Authors: Singh, Nishant K.; Brandenburg, Axel; Chitre, S. M.;
Rheinhardt, Matthias
2015MNRAS.447.3708S Altcode: 2014arXiv1404.3246S
With the ultimate aim of using the fundamental or f mode to
study helioseismic aspects of turbulence-generated magnetic flux
concentrations, we use randomly forced hydromagnetic simulations
of a piecewise isothermal layer in two dimensions with reflecting
boundaries at top and bottom. We compute numerically diagnostic
wavenumber-frequency diagrams of the vertical velocity at the interface
between the denser gas below and the less dense gas above. For an
Alfvén-to-sound speed ratio of about 0.1, a 5 per cent frequency
increase of the f mode can be measured when kxHp =
3-4, where kx is the horizontal wavenumber and Hp
is the pressure scaleheight at the surface. Since the solar radius
is about 2000 times larger than Hp, the corresponding
spherical harmonic degree would be 6000-8000. For weaker fields, a
kx-dependent frequency decrease by the turbulent motions
becomes dominant. For vertical magnetic fields, the frequency is
enhanced for kxHp ≈ 4, but decreased relative
to its nonmagnetic value for kxHp ≈ 9.

---------------------------------------------------------
Title: Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic
Field
Authors: Brandenburg, Axel; Kahniashvili, Tina; Tevzadze, Alexander G.
2015PhRvL.114g5001B Altcode: 2014arXiv1404.2238B
In the presence of magnetic helicity, inverse transfer from small to
large scales is well known in magnetohydrodynamic (MHD) turbulence and
has applications in astrophysics, cosmology, and fusion plasmas. Using
high resolution direct numerical simulations of magnetically dominated
self-similarly decaying MHD turbulence, we report a similar inverse
transfer even in the absence of magnetic helicity. We compute for the
first time spectral energy transfer rates to show that this inverse
transfer is about half as strong as with helicity, but in both cases
the magnetic gain at large scales results from velocity at similar
scales interacting with smaller-scale magnetic fields. This suggests
that both inverse transfers are a consequence of universal mechanisms
for magnetically dominated turbulence. Possible explanations include
inverse cascading of the mean squared vector potential associated
with local near two dimensionality and the shallower k2
subinertial range spectrum of kinetic energy forcing the magnetic
field with a k4 subinertial range to attain larger-scale
coherence. The inertial range shows a clear k-2 spectrum
and is the first example of fully isotropic magnetically dominated
MHD turbulence exhibiting weak turbulence scaling.

---------------------------------------------------------
Title: Simulations of Galactic Dynamos
Authors: Brandenburg, Axel
2015ASSL..407..529B Altcode: 2014arXiv1402.0212B
We review our current understanding of galactic dynamo theory, paying
particular attention to numerical simulations both of the mean-field
equations and the original three-dimensional equations relevant to
describing the magnetic field evolution for a turbulent flow. We
emphasize the theoretical difficulties in explaining non-axisymmetric
magnetic fields in galaxies and discuss the observational basis for
such results in terms of rotation measure analysis. Next, we discuss
nonlinear theory, the role of magnetic helicity conservation and
magnetic helicity fluxes. This leads to the possibility that galactic
magnetic fields may be bi-helical, with opposite signs of helicity
and large and small length scales. We discuss their observational
signatures and close by discussing the possibilities of explaining
the origin of primordial magnetic fields.

---------------------------------------------------------
Title: Dynamical quenching with non-local α and downward pumping
Authors: Brandenburg, A.; Hubbard, A. Käpylä, P. J.
2015AN....336...91B Altcode: 2014arXiv1412.0997B
In light of new results, the one-dimensional mean-field dynamo model
of Brandenburg &amp; Käpylä (2007) with dynamical quenching and a
nonlocal Babcock-Leighton \alpha effect is re-examined for the solar
dynamo. We extend the one-dimensional model to include the effects of
turbulent downward pumping (Kitchatinov &amp; Olemskoy 2011), and to
combine dynamical quenching with shear. We use both the conventional
dynamical quenching model of Kleeorin &amp; Ruzmaikin (1982) and the
alternate one of Hubbard &amp; Brandenburg (2011), and confirm that
with varying levels of non-locality in the \alpha effect, and possibly
shear as well, the saturation field strength can be independent of
the magnetic Reynolds number.

---------------------------------------------------------
Title: Traces of large-scale dynamo action in the kinematic stage
Authors: Subramanian, Kandaswamy; Brandenburg, Axel
2014MNRAS.445.2930S Altcode: 2014arXiv1408.4416S
Using direct numerical simulations (DNS), we verify that in the
kinematic regime, a turbulent helical dynamo grows in such a way that
the magnetic energy spectrum remains to high-precision shape-invariant,
i.e. at each wavenumber k the spectrum grows with the same growth
rate. Signatures of large-scale dynamo action can be identified through
the excess of magnetic energy at small k, of one of the two oppositely
polarized constituents. Also a suitably defined planar average of
the magnetic field can be chosen such that its rms value isolates the
strength of the mean field. However, these different means of analysis
suggest that the strength of the large-scale field diminishes with
increasing magnetic Reynolds number ReM like Re_M^{-1/2}
for intermediate values and like Re_M^{-3/4} for larger ones. Both an
analysis from the Kazantsev model including helicity and the DNS show
that this arises due to the magnetic energy spectrum still peaking
at resistive scales, even when helicity is present. As expected, the
amplitude of the large-scale field increases with increasing fractional
helicity, enabling us to determine the onset of large-scale dynamo
action and distinguishing it from that of the small-scale dynamo. Our
DNS show that, contrary to earlier results for smaller scale separation
(only 1.5 instead of now 4), the small-scale dynamo can still be
excited at magnetic Prandtl numbers of 0.1 and only moderate values
of the magnetic Reynolds numbers (∼160).

---------------------------------------------------------
Title: Magnetic Flux Concentrations in Stratified Turbulent Plasma
Due to Negative Effective Magnetic Pressure Instability
Authors: Jabbari, S.; Brandenburg, A.
2014AGUFMSH41B4131J Altcode:
Recent studies have suggested a new mechanism that can be used to
explain the formation of magnetic spots or bipolar regions in highly
stratified turbulent plasmas. According to this model, a large-scale
magnetic field suppresses the turbulent pressure, which leads to
a negative contribution of turbulence to the effective magnetic
pressure. Direct numerical simulations (DNS) have confirmed that the
negative contribution is large enough so that the effective magnetic
pressure becomes negative and leads to a large-scale instability,
which we refer to as negative effective magnetic pressure Instability
(NEMPI). NEMPI was used to explain the formation of active regions and
sunspots on the solar surface. One step toward improving this model
was to combine dynamo in- stability with NEMPI. The dynamo is known
to be responsible for the solar large-scale magnetic field and to
play a role in solar activity. In this context, we studied stratified
turbulent plasmas in spherical geometry, where the background field
was generated by alpha squared dynamo. For NEMPI to be excited, the
initial magnetic field should be in a proper range, so we used quenching
function for alpha. Using the Pencil Code and mean field simulations
(MFS), we showed that in the presence of dynamo-generated magnetic
fields, we deal with a coupled system, where both instabilities,
dynamo and NEMPI, work together and lead to the formation of magnetic
structures (Jabbari et al. 2013). We also studied a similar system in
plane geometry in the presence of rotation and confirmed that for slow
rotation NEMPI works, but as the Coriolis number increases, the rotation
suppresses NEMPI. By increasing the Coriolis number even further, the
combination of fast rotation and high stratification excites a dynamo,
which leads again to a coupled system of dynamo and NEMPI (Jabbari et
al. 2014). Another important finding concerning NEMPI is the case where
the instability is excited by a vertical magnetic field (Brandenburg
et al. 2013). When the field is vertical, the resulting magnetic flux
concentrations lead to the magnetic spots and can be of equipartition
field strength. DNS, MFS, and implicit large eddy simulations (ILES)
confirm that in a proper parameter regime, vertical imposed fields lead
to the formation of circular magnetic spots (Brandenburg et al. 2014).

---------------------------------------------------------
Title: Near-polytropic stellar simulations with a radiative surface
Authors: Barekat, A.; Brandenburg, A.
2014A&A...571A..68B Altcode: 2013arXiv1308.1660B
Context. Studies of solar and stellar convection often employ
simple polytropic setups using the diffusion approximation instead
of solving the proper radiative transfer equation. This allows
one to control separately the polytropic index of the hydrostatic
reference solution, the temperature contrast between top and bottom,
and the Rayleigh and Péclet numbers. Aims: Here we extend
such studies by including radiative transfer in the gray approximation
using a Kramers-like opacity with freely adjustable coefficients. We
study the properties of such models and compare them with results
from the diffusion approximation. Methods: We use the Pencil
code, which is a high-order finite difference code where radiation
is treated using the method of long characteristics. The source
function is given by the Planck function. The opacity is written as
κ = κ0ρaTb, where a = 1 in most
cases, b is varied from -3.5 to + 5, and κ0 is varied
by four orders of magnitude. We adopt a perfect monatomic gas. We
consider sets of one-dimensional models and perform a comparison
with the diffusion approximation in one- and two-dimensional
models. Results: Except for the case where b = 5, we find
one-dimensional hydrostatic equilibria with a nearly polytropic
stratification and a polytropic index close to n = (3 - b)/(1 + a),
covering both convectively stable (n&gt; 3/2) and unstable (n&lt;
3/2) cases. For b = 3 and a = -1, the value of n is undefined a
priori and the actual value of n depends then on the depth of the
domain. For large values of κ0, the thermal adjustment time
becomes long, the Péclet and Rayleigh numbers become large, and the
temperature contrast increases and is thus no longer an independent
input parameter, unless the Stefan-Boltzmann constant is considered
adjustable. Conclusions: Proper radiative transfer with
Kramers-like opacities provides a useful tool for studying stratified
layers with a radiative surface in ways that are more physical
than what is possible with polytropic models using the diffusion
approximation. Appendices are available in electronic form at <A
href="http://www.aanda.org/10.1051/0004-6361/201322461/olm">http://www.aanda.org</A>

---------------------------------------------------------
Title: Intense bipolar structures from stratified helical dynamos
Authors: Mitra, Dhrubaditya; Brandenburg, A.; Kleeorin, N.;
Rogachevskii, I.
2014MNRAS.445..761M Altcode: 2014arXiv1404.3194M
We perform direct numerical simulations of the equations of
magnetohydrodynamics with external random forcing and in the presence
of gravity. The domain is divided into two parts: a lower layer where
the forcing is helical and an upper layer where the helicity of the
forcing is zero with a smooth transition in between. At early times,
a large-scale helical dynamo develops in the bottom layer. At later
times the dynamo saturates, but the vertical magnetic field continues
to develop and rises to form dynamic bipolar structures at the top,
which later disappear and reappear. Some of the structures look
similar to δ spots observed in the Sun. This is the first example of
magnetic flux concentrations, owing to strong density stratification,
from self-consistent dynamo simulations that generate bipolar,
super-equipartition strength, magnetic structures whose energy density
can exceeds the turbulent kinetic energy by even a factor of 10.

---------------------------------------------------------
Title: On The Cause of Solar-like Equatorward Migration in Global
Convective Dynamo Simulations
Authors: Warnecke, Jörn; Käpylä, Petri J.; Käpylä, Maarit J.;
Brandenburg, Axel
2014ApJ...796L..12W Altcode: 2014arXiv1409.3213W
We present results from four convectively driven stellar dynamo
simulations in spherical wedge geometry. All of these simulations
produce cyclic and migrating mean magnetic fields. Through detailed
comparisons, we show that the migration direction can be explained by
an αΩ dynamo wave following the Parker-Yoshimura rule. We conclude
that the equatorward migration in this and previous work is due to a
positive (negative) α effect in the northern (southern) hemisphere and
a negative radial gradient of Ω outside the inner tangent cylinder of
these models. This idea is supported by a strong correlation between
negative radial shear and toroidal field strength in the region of
equatorward propagation.

---------------------------------------------------------
Title: Fanning Out of the Solar f-mode in the Presence of Non-uniform
Magnetic Fields?
Authors: Singh, Nishant K.; Brandenburg, Axel; Rheinhardt, Matthias
2014ApJ...795L...8S Altcode: 2014arXiv1407.0356S
We show that in the presence of a magnetic field that is varying
harmonically in space, the fundamental mode, or f-mode, in a stratified
layer is altered in such a way that it fans out in the diagnostic kω
diagram, with mode power also within the fan. In our simulations, the
surface is defined by a temperature and density jump in a piecewise
isothermal layer. Unlike our previous work (Singh et al. 2014),
where a uniform magnetic field was considered, here we employ a
non-uniform magnetic field together with hydromagnetic turbulence
at length scales much smaller than those of the magnetic field. The
expansion of the f-mode is stronger for fields confined to the layer
below the surface. In some of those cases, the kω diagram also reveals
a new class of low-frequency vertical stripes at multiples of twice
the horizontal wavenumber of the background magnetic field. We argue
that the study of the f-mode expansion might be a new and sensitive
tool to determine subsurface magnetic fields with azimuthal or other
horizontal periodicity.

---------------------------------------------------------
Title: Quenching and Anisotropy of Hydromagnetic Turbulent Transport
Authors: Karak, Bidya Binay; Rheinhardt, Matthias; Brandenburg, Axel;
Käpylä, Petri J.; Käpylä, Maarit J.
2014ApJ...795...16K Altcode: 2014arXiv1406.4521K
Hydromagnetic turbulence affects the evolution of large-scale magnetic
fields through mean-field effects like turbulent diffusion and the α
effect. For stronger fields, these effects are usually suppressed
or quenched, and additional anisotropies are introduced. Using
different variants of the test-field method, we determine the
quenching of the turbulent transport coefficients for the forced
Roberts flow, isotropically forced non-helical turbulence, and
rotating thermal convection. We see significant quenching only when
the mean magnetic field is larger than the equipartition value of the
turbulence. Expressing the magnetic field in terms of the equipartition
value of the quenched flows, we obtain for the quenching exponents of
the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts
flow, forced turbulence, and convection, respectively. However, when
the magnetic field is expressed in terms of the equipartition value
of the unquenched flows, these quenching exponents become about 4,
1.5, and 2.3, respectively. For the α effect, the exponent is about
1.3 for the Roberts flow and 2 for convection in the first case, but
4 and 3, respectively, in the second. In convection, the quenching of
turbulent pumping follows the same power law as turbulent diffusion,
while for the coefficient describing the {\boldsymbolΩ} × \boldsymbol
{{J}} effect nearly the same quenching exponent is obtained as for
α. For forced turbulence, turbulent diffusion proportional to the
second derivative along the mean magnetic field is quenched much less,
especially for larger values of the magnetic Reynolds number. However,
we find that in corresponding axisymmetric mean-field dynamos with
dominant toroidal field the quenched diffusion coefficients are the
same for the poloidal and toroidal field constituents.

---------------------------------------------------------
Title: Confirmation of bistable stellar differential rotation profiles
Authors: Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.
2014A&A...570A..43K Altcode: 2014arXiv1401.2981K
Context. Solar-like differential rotation is characterized by a rapidly
rotating equator and slower poles. However, theoretical models and
numerical simulations can also result in a slower equator and faster
poles when the overall rotation is slow. Aims: We study the
critical rotational influence under which differential rotation flips
from solar-like (fast equator, slow poles) to an anti-solar one (slow
equator, fast poles). We also estimate the non-diffusive (Λ effect)
and diffusive (turbulent viscosity) contributions to the Reynolds
stress. Methods: We present the results of three-dimensional
numerical simulations of mildly turbulent convection in spherical wedge
geometry. Here we apply a fully compressible setup which would suffer
from a prohibitive time step constraint if the real solar luminosity was
used. To avoid this problem while still representing the same rotational
influence on the flow as in the Sun, we increase the luminosity by a
factor of roughly 106 and the rotation rate by a factor of
102. We regulate the convective velocities by varying the
amount of heat transported by thermal conduction, turbulent diffusion,
and resolved convection. Results: Increasing the efficiency of
resolved convection leads to a reduction of the rotational influence
on the flow and a sharp transition from solar-like to anti-solar
differential rotation for Coriolis numbers around 1.3. We confirm
the recent finding of a large-scale flow bistability: contrasted
with running the models from an initial condition with unprescribed
differential rotation, the initialization of the model with certain
kind of rotation profile sustains the solution over a wider parameter
range. The anti-solar profiles are found to be more stable against
perturbations in the level of convective turbulent velocity than
the solar-type solutions. Conclusions: Our results may have
implications for real stars that start their lives as rapid rotators
implying solar-like rotation in the early main-sequence evolution. As
they slow down, they might be able to retain solar-like rotation for
lower Coriolis numbers, and thus longer in time, before switching
to anti-solar rotation. This could partially explain the puzzling
findings of anti-solar rotation profiles for models in the solar
parameter regime.

---------------------------------------------------------
Title: Superflare Occurrence and Energies on G-, K-, and M-type Dwarfs
Authors: Candelaresi, S.; Hillier, A.; Maehara, H.; Brandenburg, A.;
Shibata, K.
2014ApJ...792...67C Altcode: 2014arXiv1405.1453C
Kepler data from G-, K-, and M-type stars are used to study conditions
that lead to superflares with energies above 1034 erg. From
the 117,661 stars included, 380 show superflares with a total of 1690
such events. We study whether parameters, like effective temperature
or rotation rate, have any effect on the superflare occurrence
rate or energy. With increasing effective temperature we observe a
decrease in the superflare rate, which is analogous to the previous
findings of a decrease in dynamo activity with increasing effective
temperature. For slowly rotating stars, we find a quadratic increase
of the mean occurrence rate with the rotation rate up to a critical
point, after which the rate decreases linearly. Motivated by standard
dynamo theory, we study the behavior of the relative starspot coverage,
approximated as the relative brightness variation. For faster rotating
stars, an increased fraction of stars shows higher spot coverage,
which leads to higher superflare rates. A turbulent dynamo is used
to study the dependence of the Ohmic dissipation as a proxy of the
flare energy on the differential rotation or shear rate. The resulting
statistics of the dissipation energy as a function of dynamo number is
similar to the observed flare statistics as a function of the inverse
Rossby number and shows similarly strong fluctuations. This supports
the idea that superflares might well be possible for solar-type G stars.

---------------------------------------------------------
Title: Magnetic Prandtl Number Dependence of the Kinetic-to-magnetic
Dissipation Ratio
Authors: Brandenburg, Axel
2014ApJ...791...12B Altcode: 2014arXiv1404.6964B
Using direct numerical simulations of three-dimensional hydromagnetic
turbulence, either with helical or non-helical forcing, we show that
the kinetic-to-magnetic energy dissipation ratio always increases with
the magnetic Prandtl number, i.e., the ratio of kinematic viscosity
to magnetic diffusivity. This dependence can always be approximated
by a power law, but the exponent is not the same in all cases. For
non-helical turbulence, the exponent is around 1/3, while for helical
turbulence it is between 0.6 and 2/3. In the statistically steady state,
the rate of energy conversion from kinetic into magnetic by the dynamo
must be equal to the Joule dissipation rate. We emphasize that for
both small-scale and large-scale dynamos, the efficiency of the energy
conversion depends sensitively on the magnetic Prandtl number, and thus
on the microphysical dissipation process. To understand this behavior,
we also study shell models of turbulence and one-dimensional passive
and active scalar models. We conclude that the magnetic Prandtl number
dependence is qualitatively best reproduced in the one-dimensional
model as a result of dissipation via localized Alfvén kinks.

---------------------------------------------------------
Title: Coronal influence on dynamos
Authors: Warnecke, Jörn; Brandenburg, Axel
2014IAUS..302..134W Altcode: 2013arXiv1310.0787W
We report on turbulent dynamo simulations in a spherical wedge with
an outer coronal layer. We apply a two-layer model where the lower
layer represents the convection zone and the upper layer the solar
corona. This setup is used to study the coronal influence on the
dynamo action beneath the surface. Increasing the radial coronal
extent gradually to three times the solar radius and changing the
magnetic Reynolds number, we find that dynamo action benefits from the
additional coronal extent in terms of higher magnetic energy in the
saturated stage. The flux of magnetic helicity can play an important
role in this context.

---------------------------------------------------------
Title: Magnetic flux concentrations from dynamo-generated fields
Authors: Jabbari, S.; Brandenburg, A.; Losada, I. R.; Kleeorin, N.;
Rogachevskii, I.
2014A&A...568A.112J Altcode: 2014arXiv1401.6107J
Context. The mean-field theory of magnetized stellar convection gives
rise to two distinct instabilities: the large-scale dynamo instability,
operating in the bulk of the convection zone and a negative effective
magnetic pressure instability (NEMPI) operating in the strongly
stratified surface layers. The latter might be important in connection
with magnetic spot formation. However, as follows from theoretical
analysis, the growth rate of NEMPI is suppressed with increasing
rotation rates. On the other hand, recent direct numerical simulations
(DNS) have shown a subsequent increase in the growth rate. 
Aims: We examine quantitatively whether this increase in the growth
rate of NEMPI can be explained by an α2 mean-field dynamo,
and whether both NEMPI and the dynamo instability can operate at the
same time. Methods: We use both DNS and mean-field simulations
(MFS) to solve the underlying equations numerically either with or
without an imposed horizontal field. We use the test-field method
to compute relevant dynamo coefficients. Results: DNS show
that magnetic flux concentrations are still possible up to rotation
rates above which the large-scale dynamo effect produces mean magnetic
fields. The resulting DNS growth rates are quantitatively reproduced
with MFS. As expected for weak or vanishing rotation, the growth rate
of NEMPI increases with increasing gravity, but there is a correction
term for strong gravity and large turbulent magnetic diffusivity. Conclusions: Magnetic flux concentrations are still possible for
rotation rates above which dynamo action takes over. For the solar
rotation rate, the corresponding turbulent turnover time is about 5 h,
with dynamo action commencing in the layers beneath.

---------------------------------------------------------
Title: Quantifying the effect of turbulent magnetic diffusion on
the growth rate of the magneto-rotational instability
Authors: Väisälä, M. S.; Brandenburg, A.; Mitra, D.; Käpylä,
P. J.; Mantere, M. J.
2014A&A...567A.139V Altcode: 2013arXiv1310.3157V
Context. In astrophysics, turbulent diffusion is often used in place of
microphysical diffusion to avoid resolving the small scales. However,
we expect this approach to break down when time and length scales of the
turbulence become comparable with other relevant time and length scales
in the system. Turbulent diffusion has previously been applied to the
magneto-rotational instability (MRI), but no quantitative comparison of
growth rates at different turbulent intensities has been performed. Aims: We investigate to what extent turbulent diffusion can be
used to model the effects of small-scale turbulence on the kinematic
growth rates of the MRI, and how this depends on angular velocity
and magnetic field strength. Methods: We use direct numerical
simulations in three-dimensional shearing boxes with periodic boundary
conditions in the spanwise direction and additional random plane-wave
volume forcing to drive a turbulent flow at a given length scale. We
estimate the turbulent diffusivity using a mixing length formula and
compare with results obtained with the test-field method. 
Results: It turns out that the concept of turbulent diffusion is
remarkably accurate in describing the effect of turbulence on the
growth rate of the MRI. No noticeable breakdown of turbulent diffusion
has been found, even when time and length scales of the turbulence
become comparable with those imposed by the MRI itself. On the other
hand, quenching of turbulent magnetic diffusivity by the magnetic
field is found to be absent. Conclusions: Turbulence reduces
the growth rate of the MRI in the same way as microphysical magnetic
diffusion does. Appendix A is available in electronic form at <A
href="http://www.aanda.org/10.1051/0004-6361/201322837/olm">http://www.aanda.org</A>

---------------------------------------------------------
Title: Mean-field dynamo action from delayed transport
Authors: Rheinhardt, Matthias; Devlen, Ebru; Rädler, Karl-Heinz;
Brandenburg, Axel
2014MNRAS.441..116R Altcode: 2014arXiv1401.5026R
We analyse the nature of dynamo action that enables growing
horizontally averaged magnetic fields in two particular flows that
were studied by Roberts in 1972, namely his flows II and III. They
have zero kinetic helicity either pointwise (flow II), or on average
(flow III). Using direct numerical simulations, we determine the onset
conditions for dynamo action at moderate values of the magnetic Reynolds
number. Using the test-field method, we show that the turbulent magnetic
diffusivity is then positive for both flows. However, we demonstrate
that for both flows large-scale dynamo action occurs through delayed
transport. Mathematically speaking, the magnetic field at earlier
times contributes to the electromotive force through the off-diagonal
components of the α tensor such that a zero mean magnetic field
becomes unstable to dynamo action. This represents a qualitatively
new mean-field dynamo mechanism not previously described.

---------------------------------------------------------
Title: Faraday Signature of Magnetic Helicity from Reduced
Depolarization
Authors: Brandenburg, Axel; Stepanov, Rodion
2014ApJ...786...91B Altcode: 2014arXiv1401.4102B
Using one-dimensional models, we show that a helical magnetic field
with an appropriate sign of helicity can compensate the Faraday
depolarization resulting from the superposition of Faraday-rotated
polarization planes from a spatially extended source. For radio
emission from a helical magnetic field, the polarization as a function
of the square of the wavelength becomes asymmetric with respect to
zero. Mathematically speaking, the resulting emission occurs then either
at observable or at unobservable (imaginary) wavelengths. We demonstrate
that rotation measure (RM) synthesis allows for the reconstruction
of the underlying Faraday dispersion function in the former case,
but not in the latter. The presence of positive magnetic helicity can
thus be detected by observing positive RM in highly polarized regions
in the sky and negative RM in weakly polarized regions. Conversely,
negative magnetic helicity can be detected by observing negative
RM in highly polarized regions and positive RM in weakly polarized
regions. The simultaneous presence of two magnetic constituents with
opposite signs of helicity is shown to possess signatures that can
be quantified through polarization peaks at specific wavelengths and
the gradient of the phase of the Faraday dispersion function. Similar
polarization peaks can tentatively also be identified for the bi-helical
magnetic fields that are generated self-consistently by a dynamo from
helically forced turbulence, even though the magnetic energy spectrum
is then continuous. Finally, we discuss the possibility of detecting
magnetic fields with helical and non-helical properties in external
galaxies using the Square Kilometre Array.

---------------------------------------------------------
Title: Particle energization through time-periodic helical magnetic
fields
Authors: Mitra, Dhrubaditya; Brandenburg, Axel; Dasgupta, Brahmananda;
Niklasson, Eyvind; Ram, Abhay
2014PhRvE..89d2919M Altcode: 2013arXiv1306.0151M
We solve for the motion of charged particles in a helical time-periodic
ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field
lines of a stationary ABC field with coefficients A =B=C=1 are chaotic,
and we show that the motion of a charged particle in such a field
is also chaotic at late times with positive Lyapunov exponent. We
further show that in time-periodic ABC fields, the kinetic energy of
a charged particle can increase indefinitely with time. At late times
the mean kinetic energy grows as a power law in time with an exponent
that approaches unity. For an initial distribution of particles,
whose kinetic energy is uniformly distributed within some interval,
the probability density function of kinetic energy is, at late times,
close to a Gaussian but with steeper tails.

---------------------------------------------------------
Title: Magnetic flux concentrations in a polytropic atmosphere
Authors: Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2014A&A...564A...2L Altcode: 2013arXiv1307.4945L
Context. Strongly stratified hydromagnetic turbulence has recently been
identified as a candidate for explaining the spontaneous formation of
magnetic flux concentrations by the negative effective magnetic pressure
instability (NEMPI). Much of this work has been done for isothermal
layers, in which the density scale height is constant throughout. Aims: We now want to know whether earlier conclusions regarding
the size of magnetic structures and their growth rates carry over to
the case of polytropic layers, in which the scale height decreases
sharply as one approaches the surface. Methods: To allow
for a continuous transition from isothermal to polytropic layers,
we employ a generalization of the exponential function known as the
q-exponential. This implies that the top of the polytropic layer
shifts with changing polytropic index such that the scale height is
always the same at some reference height. We used both mean-field
simulations (MFS) and direct numerical simulations (DNS) of forced
stratified turbulence to determine the resulting flux concentrations
in polytropic layers. Cases of both horizontal and vertical applied
magnetic fields were considered. Results: Magnetic structures
begin to form at a depth where the magnetic field strength is a small
fraction of the local equipartition field strength with respect to the
turbulent kinetic energy. Unlike the isothermal case where stronger
fields can give rise to magnetic flux concentrations at larger depths,
in the polytropic case the growth rate of NEMPI decreases for structures
deeper down. Moreover, the structures that form higher up have a smaller
horizontal scale of about four times their local depth. For vertical
fields, magnetic structures of super-equipartition strengths are formed,
because such fields survive downward advection that causes NEMPI with
horizontal magnetic fields to reach premature nonlinear saturation by
what is called the "potato-sack" effect. The horizontal cross-section
of such structures found in DNS is approximately circular, which is
reproduced with MFS of NEMPI using a vertical magnetic field. 
Conclusions: Results based on isothermal models can be applied locally
to polytropic layers. For vertical fields, magnetic flux concentrations
of super-equipartition strengths form, which supports suggestions that
sunspot formation might be a shallow phenomenon.

---------------------------------------------------------
Title: Magnetic Helicity and Energy Spectra of a Solar Active Region
Authors: Zhang, Hongqi; Brandenburg, Axel; Sokoloff, D. D.
2014ApJ...784L..45Z Altcode: 2013arXiv1311.2432Z
We compute for the first time the magnetic helicity and energy spectra
of the solar active region NOAA 11158 during 2011 February 11-15 at
20° southern heliographic latitude using observational photospheric
vector magnetograms. We adopt the isotropic representation of the
Fourier-transformed two-point correlation tensor of the magnetic
field. The sign of the magnetic helicity turns out to be predominantly
positive at all wavenumbers. This sign is consistent with what is
theoretically expected for the southern hemisphere. The magnetic
helicity normalized to its theoretical maximum value, here referred
to as relative helicity, is around 4% and strongest at intermediate
wavenumbers of k ≈ 0.4 Mm-1, corresponding to a scale
of 2π/k ≈ 16 Mm. The same sign and a similar value are also found
for the relative current helicity evaluated in real space based on
the vertical components of magnetic field and current density. The
modulus of the magnetic helicity spectrum shows a k -11/3
power law at large wavenumbers, which implies a k -5/3
spectrum for the modulus of the current helicity. A k -5/3
spectrum is also obtained for the magnetic energy. The energy spectra
evaluated separately from the horizontal and vertical fields agree for
wavenumbers below 3 Mm-1, corresponding to scales above
2 Mm. This gives some justification to our assumption of isotropy
and places limits resulting from possible instrumental artifacts at
small scales.

---------------------------------------------------------
Title: α effect in a turbulent liquid-metal plane Couette flow
Authors: Rüdiger, G.; Brandenburg, A.
2014PhRvE..89c3009R Altcode: 2012arXiv1201.0652R
We calculate the mean electromotive force in plane Couette flows of
a nonrotating conducting fluid under the influence of a large-scale
magnetic field for driven turbulence. A vertical stratification of the
turbulence intensity results in an α effect owing to the presence of
horizontal shear. Here we discuss the possibility of an experimental
determination of the components of the α tensor using both quasilinear
theory and nonlinear numerical simulations. For magnetic Prandtl numbers
of the order of unity, we find that in the high-conductivity limit the
α effect in the direction of the flow clearly exceeds the component in
spanwise direction. In this limit, α runs linearly with the magnetic
Reynolds number Rm , while in the low-conductivity limit it runs with
the product Rm .Re, where Re is the kinetic Reynolds number, so that
for a given Rm the α effect grows with decreasing magnetic Prandtl
number. For the small magnetic Prandtl numbers of liquid metals,
a common value for the horizontal elements of the α tensor appears,
which makes it unimportant whether the α effect is measured in the
spanwise or the streamwise directions. The resulting effect should
lead to an observable voltage of about 0.5 mV in both directions for
magnetic fields of 1 kG and velocity fluctuations of about 1 m/s in
a channel of 50-cm height (independent of its width).

---------------------------------------------------------
Title: Mean-field and direct numerical simulations of magnetic flux
concentrations from vertical field
Authors: Brandenburg, A.; Gressel, O.; Jabbari, S.; Kleeorin, N.;
Rogachevskii, I.
2014A&A...562A..53B Altcode: 2013arXiv1309.3547B
Context. Strongly stratified hydromagnetic turbulence has previously
been found to produce magnetic flux concentrations if the domain is
large enough compared with the size of turbulent eddies. Mean-field
simulations (MFS) using parameterizations of the Reynolds and
Maxwell stresses show a large-scale negative effective magnetic
pressure instability and have been able to reproduce many aspects of
direct numerical simulations (DNS) regarding growth rate, shape of
the resulting magnetic structures, and their height as a function of
magnetic field strength. Unlike the case of an imposed horizontal field,
for a vertical one, magnetic flux concentrations of equipartition
strength with the turbulence can be reached, resulting in magnetic
spots that are reminiscent of sunspots. Aims: We determine
under what conditions magnetic flux concentrations with vertical field
occur and what their internal structure is. Methods: We use a
combination of MFS, DNS, and implicit large-eddy simulations (ILES)
to characterize the resulting magnetic flux concentrations in forced
isothermal turbulence with an imposed vertical magnetic field. 
Results: Using DNS, we confirm earlier results that in the kinematic
stage of the large-scale instability the horizontal wavelength of
structures is about 10 times the density scale height. At later times,
even larger structures are being produced in a fashion similar to
inverse spectral transfer in helically driven turbulence. Using ILES,
we find that magnetic flux concentrations occur for Mach numbers
between 0.1 and 0.7. They occur also for weaker stratification and
larger turbulent eddies if the domain is wide enough. Using MFS,
the size and aspect ratio of magnetic structures are determined as
functions of two input parameters characterizing the parameterization
of the effective magnetic pressure. DNS, ILES, and MFS show magnetic
flux tubes with mean-field energies comparable to the turbulent kinetic
energy. These tubes can reach a length of about eight density scale
heights. Despite being ≤1% equipartition strength, it is important
that their lower part is included within the computational domain to
achieve the full strength of the instability. Conclusions:
The resulting vertical magnetic flux tubes are being confined by
downflows along the tubes and corresponding inflow from the sides,
which keep the field concentrated. Application to sunspots remains a
viable possibility.

---------------------------------------------------------
Title: Astrophysical Hydromagnetic Turbulence
Authors: Brandenburg, A.; Lazarian, A.
2014mpcp.book...87B Altcode: 2014mcp..book...87B
Recent progress in astrophysical hydromagnetic turbulence
is being reviewed. The physical ideas behind the now widely
accepted Goldreich-Sridhar model and its extension to compressible
magnetohydrodynamic turbulence are introduced. Implications for cosmic
ray diffusion and acceleration is being discussed. Dynamo-generated
magnetic fields with and without helicity are contrasted against each
other. Certain turbulent transport processes are being modified and
often suppressed by anisotropy and inhomogeneities of the turbulence,
while others are being produced by such properties, which can lead to
new large-scale instabilities of the turbulent medium. Applications
of various such processes to astrophysical systems are being considered.

---------------------------------------------------------
Title: Microphysics of Cosmic Ray Driven Plasma Instabilities
Authors: Bykov, A. M.; Brandenburg, A.; Malkov, M. A.; Osipov, S. M.
2014mpcp.book..125B Altcode: 2014mcp..book..125B
Energetic nonthermal particles (cosmic rays, CRs) are accelerated
in supernova remnants, relativistic jets and other astrophysical
objects. The CR energy density is typically comparable with that
of the thermal components and magnetic fields. In this review we
discuss mechanisms of magnetic field amplification due to instabilities
induced by CRs. We derive CR kinetic and magnetohydrodynamic equations
that govern cosmic plasma systems comprising the thermal background
plasma, comic rays and fluctuating magnetic fields to study CR-driven
instabilities. Both resonant and non-resonant instabilities are
reviewed, including the Bell short-wavelength instability, and the
firehose instability. Special attention is paid to the longwavelength
instabilities driven by the CR current and pressure gradient. The
helicity production by the CR current-driven instabilities is discussed
in connection with the dynamo mechanisms of cosmic magnetic field
amplification.

---------------------------------------------------------
Title: An Azimuthal Dynamo Wave in Spherical Shell Convection
Authors: Cole, Elizabeth; Käpylä, Petri J.; Mantere, Maarit J.;
Brandenburg, Axel
2014ApJ...780L..22C Altcode: 2013arXiv1309.6802C
We report the discovery of an azimuthal dynamo wave of a low-order (m =
1) mode in direct numerical simulations (DNS) of turbulent convection in
spherical shells. Such waves are predicted by mean-field dynamo theory
and have been obtained previously in mean-field models. An azimuthal
dynamo wave has been proposed as a possible explanation for the
persistent drifts of spots observed on several rapidly rotating stars,
as revealed through photometry and Doppler imaging. However, this has
been judged unlikely because evidence for such waves from DNS has been
lacking. Here we present DNS of large-scale magnetic fields showing
a retrograde m = 1 mode. Its pattern speed is nearly independent of
latitude and does not reflect the speed of the differential rotation at
any depth. The extrema of magnetic m = 1 structures coincide reasonably
well with the maxima of m = 2 structures of the temperature. These
results provide direct support for the observed drifts being due to
an azimuthal dynamo wave.

---------------------------------------------------------
Title: Spoke-like Differential Rotation in a Convective Dynamo with
a Coronal Envelope
Authors: Warnecke, Jörn; Käpylä, Petri J.; Mantere, Maarit J.;
Brandenburg, Axel
2013ApJ...778..141W Altcode: 2013arXiv1301.2248W
We report on the results of four convective dynamo simulations with
an outer coronal layer. The magnetic field is self-consistently
generated by the convective motions beneath the surface. Above the
convection zone, we include a polytropic layer that extends to 1.6
solar radii. The temperature increases in this region to ≈8 times the
value at the surface, corresponding to ≈1.2 times the value at the
bottom of the spherical shell. We associate this region with the solar
corona. We find solar-like differential rotation with radial contours of
constant rotation rate, together with a near-surface shear layer. This
non-cylindrical rotation profile is caused by a non-zero latitudinal
entropy gradient that offsets the Taylor-Proudman balance through the
baroclinic term. The meridional circulation is multi-cellular with a
solar-like poleward flow near the surface at low latitudes. In most
of the cases, the mean magnetic field is oscillatory with equatorward
migration in two cases. In other cases, the equatorward migration is
overlaid by stationary or even poleward migrating mean fields.

---------------------------------------------------------
Title: Effects of Enhanced Stratification on Equatorward Dynamo
Wave Propagation
Authors: Käpylä, Petri J.; Mantere, Maarit J.; Cole, Elizabeth;
Warnecke, Jörn; Brandenburg, Axel
2013ApJ...778...41K Altcode: 2013arXiv1301.2595K
We present results from simulations of rotating magnetized turbulent
convection in spherical wedge geometry representing parts of the
latitudinal and longitudinal extents of a star. Here we consider a
set of runs for which the density stratification is varied, keeping
the Reynolds and Coriolis numbers at similar values. In the case
of weak stratification, we find quasi-steady dynamo solutions for
moderate rotation and oscillatory ones with poleward migration of
activity belts for more rapid rotation. For stronger stratification,
the growth rate tends to become smaller. Furthermore, a transition
from quasi-steady to oscillatory dynamos is found as the Coriolis
number is increased, but now there is an equatorward migrating branch
near the equator. The breakpoint where this happens corresponds to a
rotation rate that is about three to seven times the solar value. The
phase relation of the magnetic field is such that the toroidal field
lags behind the radial field by about π/2, which can be explained by
an oscillatory α2 dynamo caused by the sign change of the
α-effect about the equator. We test the domain size dependence of our
results for a rapidly rotating run with equatorward migration by varying
the longitudinal extent of our wedge. The energy of the axisymmetric
mean magnetic field decreases as the domain size increases and we
find that an m = 1 mode is excited for a full 2π azimuthal extent,
reminiscent of the field configurations deduced from observations of
rapidly rotating late-type stars.

---------------------------------------------------------
Title: Bipolar Magnetic Structures Driven by Stratified Turbulence
with a Coronal Envelope
Authors: Warnecke, Jörn; Losada, Illa R.; Brandenburg, Axel; Kleeorin,
Nathan; Rogachevskii, Igor
2013ApJ...777L..37W Altcode: 2013arXiv1308.1080W
We report the spontaneous formation of bipolar magnetic structures in
direct numerical simulations of stratified forced turbulence with an
outer coronal envelope. The turbulence is forced with transverse random
waves only in the lower (turbulent) part of the domain. Our initial
magnetic field is either uniform in the entire domain or confined
to the turbulent layer. After about 1-2 turbulent diffusion times, a
bipolar magnetic region of vertical field develops with two coherent
circular structures that live during one turbulent diffusion time,
and then decay during 0.5 turbulent diffusion times. The resulting
magnetic field strengths inside the bipolar region are comparable to the
equipartition value with respect to the turbulent kinetic energy. The
bipolar magnetic region forms a loop-like structure in the upper coronal
layer. We associate the magnetic structure formation with the negative
effective magnetic pressure instability in the two-layer model.

---------------------------------------------------------
Title: Self-assembly of Shallow Magnetic Spots through Strongly
Stratified Turbulence
Authors: Brandenburg, Axel; Kleeorin, Nathan; Rogachevskii, Igor
2013ApJ...776L..23B Altcode: 2013arXiv1306.4915B
Recent studies have demonstrated that in fully developed turbulence,
the effective magnetic pressure of a large-scale field (non-turbulent
plus turbulent contributions) can become negative. In the presence
of strongly stratified turbulence, this was shown to lead to a
large-scale instability that produces spontaneous magnetic flux
concentrations. Furthermore, using a horizontal magnetic field,
elongated flux concentrations with a strength of a few percent of the
equipartition value were found. Here we show that a uniform vertical
magnetic field leads to circular magnetic spots of equipartition
field strengths. This could represent a minimalistic model of sunspot
formation and highlights the importance of two critical ingredients:
turbulence and strong stratification. Radiation, ionization, and
supergranulation may be important for realistic simulations, but are
not critical at the level of a minimalistic model of magnetic spot
formation.

---------------------------------------------------------
Title: Microphysics of Cosmic Ray Driven Plasma Instabilities
Authors: Bykov, A. M.; Brandenburg, A.; Malkov, M. A.; Osipov, S. M.
2013SSRv..178..201B Altcode: 2013SSRv..tmp...61B; 2013arXiv1304.7081B
Energetic nonthermal particles (cosmic rays, CRs) are accelerated
in supernova remnants, relativistic jets and other astrophysical
objects. The CR energy density is typically comparable with that
of the thermal components and magnetic fields. In this review we
discuss mechanisms of magnetic field amplification due to instabilities
induced by CRs. We derive CR kinetic and magnetohydrodynamic equations
that govern cosmic plasma systems comprising the thermal background
plasma, comic rays and fluctuating magnetic fields to study CR-driven
instabilities. Both resonant and non-resonant instabilities are
reviewed, including the Bell short-wavelength instability, and the
firehose instability. Special attention is paid to the longwavelength
instabilities driven by the CR current and pressure gradient. The
helicity production by the CR current-driven instabilities is discussed
in connection with the dynamo mechanisms of cosmic magnetic field
amplification.

---------------------------------------------------------
Title: Active Region Formation through the Negative Effective Magnetic
Pressure Instability
Authors: Kemel, Koen; Brandenburg, Axel; Kleeorin, Nathan; Mitra,
Dhrubaditya; Rogachevskii, Igor
2013SoPh..287..293K Altcode: 2012arXiv1203.1232K; 2012SoPh..tmp..154K
The negative effective magnetic-pressure instability operates on scales
encompassing many turbulent eddies, which correspond to convection
cells in the Sun. This instability is discussed here in connection
with the formation of active regions near the surface layers of the
Sun. This instability is related to the negative contribution of
turbulence to the mean magnetic pressure that causes the formation
of large-scale magnetic structures. For an isothermal layer, direct
numerical simulations and mean-field simulations of this phenomenon are
shown to agree in many details, for example the onset of the instability
occurs at the same depth. This depth increases with increasing field
strength, such that the growth rate of this instability is independent
of the field strength, provided the magnetic structures are fully
contained within the domain. A linear stability analysis is shown to
support this finding. The instability also leads to a redistribution
of turbulent intensity and gas pressure that could provide direct
observational signatures.

---------------------------------------------------------
Title: Astrophysical Hydromagnetic Turbulence
Authors: Brandenburg, A.; Lazarian, A.
2013SSRv..178..163B Altcode: 2013arXiv1307.5496B; 2013SSRv..tmp...83B
Recent progress in astrophysical hydromagnetic turbulence
is being reviewed. The physical ideas behind the now widely
accepted Goldreich-Sridhar model and its extension to compressible
magnetohydrodynamic turbulence are introduced. Implications for cosmic
ray diffusion and acceleration is being discussed. Dynamo-generated
magnetic fields with and without helicity are contrasted against each
other. Certain turbulent transport processes are being modified and
often suppressed by anisotropy and inhomogeneities of the turbulence,
while others are being produced by such properties, which can lead to
new large-scale instabilities of the turbulent medium. Applications
of various such processes to astrophysical systems are being considered.

---------------------------------------------------------
Title: Can Planetesimals Form by Collisional Fusion?
Authors: Mitra, Dhrubaditya; Wettlaufer, J. S.; Brandenburg, Axel
2013ApJ...773..120M Altcode: 2013arXiv1306.3672M
As a test bed for the growth of protoplanetary bodies in a turbulent
circumstellar disk, we examine the fate of a boulder using direct
numerical simulations of particle seeded gas flowing around it. We
provide an accurate description of the flow by imposing no-slip and
non-penetrating boundary conditions on the boulder surface using the
immersed boundary method pioneered by Peskin. Advected by the turbulent
disk flow, the dust grains collide with the boulder and we compute the
probability density function of the normal component of the collisional
velocity. Through this examination of the statistics of collisional
velocities, we test the recently developed concept of collisional fusion
which provides a physical basis for a range of collisional velocities
exhibiting perfect sticking. A boulder can then grow sufficiently
rapidly to settle into a Keplerian orbit on disk evolution timescales.

---------------------------------------------------------
Title: Surface flux concentrations in a spherical α2
dynamo
Authors: Jabbari, S.; Brandenburg, A.; Kleeorin, N.; Mitra, D.;
Rogachevskii, I.
2013A&A...556A.106J Altcode: 2013arXiv1302.5841J
Context. In the presence of strong density stratification, turbulence
can lead to the large-scale instability of a horizontal magnetic
field if its strength is in a suitable range (around a few percent of
the turbulent equipartition value). This instability is related to a
suppression of the turbulent pressure so that the turbulent contribution
to the mean magnetic pressure becomes negative. This results in the
excitation of a negative effective magnetic pressure instability
(NEMPI). This instability has so far only been studied for an imposed
magnetic field. Aims: We want to know how NEMPI works when the
mean magnetic field is generated self-consistently by an α2
dynamo, whether it is affected by global spherical geometry, and
whether it can influence the properties of the dynamo itself. 
Methods: We adopt the mean-field approach, which has previously been
shown to provide a realistic description of NEMPI in direct numerical
simulations. We assume axisymmetry and solve the mean-field equations
with the Pencil Code for an adiabatic stratification at a total density
contrast in the radial direction of ≈4 orders of magnitude. 
Results: NEMPI is found to work when the dynamo-generated field is
about 4% of the equipartition value, which is achieved through strong
α quenching. This instability is excited in the top 5% of the outer
radius, provided the density contrast across this top layer is at
least 10. NEMPI is found to occur at lower latitudes when the mean
magnetic field is stronger. For weaker fields, NEMPI can make the
dynamo oscillatory with poleward migration. Conclusions: NEMPI
is a viable mechanism for producing magnetic flux concentrations in
a strongly stratified spherical shell in which a magnetic field is
generated by a strongly quenched α effect dynamo.

---------------------------------------------------------
Title: Data assimilation for stratified convection
Authors: Svedin, Andreas; Cuéllar, Milena C.; Brandenburg, Axel
2013MNRAS.433.2278S Altcode: 2012arXiv1207.7314S; 2013MNRAS.tmp.1606S
We show how the 3DVAR data assimilation methodology can be used in the
astrophysical context of a two-dimensional convection flow. We study
the way in which this variational approach finds best estimates of
the current state of the flow from a weighted average of model states
and observations. We use numerical simulations to generate synthetic
observations of a vertical two-dimensional slice of the outer part
of the solar convection zone for varying noise levels, and implement
3DVAR when the covariance matrices are diagonal and proportional to the
identity matrix. Our simulation results demonstrate the capability of
3DVAR to produce error estimates of system states that can be more than
two orders of magnitude below the original noise level present in the
observations. This work illustrates the importance of applying data
to obtain accurate model estimates given a set of observations. It
also exemplifies how data assimilation techniques can be applied to
simulations of stratified convection.

---------------------------------------------------------
Title: Coherent structures and the saturation of a nonlinear dynamo
Authors: Rempel, Erico L.; Chian, Abraham C. -L.; Brandenburg, Axel;
Muñoz, Pablo R.; Shadden, Shawn C.
2013JFM...729..309R Altcode: 2012arXiv1210.6637R
Eulerian and Lagrangian tools are used to detect coherent structures in
the velocity and magnetic fields of a mean--field dynamo, produced by
direct numerical simulations of the three--dimensional compressible
magnetohydrodynamic equations with an isotropic helical forcing
and moderate Reynolds number. Two distinct stages of the dynamo are
studied, the kinematic stage, where a seed magnetic field undergoes
exponential growth, and the saturated regime. It is shown that
the Lagrangian analysis detects structures with greater detail,
besides providing information on the chaotic mixing properties of
the flow and the magnetic fields. The traditional way of detecting
Lagrangian coherent structures using finite--time Lyapunov exponents
is compared with a recently developed method called function M. The
latter is shown to produce clearer pictures which readily permit the
identification of hyperbolic regions in the magnetic field, where
chaotic transport/dispersion of magnetic field lines is highly enhanced.

---------------------------------------------------------
Title: Competition of rotation and stratification in flux
concentrations
Authors: Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2013A&A...556A..83L Altcode: 2012arXiv1212.4077L
Context. In a strongly stratified turbulent layer, a uniform horizontal
magnetic field can become unstable and spontaneously form local flux
concentrations due to a negative contribution of turbulence to the
large-scale (mean-field) magnetic pressure. This mechanism, which
is called negative effective magnetic pressure instability (NEMPI),
is of interest in connection with dynamo scenarios in which most of
the magnetic field resides in the bulk of the convection zone and
not at the bottom, as is often assumed. Recent work using mean-field
hydromagnetic equations has shown that NEMPI becomes suppressed at
rather low rotation rates with Coriolis numbers as low as 0.1. Aims: Here we extend these earlier investigations by studying
the effects of rotation both on the development of NEMPI and on the
effective magnetic pressure. We also quantify the kinetic helicity
resulting from direct numerical simulations (DNS) with Coriolis
numbers and strengths of stratification comparable to values near
the solar surface and compare it with earlier work at smaller scale
separation ratios. Further, we estimate the expected observable
signals of magnetic helicity at the solar surface. Methods:
To calculate the rotational effect on the effective magnetic pressure
we consider both DNS and analytical studies using the τ approach. To
study the effects of rotation on the development of NEMPI we use both
DNS and mean-field calculations of the three-dimensional hydromagnetic
equations in a Cartesian domain. Results: We find that the
growth rates of NEMPI from earlier mean-field calculations are well
reproduced with DNS, provided the Coriolis number is below 0.06. In
that case, kinetic and magnetic helicities are found to be weak and
the rotational effect on the effective magnetic pressure is negligible
as long as the production of flux concentrations is not inhibited by
rotation. For faster rotation, dynamo action becomes possible. However,
there is an intermediate range of rotation rates where dynamo action on
its own is not yet possible, but the rotational suppression of NEMPI
is being alleviated. Conclusions: Production of magnetic flux
concentrations through the suppression of turbulent pressure appears
to be possible only in the uppermost layers of the Sun, where the
convective turnover time is less than two hours.

---------------------------------------------------------
Title: Solar-like differential rotation and equatorward migration
in a convective dynamo with a coronal envelope
Authors: Warnecke, J.; Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2013IAUS..294..307W Altcode: 2012arXiv1211.0452W
We present results of convective turbulent dynamo simulations including
a coronal layer in a spherical wedge. We find an equatorward migration
of the radial and azimuthal fields similar to the behavior of sunspots
during the solar cycle. The migration of the field coexist with a
spoke-like differential rotation and anti-solar (clockwise) meridional
circulation. Even though the migration extends over the whole convection
zone, the mechanism causing this is not yet fully understood.

---------------------------------------------------------
Title: Non-linear and chaotic dynamo regimes
Authors: Brandenburg, Axel
2013IAUS..294..387B Altcode: 2013arXiv1305.1952B
An update is given on the current status of solar and stellar
dynamos. At present, it is still unclear why stellar cycle frequencies
increase with rotation frequency in such a way that their ratio
increases with stellar activity. The small-scale dynamo is expected
to operate in spite of a small value of the magnetic Prandtl number
in stars. Whether or not the global magnetic activity in stars is a
shallow or deeply rooted phenomenon is another open question. Progress
in demonstrating the presence and importance of magnetic helicity fluxes
in dynamos is briefly reviewed, and finally the role of nonlocality is
emphasized in modeling stellar dynamos using the mean-field approach. On
the other hand, direct numerical simulations have now come to the point
where the models show solar-like equatorward migration that can be
compared with observations and that need to be understood theoretically.

---------------------------------------------------------
Title: Topological constraints on magnetic field relaxation
Authors: Candelaresi, Simon; Brandenburg, Axel
2013IAUS..294..353C Altcode: 2012arXiv1212.0879C
Magnetic field relaxation is determined by both the field's geometry
and its topology. For relaxation processes, however, it turns out that
its topology is a much more stringent constraint. As quantifier for the
topology we use magnetic helicity and test whether it is a stronger
condition than the linking of field lines. Further, we search for
evidence of other topological invariants, which give rise to further
restrictions in the field's relaxation. We find that magnetic helicity
is the sole determinant in most cases. Nevertheless, we see evidence
for restrictions not captured through magnetic helicity.

---------------------------------------------------------
Title: Non-uniformity effects in the negative effective magnetic
pressure instability
Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2013PhST..155a4027K Altcode: 2012arXiv1208.0517K
In direct numerical simulations of strongly stratified turbulence
we have previously studied the development of large scale magnetic
structures starting from a uniform background field. This is caused by
an instability resulting from a negative contribution of small-scale
turbulence to the effective (mean-field) magnetic pressure, and was
qualitatively reproduced in mean-field simulations (MFS) where this
pressure reduction was modeled as a function of the mean magnetic field
normalized by the equipartition field. We now investigate the effect
of mean current density on the turbulent pressure reduction. In our
MFS, such currents are associated with sharp gradients of the growing
structures. We find that an enhanced mean current density increases
the suppression of the turbulent pressure.

---------------------------------------------------------
Title: Flux concentrations in turbulent convection
Authors: Käpylä, Petri J.; Brandenburg, Axel; Kleeorin, Nathan;
Mantere, Maarit J.; Rogachevskii, Igor
2013IAUS..294..283K Altcode: 2012arXiv1211.2962K
We present preliminary results from high resolution magneto-convection
simulations where we find the formation of flux concentrations from
an initially uniform magnetic field. The structures appear in roughly
ten convective turnover times and live close to a turbulent diffusion
time. The time scales are compatible with the negative effective
magnetic pressure instability (NEMPI), although structure formation
is not restricted to regions where the effective magnetic pressure
is negative.

---------------------------------------------------------
Title: A mean field dynamo from negative eddy diffusivity
Authors: Devlen, Ebru; Brandenburg, Axel; Mitra, Dhrubaditya
2013MNRAS.432.1651D Altcode: 2013MNRAS.tmp.1243D; 2012arXiv1212.2626D
Using direct numerical simulations, we verify that Roberts-IV
flow exhibits dynamo action dominated by horizontally averaged
large-scale magnetic field. With the test-field method, we compute
the turbulent magnetic diffusivity and find that it is negative and
overcomes the molecular diffusivity, thus explaining quantitatively
the large-scale dynamo for magnetic Reynolds numbers above ≈8. As
expected for a dynamo of this type, but contrary to α-effect dynamos,
the two horizontal field components grow independently of each other
and have arbitrary amplitude ratios and phase differences. Small
length-scales of the mean magnetic field are shown to be stabilized
by the turbulent magnetic diffusivity becoming positive at larger
wavenumbers. Oscillatory decaying or growing solutions have also been
found in certain wavenumber intervals and sufficiently large values
of the magnetic Reynolds number. For magnetic Reynolds numbers below
≈0.5, the turbulent magnetic diffusivity is confirmed to be positive,
as expected for all incompressible flows. Earlier claims of a dynamo
driven by a modified Taylor-Green flow through negative eddy diffusivity
could not be confirmed.

---------------------------------------------------------
Title: Evolution of primordial magnetic fields from phase transitions
Authors: Kahniashvili, Tina; Tevzadze, Alexander G.; Brandenburg,
Axel; Neronov, Andrii
2013PhRvD..87h3007K Altcode: 2012arXiv1212.0596K
We consider the evolution of primordial magnetic fields generated during
cosmological, electroweak, or QCD phase transitions. We assume that the
magnetic field generation can be described as an injection of magnetic
energy to cosmological plasma at a given scale determined by the moment
of magnetic field generation. A high Reynolds number ensures strong
coupling between the magnetic field and fluid motions. The subsequent
evolution of the magnetic field is governed by decaying hydromagnetic
turbulence. Both our numerical simulations and a phenomenological
description allow us to recover “universal” laws for the decay of
magnetic energy and the growth of magnetic correlation length in the
turbulent (low-viscosity) regime. In particular, we show that during
the radiation-dominated epoch, the energy and correlation length of
nonhelical magnetic fields scale as conformal time to the powers -1/2
and +1/2, respectively. For helical magnetic fields, the energy and
correlation length scale as conformal time to the powers -1/3 and +2/3,
respectively. The universal decay law of the magnetic field implies
that the strength of the magnetic field generated during the QCD
phase transition could reach ∼10-9G with the present-day
correlation length ∼50kpc. The fields generated at the electroweak
phase transition could be as strong as ∼10-10G with
correlation lengths reaching ∼0.3kpc. These values of the magnetic
fields are consistent with the lower bounds of the extragalactic
magnetic fields.

---------------------------------------------------------
Title: Kinetic helicity needed to drive large-scale dynamos
Authors: Candelaresi, Simon; Brandenburg, Axel
2013PhRvE..87d3104C Altcode: 2012arXiv1208.4529C
Magnetic field generation on scales that are large compared with the
scale of the turbulent eddies is known to be possible via the so-called
α effect when the turbulence is helical and if the domain is large
enough for the α effect to dominate over turbulent diffusion. Using
three-dimensional turbulence simulations, we show that the energy of the
resulting mean magnetic field of the saturated state increases linearly
with the product of normalized helicity and the ratio of domain scale to
eddy scale, provided this product exceeds a critical value of around
unity. This implies that large-scale dynamo action commences when
the normalized helicity is larger than the inverse scale ratio. Our
results show that the emergence of small-scale dynamo action does not
have any noticeable effect on the large-scale dynamo. Recent findings by
Pietarila Graham [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.066406
85, 066406 (2012)] of a smaller minimal helicity may be an artifact
due to the onset of small-scale dynamo action at large magnetic
Reynolds numbers. However, the onset of large-scale dynamo action is
difficult to establish when the kinetic helicity is small. Instead of
random forcing, they used an ABC flow with time-dependent phases. We
show that such dynamos saturate prematurely in a way that is
reminiscent of inhomogeneous dynamos with internal magnetic helicity
fluxes. Furthermore, even for very low fractional helicities, such
dynamos display large-scale fields that change direction, which is
uncharacteristic of turbulent dynamos.

---------------------------------------------------------
Title: Oscillatory large-scale dynamos from Cartesian convection
simulations
Authors: Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2013GApFD.107..244K Altcode: 2011arXiv1111.6894K
We present results from compressible Cartesian convection simulations
with and without imposed shear. In the former case the dynamo
is expected to be of α2 Ω type, which is generally
expected to be relevant for the Sun, whereas the latter case refers
to α2 dynamos that are more likely to occur in more
rapidly rotating stars whose differential rotation is small. We
perform a parameter study where the shear flow and the rotational
influence are varied to probe the relative importance of both types of
dynamos. Oscillatory solutions are preferred both in the kinematic and
saturated regimes when the negative ratio of shear to rotation rates,
q ≡ -S/Ω, is between 1.5 and 2, i.e. when shear and rotation are
of comparable strengths. Other regions of oscillatory solutions are
found with small values of q, i.e. when shear is weak in comparison to
rotation, and in the regime of large negative qs, when shear is very
strong in comparison to rotation. However, exceptions to these rules
also appear so that for a given ratio of shear to rotation, solutions
are non-oscillatory for small and large shear, but oscillatory in the
intermediate range. Changing the boundary conditions from vertical field
to perfect conductor ones changes the dynamo mode from oscillatory to
quasi-steady. Furthermore, in many cases an oscillatory solution exists
only in the kinematic regime whereas in the nonlinear stage the mean
fields are stationary. However, the cases with rotation and no shear
are always oscillatory in the parameter range studied here and the
dynamo mode does not depend on the magnetic boundary conditions. The
strengths of total and large-scale components of the magnetic field
in the saturated state, however, are sensitive to the chosen boundary
conditions.

---------------------------------------------------------
Title: Introduction
Authors: Brandenburg, Axel; Rogachevskii, Igor
2013GApFD.107....1B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Yoshizawa's cross-helicity effect and its quenching
Authors: Brandenburg, A.; Rädler, K. -H.
2013GApFD.107..207B Altcode: 2011arXiv1112.1237B
A central quantity in mean-field magnetohydrodynamics is the mean
electromotive force overlineBE, which in general depends on
the mean magnetic field. It may however also have a part independent
of the mean magnetic field. Here we study an example of a rotating
conducting body of turbulent fluid with non-zero cross-helicity, in
which a contribution to overlineBE proportional to the
angular velocity occurs (Yoshizawa, A., Self-consistent turbulent
dynamo modeling of reversed field pinches and planetary magnetic
fields. Phys. Fluids B 1990, 2, 1589-1600). If the forcing is helical,
it also leads to an α effect, and large-scale magnetic fields can
be generated. For not too rapid rotation, the field configuration
is such that Yoshizawa's contribution to overlineBE is
considerably reduced compared to the case without α effect. In that
case, large-scale flows are also found to be generated.

---------------------------------------------------------
Title: Turbulent dynamos with advective magnetic helicity flux
Authors: Del Sordo, F.; Guerrero, G.; Brandenburg, A.
2013MNRAS.429.1686D Altcode: 2012arXiv1205.3502D; 2012MNRAS.tmp..344D
Many astrophysical bodies harbour magnetic fields that are thought to
be sustained by a dynamo process. However, it has been argued that the
production of large-scale magnetic fields by mean-field dynamo action
is strongly suppressed at large magnetic Reynolds numbers owing to
the conservation of magnetic helicity. This phenomenon is known as
catastrophic quenching. Advection of magnetic fields by stellar and
galactic winds towards the outer boundaries and away from the dynamo
is expected to alleviate such quenching. Here we explore the relative
roles played by advective and turbulent-diffusive fluxes of magnetic
helicity in the dynamo. In particular, we study how the dynamo is
affected by advection. We do this by performing direct numerical
simulations of a turbulent dynamo of α2 type driven by
forced turbulence in a Cartesian domain in the presence of a flow away
from the equator where helicity changes sign. Our results indicate that
in the presence of advection, the dynamo, otherwise stationary, becomes
oscillatory. We confirm an earlier result for turbulent-diffusive
magnetic helicity fluxes that for small magnetic Reynolds numbers (Rm
≲ 100...200, based on the wavenumber of the energy-carrying eddies)
the magnetic helicity flux scales less strongly with magnetic Reynolds
number (Rm-1/2) than the term describing magnetic helicity
destruction by resistivity (Rm-1). Our new results now
suggest that for larger Rm the former becomes approximately independent
of Rm, while the latter falls off more slowly. We show for the first
time that both for weak and stronger winds, the magnetic helicity
flux term becomes comparable to the resistive term for Rm ≳ 1000,
which is necessary for alleviating catastrophic quenching.

---------------------------------------------------------
Title: Current Status of Turbulent Dynamo Theory
Authors: Brandenburg, Axel; Sokoloff, Dmitry; Subramanian, Kandaswamy
2013lsmf.book..371B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: New Scaling for the Alpha Effect in Slowly Rotating Turbulence
Authors: Brandenburg, A.; Gressel, O.; Käpylä, P. J.; Kleeorin,
N.; Mantere, M. J.; Rogachevskii, I.
2013ApJ...762..127B Altcode: 2012arXiv1208.5004B
Using simulations of slowly rotating stratified turbulence, we show that
the α effect responsible for the generation of astrophysical magnetic
fields is proportional to the logarithmic gradient of kinetic energy
density rather than that of momentum, as was previously thought. This
result is in agreement with a new analytic theory developed in
this paper for large Reynolds numbers and slow rotation. Thus, the
contribution of density stratification is less important than that
of turbulent velocity. The α effect and other turbulent transport
coefficients are determined by means of the test-field method. In
addition to forced turbulence, we also investigate supernova-driven
turbulence and stellar convection. In some cases (intermediate rotation
rate for forced turbulence, convection with intermediate temperature
stratification, and supernova-driven turbulence), we find that the
contribution of density stratification might be even less important
than suggested by the analytic theory.

---------------------------------------------------------
Title: Rotational effects on the negative magnetic pressure
instability
Authors: Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Mitra, D.;
Rogachevskii, I.
2012A&A...548A..49L Altcode: 2012arXiv1207.5392L
Context. The surface layers of the Sun are strongly stratified. In the
presence of turbulence with a weak mean magnetic field, a large-scale
instability resulting in the formation of nonuniform magnetic
structures, can be excited on the scale of many (more than ten)
turbulent eddies (or convection cells). This instability is caused by
a negative contribution of turbulence to the effective (mean-field)
magnetic pressure and has previously been discussed in connection with
the formation of active regions. Aims: We want to understand
the effects of rotation on this instability in both two and three
dimensions. Methods: We use mean-field magnetohydrodynamics in
a parameter regime in which the properties of the negative effective
magnetic pressure instability have previously been found to agree
with properties of direct numerical simulations. Results: We
find that the instability is already suppressed for relatively slow
rotation with Coriolis numbers (i.e. inverse Rossby numbers) around
0.2. The suppression is strongest at the equator. In the nonlinear
regime, we find traveling wave solutions with propagation in the
prograde direction at the equator with additional poleward migration
away from the equator. Conclusions: We speculate that the
prograde rotation of the magnetic pattern near the equator might be a
possible explanation for the faster rotation speed of magnetic tracers
relative to the plasma velocity on the Sun. In the bulk of the domain,
kinetic and current helicities are negative in the northern hemisphere
and positive in the southern.

---------------------------------------------------------
Title: Magnetic Fields from QCD Phase Transitions
Authors: Tevzadze, Alexander G.; Kisslinger, Leonard; Brandenburg,
Axel; Kahniashvili, Tina
2012ApJ...759...54T Altcode: 2012arXiv1207.0751T
We study the evolution of QCD phase transition-generated magnetic fields
(MFs) in freely decaying MHD turbulence of the expanding universe. We
consider an MF generation model that starts from basic non-perturbative
QCD theory and predicts stochastic MFs with an amplitude of the order
of 0.02 μG and small magnetic helicity. We employ direct numerical
simulations to model the MHD turbulence decay and identify two different
regimes: a "weakly helical" turbulence regime, when magnetic helicity
increases during decay, and "fully helical" turbulence, when maximal
magnetic helicity is reached and an inverse cascade develops. The
results of our analysis show that in the most optimistic scenario the
magnetic correlation length in the comoving frame can reach 10 kpc
with the amplitude of the effective MF being 0.007 nG. We demonstrate
that the considered model of magnetogenesis can provide the seed MF
for galaxies and clusters.

---------------------------------------------------------
Title: Evolution of inflation-generated magnetic field through
phase transitions
Authors: Kahniashvili, Tina; Brandenburg, Axel; Campanelli, Leonardo;
Ratra, Bharat; Tevzadze, Alexander G.
2012PhRvD..86j3005K Altcode: 2012arXiv1206.2428K
We study the evolution of an inflation-generated magnetic field, due to
its coupling to fluid motions, during cosmological phase transitions. We
find that the magnetic field stays almost unchanged on large scales,
while on small scales, the spectrum is modified in such a way that
power at small scales becomes progressively suppressed. We also show
that the magnetic field generates turbulent motions in the initially
turbulence-free plasma. On large scales, the slope of the resulting
kinetic energy spectrum is consistent with that of white noise.

---------------------------------------------------------
Title: Spontaneous Formation of Magnetic Flux Concentrations in
Stratified Turbulence
Authors: Kemel, Koen; Brandenburg, Axel; Kleeorin, Nathan; Mitra,
Dhrubaditya; Rogachevskii, Igor
2012SoPh..280..321K Altcode: 2012SoPh..tmp...48K; 2011arXiv1112.0279K
The negative effective magnetic pressure instability discovered
recently in direct numerical simulations (DNSs) may play a crucial
role in the formation of sunspots and active regions in the Sun
and stars. This instability is caused by a negative contribution of
turbulence to the effective mean Lorentz force (the sum of turbulent and
non-turbulent contributions) and results in the formation of large-scale
inhomogeneous magnetic structures from an initially uniform magnetic
field. Earlier investigations of this instability in DNSs of stably
stratified, externally forced, isothermal hydromagnetic turbulence
in the regime of large plasma β are now extended into the regime of
larger scale separation ratios where the number of turbulent eddies
in the computational domain is about 30. Strong spontaneous formation
of large-scale magnetic structures is seen even without performing any
spatial averaging. These structures encompass many turbulent eddies. The
characteristic time of the instability is comparable to the turbulent
diffusion time, L2/ηt, where ηt
is the turbulent diffusivity and L is the scale of the domain. DNSs
are used to confirm that the effective magnetic pressure does indeed
become negative for magnetic field strengths below the equipartition
field. The dependence of the effective magnetic pressure on the
field strength is characterized by fit parameters that seem to show
convergence for larger values of the magnetic Reynolds number.

---------------------------------------------------------
Title: Ejections of Magnetic Structures Above a Spherical Wedge
Driven by a Convective Dynamo with Differential Rotation
Authors: Warnecke, Jörn; Käpylä, Petri J.; Mantere, Maarit J.;
Brandenburg, Axel
2012SoPh..280..299W Altcode: 2012SoPh..tmp..214W; 2011arXiv1112.0505W
We combine a convectively driven dynamo in a spherical shell with a
nearly isothermal density-stratified cooling layer that mimics some
aspects of a stellar corona to study the emergence and ejections
of magnetic field structures. This approach is an extension of
earlier models, where forced turbulence simulations were employed to
generate magnetic fields. A spherical wedge is used which consists of
a convection zone and an extended coronal region to ≈ 1.5 times the
radius of the sphere. The wedge contains a quarter of the azimuthal
extent of the sphere and 150∘ in latitude. The magnetic
field is self-consistently generated by the turbulent motions due to
convection beneath the surface. Magnetic fields are found to emerge at
the surface and are ejected to the coronal part of the domain. These
ejections occur at irregular intervals and are weaker than in earlier
work. We tentatively associate these events with coronal mass ejections
on the Sun, even though our model of the solar atmosphere is rather
simplistic.

---------------------------------------------------------
Title: Mean-field transport in stratified and/or rotating turbulence
(Corrigendum)
Authors: Brandenburg, A.; Rädler, K. -H.; Kemel, K.
2012A&A...545C...1B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Current Status of Turbulent Dynamo Theory. From Large-Scale
to Small-Scale Dynamos
Authors: Brandenburg, Axel; Sokoloff, Dmitry; Subramanian, Kandaswamy
2012SSRv..169..123B Altcode: 2012SSRv..tmp...57B; 2012arXiv1203.6195B
Several recent advances in turbulent dynamo theory are reviewed. High
resolution simulations of small-scale and large-scale dynamo action
in periodic domains are compared with each other and contrasted with
similar results at low magnetic Prandtl numbers. It is argued that
all the different cases show similarities at intermediate length
scales. On the other hand, in the presence of helicity of the
turbulence, power develops on large scales, which is not present
in non-helical small-scale turbulent dynamos. At small length
scales, differences occur in connection with the dissipation cutoff
scales associated with the respective value of the magnetic Prandtl
number. These differences are found to be independent of whether or
not there is large-scale dynamo action. However, large-scale dynamos
in homogeneous systems are shown to suffer from resistive slow-down
even at intermediate length scales. The results from simulations are
connected to mean field theory and its applications. Recent work on
magnetic helicity fluxes to alleviate large-scale dynamo quenching,
shear dynamos, nonlocal effects and magnetic structures from strong
density stratification are highlighted. Several insights which arise
from analytic considerations of small-scale dynamos are discussed.

---------------------------------------------------------
Title: Magnetic twist: a source and property of space weather
Authors: Warnecke, Jörn; Brandenburg, Axel; Mitra, Dhrubaditya AB(; )
2012JSWSC...2A..11W Altcode: 2012arXiv1203.0959W
Aim: We present evidence for finite magnetic helicity density in the
heliosphere and numerical models thereof, and relate it to the magnetic
field properties of the dynamo in the solar convection zone. Methods: We
use simulations and solar wind data to compute magnetic helicity either
directly from the simulations or indirectly using time series of the
skew-symmetric components of the magnetic correlation tensor. Results:
We find that the solar dynamo produces negative magnetic helicity at
small scales and positive at large scales. However, in the heliosphere
these properties are reversed and the magnetic helicity is now positive
at small scales and negative at large scales. We explain this by the
fact that a negative diffusive magnetic helicity flux corresponds to
a positive gradient of magnetic helicity, which leads to a change of
sign from negative to positive values at some radius in the northern
hemisphere.

---------------------------------------------------------
Title: Cyclic Magnetic Activity due to Turbulent Convection in
Spherical Wedge Geometry
Authors: Käpylä, Petri J.; Mantere, Maarit J.; Brandenburg, Axel
2012ApJ...755L..22K Altcode: 2012arXiv1205.4719K
We report on simulations of turbulent, rotating, stratified,
magnetohydrodynamic convection in spherical wedge geometry. An initially
small-scale, random, weak-amplitude magnetic field is amplified by
several orders of magnitude in the course of the simulation to form
oscillatory large-scale fields in the saturated state of the dynamo. The
differential rotation is solar-like (fast equator), but neither coherent
meridional poleward circulation nor near-surface shear layer develop in
these runs. In addition to a poleward branch of magnetic activity beyond
50° latitude, we find for the first time a pronounced equatorward
branch at around 20° latitude, reminiscent of the solar cycle.

---------------------------------------------------------
Title: Cycles and cycle modulations
Authors: Brandenburg, Axel; Guerrero, Gustavo
2012IAUS..286...37B Altcode: 2011arXiv1111.3351B
Some selected concepts of the solar activity cycle are reviewed. Cycle
modulations through a stochastic α effect are being identified
with limited scale separation ratios. Three-dimensional turbulence
simulations with helicity and shear are compared at two different
scale separation ratios. In both cases the level of fluctuations shows
relatively little variation with the dynamo cycle. Prospects for a
shallow origin of sunspots are discussed in terms of the negative
effective magnetic pressure instability. Tilt angles of bipolar
active regions are discussed as a consequence of shear rather than
the Coriolis force.

---------------------------------------------------------
Title: Cosmic-Ray Current-driven Turbulence and Mean-field Dynamo
Effect
Authors: Rogachevskii, Igor; Kleeorin, Nathan; Brandenburg, Axel;
Eichler, David
2012ApJ...753....6R Altcode: 2012arXiv1204.4246R
We show that an α effect is driven by the cosmic-ray (CR) Bell
instability exciting left-right asymmetric turbulence. Alfvén waves
of a preferred polarization have maximally helical motion, because the
transverse motion of each mode is parallel to its curl. We show how
large-scale Alfvén modes, when rendered unstable by CR streaming,
can create new net flux over any finite region, in the direction
of the original large-scale field. We perform direct numerical
simulations (DNSs) of a magnetohydrodynamic fluid with a forced CR
current and use the test-field method to determine the α effect and
the turbulent magnetic diffusivity. As follows from DNS, the dynamics
of the instability has the following stages: (1) in the early stage,
the small-scale Bell instability that results in the production of
small-scale turbulence is excited; (2) in the intermediate stage,
there is formation of larger-scale magnetic structures; (3) finally,
quasi-stationary large-scale turbulence is formed at a growth rate
that is comparable to that expected from the dynamo instability, but
its amplitude over much longer timescales remains unclear. The results
of DNS are in good agreement with the theoretical estimates. It is
suggested that this dynamo is what gives weakly magnetized relativistic
shocks such as those from gamma-ray bursts (GRBs) a macroscopic
correlation length. It may also be important for large-scale magnetic
field amplification associated with CR production and diffusive
shock acceleration in supernova remnants (SNRs) and blast waves from
GRBs. Magnetic field amplification by Bell turbulence in SNRs is found
to be significant, but it is limited owing to the finite time available
to the super-Alfvénicly expanding remnant. The effectiveness of the
mechanisms is shown to be dependent on the shock velocity. Limits on
magnetic field growth in longer-lived systems, such as the Galaxy and
unconfined intergalactic CRs, are also discussed.

---------------------------------------------------------
Title: Lagrangian chaos in an ABC-forced nonlinear dynamo
Authors: Rempel, Erico L.; C-L Chian, Abraham; Brandenburg, Axel
2012PhyS...86a8405R Altcode: 2012arXiv1201.4324R
The Lagrangian properties of the velocity field in a magnetized
fluid are studied using three-dimensional simulations of a helical
magnetohydrodynamic dynamo. We compute the attracting and repelling
Lagrangian coherent structures (LCS), which are dynamic lines and
surfaces in the velocity field that delineate particle transport in
flows with chaotic streamlines and act as transport barriers. Two
dynamo regimes are explored, one with a robust coherent mean magnetic
field and the other with intermittent bursts of magnetic energy. The
LCS and the statistics of the finite-time Lyapunov exponents indicate
that the stirring/mixing properties of the velocity field decay as
a linear function of magnetic energy. The relevance of this study to
the solar dynamo problem is also discussed.

---------------------------------------------------------
Title: Spontaneous chiral symmetry breaking in the Tayler instability
Authors: Del Sordo, Fabio; Bonanno, Alfio; Brandenburg, Axel; Mitra,
Dhrubaditya
2012IAUS..286...65D Altcode: 2011arXiv1111.1742D
The chiral symmetry breaking properties of the Tayler instability
are discussed. Effective amplitude equations are determined in
one case. This model has three free parameters that are determined
numerically. Comparison with chiral symmetry breaking in biochemistry
is made.

---------------------------------------------------------
Title: Coronal ejections from convective spherical shell dynamos
Authors: Warnecke, J.; Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2012IAUS..286..154W Altcode: 2011arXiv1111.1763W
We present a three-dimensional model of rotating convection combined
with a simplified model of a corona in spherical coordinates. The
motions in the convection zone generate a large-scale magnetic
field which is sporadically ejected into the outer layers above. Our
model corona is approximately isothermal, but it includes density
stratification due to gravity.

---------------------------------------------------------
Title: Breakdown of chiral symmetry during saturation of the Tayler
instability
Authors: Bonanno, Alfio; Brandenburg, Axel; Del Sordo, Fabio; Mitra,
Dhrubaditya
2012PhRvE..86a6313B Altcode: 2012arXiv1204.0081B
We study spontaneous breakdown of chiral symmetry during the nonlinear
evolution of the Tayler instability. We start with an initial steady
state of zero helicity. Within linearized perturbation calculations,
helical perturbations of this initial state have the same growth rate
for either sign of helicity. Direct numerical simulations (DNS) of the
fully nonlinear equations, however, show that an infinitesimal excess
of one sign of helicity in the initial perturbation gives rise to a
saturated helical state. We further show that this symmetry breaking
can be described by weakly nonlinear finite-amplitude equations with
undetermined coefficients which can be deduced solely from symmetry
consideration. By fitting solutions of the amplitude equations to
data from DNS, we further determine the coefficients of the amplitude
equations.

---------------------------------------------------------
Title: Mean-field closure parameters for passive scalar turbulence
Authors: Snellman, J. E.; Rheinhardt, M.; Käpylä, P. J.; Mantere,
M. J.; Brandenburg, A.
2012PhyS...86a8406S Altcode: 2011arXiv1112.4777S
Direct numerical simulations (DNSs) of isotropically forced
homogeneous stationary turbulence with an imposed passive scalar
concentration gradient are compared with an analytical closure model
which provides evolution equations for the mean passive scalar flux
and variance. Triple correlations of fluctuations appearing in these
equations are described in terms of relaxation terms proportional to
the quadratic correlations. Three methods are used to extract the
relaxation timescales τi from DNSs. Firstly, we insert
the closure ansatz into our equations, assume stationarity and solve
for τi. Secondly, we use only the closure ansatz itself
and obtain τi from the ratio of quadratic and triple
correlations. Thirdly, we remove the imposed passive scalar gradient and
fit an exponential law to the decaying solution. We vary the Reynolds
(Re) and Péclet numbers (while fixing their ratio at unity) and the
degree of scale separation and find for large Re a fair correspondence
between the different methods. The ratio of the turbulent relaxation
time of the passive scalar flux to the turnover time of the turbulent
eddies is of the order of 3, which is in remarkable agreement with
earlier work. Finally, we make an effort to extract the relaxation
timescales relevant for the viscous and diffusive effects. We find two
regimes that are valid for small and large Re, respectively, but the
dependence of the parameters on scale separation suggests that they
are not universal.

---------------------------------------------------------
Title: Detection of turbulent thermal diffusion of particles in
numerical simulations
Authors: Haugen, Nils Erland L.; Kleeorin, Nathan; Rogachevskii,
Igor; Brandenburg, Axel
2012PhFl...24g5106H Altcode: 2011arXiv1101.4188H
The phenomenon of turbulent thermal diffusion in temperature-stratified
turbulence causing a non-diffusive turbulent flux (i.e.,
non-counter-gradient transport) of inertial and non-inertial particles
in the direction of the turbulent heat flux is found using direct
numerical simulations (DNS). In simulations with and without gravity,
this phenomenon is found to cause a peak in the particle number density
around the minimum of the mean fluid temperature for Stokes numbers
less than 1, where the Stokes number is the ratio of particle Stokes
time to turbulent Kolmogorov time at the viscous scale. Turbulent
thermal diffusion causes the formation of inhomogeneities in the
spatial distribution of inertial particles whose scale is large in
comparison with the integral scale of the turbulence. The strength of
this effect is maximum for Stokes numbers around unity, and decreases
again for larger values. The dynamics of inertial particles is studied
using Lagrangian modelling in forced temperature-stratified turbulence,
whereas non-inertial particles and the fluid are described using DNS
in an Eulerian framework.

---------------------------------------------------------
Title: Magnetic helicity fluxes and their effect on stellar dynamos
Authors: Candelaresi, Simon; Brandenburg, Axel
2012IAUS..286...49C Altcode: 2011arXiv1111.2023C
Magnetic helicity fluxes in turbulently driven α2 dynamos
are studied to demonstrate their ability to alleviate catastrophic
quenching. A one-dimensional mean-field formalism is used to achieve
magnetic Reynolds numbers of the order of 105. We study
both diffusive magnetic helicity fluxes through the mid-plane as
well as those resulting from the recently proposed alternate dynamic
quenching formalism. By adding shear we make a parameter scan for the
critical values of the shear and forcing parameters for which dynamo
action occurs. For this αΩ dynamo we find that the preferred mode
is antisymmetric about the mid-plane. This is also verified in 3-D
direct numerical simulations.

---------------------------------------------------------
Title: Special issue on current research in astrophysical magnetism
Authors: Kosovichev, Alexander; Lundstedt, Henrik; Brandenburg, Axel
2012PhyS...86a0201K Altcode:
Much of what Hannes Alfvén envisaged some 70 years ago has now
penetrated virtually all branches of astrophysical research. Indeed,
magnetic fields can display similar properties over a large range
of scales. We have therefore been able to take advantage of the
transparency of galaxies and the interstellar medium to obtain
measurements inside them. On the other hand, the Sun is much closer,
allowing us to obtain a detailed picture of the interaction of flows
and magnetic fields at the surface, and more recently in the interior
by helioseismology. Moreover, the solar timescales are generally
much shorter, making studies of dynamical processes more direct. This special issue on current research in astrophysical magnetism
is based on work discussed during a one month Nordita program Dynamo,
Dynamical Systems and Topology and comprises papers that fall into four
different categories (A)-(D). (A) Papers on small-scale magnetic
fields and flows in astrophysics 1. E M de Gouveia Dal Pino, M R M
Leão, R Santos-Lima, G Guerrero, G Kowal and A Lazarian Magnetic flux
transport by turbulent reconnection in astrophysical flows 2. Philip
R Goode, Valentyna Abramenko and Vasyl Yurchyshyn New solar telescope
in Big Bear: evidence for super-diffusivity and small-scale solar
dynamos? 3. I N Kitiashvili, A G Kosovichev, N N Mansour, S K Lele
and A A Wray Vortex tubes of turbulent solar convection The above
collection of papers begins with a review of astrophysical reconnection
and introduces the concept of dynamos necessary to explain the existence
of contemporary magnetic fields both on galactic and solar scales
(paper 1). This is complemented by observations with the new Big
Bear Solar Observatory telescope, allowing us to see magnetic field
amplification on small scales (paper 2). This in turn is complemented
by realistic simulations of subsurface and surface flow patterns
(paper 3). (B) Papers on theoretical approaches to turbulent
fluctuations 4. Nathan Kleeorin and Igor Rogachevskii Growth rate
of small-scale dynamo at low magnetic Prandtl numbers 5. Erico L
Rempel, Abraham C-L Chian and Axel Brandenburg Lagrangian chaos in
an ABC-forced nonlinear dynamo 6. J E Snellman, M Rheinhardt, P J
Käpylä, M J Mantere and A Brandenburg Mean-field closure parameters
for passive scalar turbulence Research in dynamo theory has been
actively pursued for over half a century. It started by trying to
understand the large-scale magnetic fields of the Sun and the Earth,
and subsequently also in galaxies. Such large-scale fields can nowadays
be understood in terms of mean-field dynamo theory that explains the
possibility of large-scale field generation under anisotropic conditions
lacking mirror symmetry. However, even when none of this is the case,
dynamos can still work, and they are called small-scale dynamos that
were referred to in paper 2. This was studied originally under the
assumption that the flow is smooth compared with the magnetic field,
but in the Sun the opposite is the case. This is because viscosity
is much smaller than magnetic diffusivity, i.e., their ratio, which
is the magnetic Prandtl number, is small. In that case the physics
of small-scale dynamos changes, but dynamos still exist even then
(paper 4). Tracing the flow lines in nonlinear small-scale dynamos is
important for understanding their mixing properties (paper 5). Turbulent
mixing is a generic concept that applies not only to magnetic field,
but also to passive scalars which are often used as a prototype for
studying this. Turbulence simulations have helped tremendously in
quantifying the ability of turbulent flows to mix, but the more we
know, the more complicated it becomes. It turns out that spatial and
temporal coupling is an important consideration for allowing accurate
comparison between numerical simulations and mean-field theory (paper
6). (C) The large-scale solar cycle 7. V V Pipin and D D Sokoloff
The fluctuating α-effect and Waldmeier relations in the nonlinear
dynamo models1 8. Radostin D Simitev and Friedrich H Busse
Solar cycle properties described by simple convection-driven dynamos
The mean-field concept has helped us constructing detailed models
of the solar cycle and to make comparison with observed features of
the solar 11-year cycle. One such feature is the Waldmeier relation
between growth time and amplitude of the cycle, and there is another
relation for the declining part of the cycle. These relations
reflect nonlinear aspects of the model and therefore constitute an
important test of the model (paper 7). While mean-field theory is
a useful concept for modeling solar activity, it must eventually be
tested against fully three-dimensional simulations. At present, such
simulations are often quite idealized, because only the large scales
of the turbulent convection of stars can be resolved. Nevertheless,
numerical simulations begin to show many properties that are also seen
in the Sun (paper 8). (D) Flow and dynamo properties in spherical
shells 9. Maxim Reshetnyak and Pavel Hejda Kinetic energy cascades
in quasi-geostrophic convection in a spherical shell 10. Radostin
D Simitev and Friedrich H Busse Bistable attractors in a model of
convection-driven spherical dynamos As the rotation speed is
increased, the flow becomes more strongly constrained by the Coriolis
force. In a spherical shell, such a flow is additionally constrained
by gravity, or at least by the geometry of the domain. Such flows
are called geostrophic. Only now are we beginning to learn about the
subtle properties of the kinetic energy cascade in such flows (paper
9). Turbulent systems are highly nonlinear and it is in principle
possible to find multiple solutions of the equations even for the same
boundary and initial conditions. For turbulent systems, we can only ask
about the statistical properties of the solutions, and the question
of multiple solutions is then less obvious. However, in turbulent
dynamos in convective shells, a nice example has been found where
this is possible. A detailed account of this is given in paper 10. Most of the participants of the Nordita program were able to stay for
the full month of the program, allowing them to think about new ideas
that will be reflected not only in papers on the short term, but also
in new projects and collaborations on a larger scale in the years to
come. We therefore thank Nordita for providing a stimulating atmosphere
and acknowledge the generous support. 1This paper
has been published as V V Pipin and D D Sokoloff 2011 Phys. Scr. <A
href="http://iopscience.iop.org/1402-4896/84/6/065903"> 84 065903</A>.

---------------------------------------------------------
Title: Negative effective magnetic pressure in turbulent convection
Authors: Käpylä, P. J.; Brandenburg, A.; Kleeorin, N.; Mantere,
M. J.; Rogachevskii, I.
2012MNRAS.422.2465K Altcode: 2011arXiv1104.4541K
We investigate the effects of weakly and strongly stratified turbulent
convection on the mean effective Lorentz force, and especially on the
mean effective magnetic pressure. Earlier studies with isotropically
forced non-stratified and stratified turbulence have shown that
the contribution of the turbulence to the mean magnetic pressure is
negative for mean horizontal magnetic fields that are smaller than the
equipartition strength, so that the effective mean magnetic pressure
that takes into account the turbulence effects can be negative. Compared
with earlier cases of forced turbulence with an isothermal equation of
state, we find that the turbulence effect is similar to or even stronger
in the present case of turbulent convection. This is argued to be due
to the anisotropy of turbulence in the vertical direction. Another
important difference compared with earlier studies is the presence of
an evolution equation for the specific entropy. Mean-field modelling
with entropy evolution indicates that the negative effective magnetic
pressure can still lead to a large-scale instability which forms
local flux concentrations, even though the specific entropy evolution
tends to have a stabilizing effect when applied to a stably stratified
(e.g. isothermal) layer. It is argued that this large-scale instability
could be important for the formation of solar large-scale magnetic
structures such as active regions.

---------------------------------------------------------
Title: Transport of angular momentum and chemical species by
anisotropic mixing in stellar radiative interiors
Authors: Kitchatinov, L. L.; Brandenburg, A.
2012AN....333..230K Altcode: 2012arXiv1201.2484K
Small levels of turbulence can be present in stellar radiative interiors
due to, e.g., the instability of rotational shear. In this paper
we estimate turbulent transport coefficients for stably stratified
rotating stellar radiation zones. Stable stratification induces
strong anisotropy with a very small ratio of radial-to-horizontal
turbulence intensities. Angular momentum is transported mainly due
to the correlation between azimuthal and radial turbulent motions
induced by the Coriolis force. This non-diffusive transport known
as the Λ-effect has outward direction in radius and is much more
efficient compared to the effect of radial eddy viscosity. Chemical
species are transported by small radial diffusion only. This result
is confirmed using direct numerical simulations combined with the
test-scalar method. As a consequence of the non-diffusive transport
of angular momentum, the estimated characteristic time of rotational
coupling (⪉100 Myr) between radiative core and convective envelope
in young solar-type stars is much shorter compared to the time-scale
of Lithium depletion (∼1 Gyr).

---------------------------------------------------------
Title: Kinetic helicity decay in linearly forced turbulence
Authors: Brandenburg, A.; Petrosyan, A.
2012AN....333..195B Altcode: 2010arXiv1012.1464B
The decay of kinetic helicity is studied in numerical models of forced
turbulence using either an externally imposed forcing function as an
inhomogeneous term in the equations or, alternatively, a term linear
in the velocity giving rise to a linear instability. The externally
imposed forcing function injects energy at the largest scales, giving
rise to a turbulent inertial range with nearly constant energy flux
while for linearly forced turbulence the spectral energy is maximum
near the dissipation wavenumber. Kinetic helicity is injected once a
statistically steady state is reached, but it is found to decay on a
turbulent time scale regardless of the nature of the forcing and the
value of the Reynolds number.

---------------------------------------------------------
Title: Commission 12: Solar Radiation and Structure
Authors: Kosovichev, Alexander; Cauzzi, Gianna; Pillet, Valentin
Martinez; Asplund, Martin; Brandenburg, Axel; Chou, Dean-Yi;
Christensen-Dalsgaard, Jorgen; Gan, Weiqun; Kuznetsov, Vladimir D.;
Rovira, Marta G.; Shchukina, Nataliya; Venkatakrishnan, P.
2012IAUTA..28...81K Altcode: 2012IAUTB..28...81K
Commission 12 of the International Astronomical Union encompasses
investigations of the internal structure and dynamics of the Sun, mostly
accessible through the techniques of local and global helioseismology,
the quiet solar atmosphere, solar radiation and its variability, and
the nature of relatively stable magnetic structures like sunspots,
faculae and the magnetic network. The Commission sees participation
of over 350 scientists worldwide.

---------------------------------------------------------
Title: The Negative Effective Magnetic Pressure in Stratified Forced
Turbulence
Authors: Brandenburg, Axel; Kemel, Koen; Kleeorin, Nathan;
Rogachevskii, Igor
2012ApJ...749..179B Altcode: 2010arXiv1005.5700B
To understand the basic mechanism of the formation of magnetic
flux concentrations, we determine by direct numerical simulations
the turbulence contributions to the mean magnetic pressure in a
strongly stratified isothermal layer with large plasma beta, where a
weak uniform horizontal mean magnetic field is applied. The negative
contribution of turbulence to the effective mean magnetic pressure is
determined for strongly stratified forced turbulence over a range of
values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo
action is shown to reduce the negative effect of turbulence on the
effective mean magnetic pressure. However, the turbulence coefficients
describing the negative effective magnetic pressure phenomenon are
found to converge for magnetic Reynolds numbers between 60 and 600,
which is the largest value considered here. In all these models,
the turbulent intensity is arranged to be nearly independent of
height, so the kinetic energy density decreases with height due to
the decrease in density. In a second series of numerical experiments,
the turbulent intensity increases with height such that the turbulent
kinetic energy density is nearly independent of height. Turbulent
magnetic diffusivity and turbulent pumping velocity are determined
with the test-field method for both cases. The vertical profile of the
turbulent magnetic diffusivity is found to agree with what is expected
based on simple mixing length expressions. Turbulent pumping is shown
to be down the gradient of turbulent magnetic diffusivity, but it is
twice as large as expected. Corresponding numerical mean-field models
are used to show that a large-scale instability can occur in both cases,
provided the degree of scale separation is large enough and hence the
turbulent magnetic diffusivity small enough.

---------------------------------------------------------
Title: Catastrophic Quenching in αΩ Dynamos Revisited
Authors: Hubbard, Alexander; Brandenburg, Axel
2012ApJ...748...51H Altcode: 2011arXiv1107.0238H
At large magnetic Reynolds numbers, magnetic helicity evolution plays an
important role in astrophysical large-scale dynamos. The recognition
of this fact led to the development of the dynamical α quenching
formalism, which predicts catastrophically low mean fields in open
systems. Here, we show that in oscillatory αΩ dynamos this formalism
predicts an unphysical magnetic helicity transfer between scales. An
alternative technique is proposed where this artifact is removed by
using the evolution equation for the magnetic helicity of the total
field in the shearing advective gauge. In the traditional dynamical α
quenching formalism, this can be described by an additional magnetic
helicity flux of small-scale fields that does not appear in homogeneous
α2 dynamos. In αΩ dynamos, the alternative formalism is
shown to lead to larger saturation fields than what has been obtained
in some earlier models with the traditional formalism. We have compared
the predictions of the two formalisms to results of direct numerical
simulations, finding that the alternative formulation provides a better
fit. This suggests that worries about catastrophic dynamo behavior in
the limit of large magnetic Reynolds number are unfounded.

---------------------------------------------------------
Title: Dynamics of saturated energy condensation in two-dimensional
turbulence
Authors: Chan, Chi-kwan; Mitra, Dhrubaditya; Brandenburg, Axel
2012PhRvE..85c6315C Altcode: 2011arXiv1109.6937C
In two-dimensional forced Navier-Stokes turbulence, energy cascades
to the largest scales in the system to form a pair of coherent
vortices known as the Bose condensate. We show, both numerically and
analytically, that the energy condensation saturates and the system
reaches a statistically stationary state. The time scale of saturation
is inversely proportional to the viscosity and the saturation energy
level is determined by both the viscosity and the force. We further
show that, without sufficient resolution to resolve the small-scale
enstrophy spectrum, numerical simulations can give a spurious result
for the saturation energy level. We also find that the movement of
the condensate is similar to the motion of an inertial particle with
an effective drag force. Furthermore, we show that the profile of the
saturated coherent vortices can be described by a Gaussian core with
exponential wings.

---------------------------------------------------------
Title: Scaling and intermittency in incoherent α-shear dynamo
Authors: Mitra, Dhrubaditya; Brandenburg, Axel
2012MNRAS.420.2170M Altcode: 2011arXiv1107.2419M
We consider mean-field dynamo models with fluctuating α effect,
both with and without large-scale shear. The α effect is chosen to
be Gaussian white noise with zero mean and a given covariance. In
the presence of shear, we show analytically that (in infinitely large
domains) the mean-squared magnetic field shows exponential growth. The
growth rate of the fastest growing mode is proportional to the shear
rate. This result agrees with earlier numerical results of Yousef et
al. and the recent analytical treatment by Heinemann, McWilliams &amp;
Schekochihin who use a method different from ours. In the absence of
shear, an incoherent α2 dynamo may also be possible. We
further show by explicit calculation of the growth rate of third-
and fourth-order moments of the magnetic field that the probability
density function of the mean magnetic field generated by this dynamo
is non-Gaussian.

---------------------------------------------------------
Title: Mean-field transport in stratified and/or rotating turbulence
Authors: Brandenburg, A.; Rädler, K. -H.; Kemel, K.
2012A&A...539A..35B Altcode: 2011arXiv1108.2264B
Context. The large-scale magnetic fields of stars and galaxies are often
described in the framework of mean-field dynamo theory. At moderate
magnetic Reynolds numbers, the transport coefficients defining the
mean electromotive force can be determined from simulations. This
applies analogously also to passive scalar transport. Aims:
We investigate the mean electromotive force in the kinematic
framework, that is, ignoring the back-reaction of the magnetic
field on the fluid velocity, under the assumption of axisymmetric
turbulence determined by the presence of either rotation, density
stratification, or both. We use an analogous approach for the mean
passive scalar flux. As an alternative to convection, we consider
forced turbulence in an isothermal layer. When using standard ansatzes,
the mean magnetic transport is then determined by nine, and the mean
passive scalar transport by four coefficients. We give results for all
these transport coefficients. Methods: We use the test-field
method and the test-scalar method, where transport coefficients are
determined by solving sets of equations with properly chosen mean
magnetic fields or mean scalars. These methods are adapted to mean
fields which may depend on all three space coordinates. Results:
We find the anisotropy of turbulent diffusion to be moderate in spite
of rapid rotation or strong density stratification. Contributions
to the mean electromotive force determined by the symmetric part of
the gradient tensor of the mean magnetic field, which were ignored
in several earlier investigations, turn out to be important. In
stratified rotating turbulence, the α effect is strongly anisotropic,
suppressed along the rotation axis on large length scales, but strongly
enhanced at intermediate length scales. Also the OO×meanJJ effect is
enhanced at intermediate length scales. The turbulent passive scalar
diffusivity is typically almost twice as large as the turbulent
magnetic diffusivity. Both magnetic and passive scalar diffusion
are slightly enhanced along the rotation axis, but decreased if
there is gravity. Conclusions: The test-field and test-scalar
methods provide powerful tools for analyzing transport properties of
axisymmetric turbulence. Future applications are proposed ranging from
anisotropic turbulence due to the presence of a uniform magnetic field
to inhomogeneous turbulence where the specific entropy is nonuniform,
for example. Some of the contributions to the mean electromotive
force which have been ignored in several earlier investigations, in
particular those given by the symmetric part of the gradient tensor
of the mean magnetic field, turn out to be of significant magnitude.

---------------------------------------------------------
Title: Vorticity production and survival in viscous and magnetized
cosmologies
Authors: Dosopoulou, F.; Del Sordo, F.; Tsagas, C. G.; Brandenburg, A.
2012PhRvD..85f3514D Altcode: 2011arXiv1112.6164D
We study the role of viscosity and the effects of a magnetic field on a
rotating, self-gravitating fluid, using Newtonian theory and adopting
the ideal magnetohydrodynamic approximation. Our results confirm
that viscosity can generate vorticity in inhomogeneous environments,
while the magnetic tension can produce vorticity even in the absence
of fluid pressure and density gradients. Linearizing our equations
around an Einstein-de Sitter cosmology, we find that viscosity adds to
the diluting effect of the universal expansion. Typically, however,
the dissipative viscous effects are confined to relatively small
scales. We also identify the characteristic length below which the
viscous dissipation is strong and beyond which viscosity is essentially
negligible. In contrast, magnetism seems to favor cosmic rotation. The
magnetic presence is found to slow down the standard decay rate of
linear vortices, thus leading to universes with more residual rotation
than generally anticipated.

---------------------------------------------------------
Title: Plasma flow versus magnetic feature-tracking speeds in the Sun
Authors: Guerrero, G.; Rheinhardt, M.; Brandenburg, A.; Dikpati, M.
2012MNRAS.420L...1G Altcode: 2011MNRAS.tmpL.375G; 2011arXiv1107.4801G
We simulate the magnetic feature-tracking (MFT) speed using
axisymmetric advective-diffusive transport models in both one and
two dimensions. By depositing magnetic bipolar regions at different
latitudes at the Sun’s surface and following their evolution for a
prescribed meridional circulation and magnetic diffusivity profiles,
we derive the MFT speed as a function of latitude. We find that in
a one-dimensional surface-transport model the simulated MFT speed at
the surface is always the same as the meridional flow speed used as
input to the model, but is different in a two-dimensional transport
model in the meridional (r, θ) plane. The difference depends on the
value of the magnetic diffusivity and on the radial gradient of the
latitudinal velocity. We have confirmed our results with two different
codes in spherical and Cartesian coordinates.

---------------------------------------------------------
Title: Properties of the negative effective magnetic pressure
instability
Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2012AN....333...95K Altcode: 2011arXiv1107.2752K
As was demonstrated in earlier studies, turbulence can result in a
negative contribution to the effective mean magnetic pressure, which, in
turn, can cause a large-scale instability. In this study, hydromagnetic
mean-field modelling is performed for an isothermally stratified
layer in the presence of a horizontal magnetic field. The negative
effective magnetic pressure instability (NEMPI) is comprehensively
investigated. It is shown that, if the effect of turbulence on the
mean magnetic tension force vanishes, which is consistent with results
from direct numerical simulations of forced turbulence, the fastest
growing eigenmodes of NEMPI are two-dimensional. The growth rate is
found to depend on a parameter β_{star} characterizing the turbulent
contribution of the effective mean magnetic pressure for moderately
strong mean magnetic fields. A fit formula is proposed that gives
the growth rate as a function of turbulent kinematic viscosity,
turbulent magnetic diffusivity, the density scale height, and the
parameter β_{star}. The strength of the imposed magnetic field does
not explicitly enter provided the location of the vertical boundaries
are chosen such that the maximum of the eigenmode of NEMPI fits into
the domain. The formation of sunspots and solar active regions is
discussed as possible applications of NEMPI.

---------------------------------------------------------
Title: Verification of Reynolds stress parameterizations from
simulations
Authors: Snellman, J. E.; Brandenburg, A.; Käpylä, P. J.; Mantere,
M. J.
2012AN....333...78S Altcode: 2011arXiv1109.4857S
We determine the timescales associated with turbulent decay }and
isotropization in closure models using anisotropically forced and
freely decaying turbulence simulations and study the applicability
of these models. We compare the results from anisotropically forced
three-dimensional numerical simulations with the predictions of the
closure models and obtain the turbulent timescales mentioned above
as functions of the Reynolds number. In a second set of simulations,
turning the forcing off enables us to study the validity of the
closures in freely decaying turbulence. Both types of experiments
suggest that the timescale of turbulent decay converges to a constant
value at higher Reynolds numbers. Furthermore, the relative importance
of isotropization is found to be about 2.5 times larger at higher
Reynolds numbers than in the more viscous regime.

---------------------------------------------------------
Title: Modeling spatio-temporal nonlocality in mean-field dynamos
Authors: Rheinhardt, M.; Brandenburg, A.
2012AN....333...71R Altcode: 2011arXiv1110.2891R
When scale separation in space and time is poor, the alpha effect and
turbulent diffusivity have to be replaced by integral kernels. Earlier
work in computing these kernels using the test-field method is now
generalized to the case in which both spatial and temporal scale
separations are poor. The approximate form of the kernel is such that
it can be treated in a straightforward manner by solving a partial
differential equation for the mean electromotive force. The resulting
mean-field equations are solved for oscillatory alpha-shear dynamos
as well as alpha^2 dynamos in which alpha is antisymmetric about
the equator, making this dynamo also oscillatory. In both cases, the
critical values of the dynamo number is lowered by the fact that the
dynamo is oscillatory.

---------------------------------------------------------
Title: Theoretical comparison of plasma and magnetic feature tracking
(MFT) flows: a perspective for assimilating meridional flow data in
flux-transport models
Authors: Guerrero, G.; Rheinhardt, M.; Brandenburg, A.; Dikpati, M.
2011AGUFMSH54A..03G Altcode:
Doppler measurements of the poleward flow speed at the solar surface
reveal a systematic difference from the speed inferred from magnetic
feature-tracking (MFT). In order to understand the reason for this
difference we simulate the MFT speed using advective-diffusive transport
models in both one and two dimensions. By depositing magnetic bipolar
regions at different latitudes at the Sun's surface and following
their evolution for a prescribed meridional circulation and magnetic
diffusivity profiles, we derive the MFT speed as a function of
latitude. We find that in a one dimensional surface-transport model
the simulated MFT speed at the surface is always the same as the
meridional flow-speed used as input to the model, but is different in
a two-dimensional transport model in the meridional (r,θ) plane. The
difference depends on the value of the magnetic diffusivity and on
the radial gradient of the latitudinal velocity. We have confirmed
our results with two different codes in spherical and Cartesian
coordinates. The possibility of assimilate time-varying meridional
flow data in flux-transport dynamo models is also discussed.

---------------------------------------------------------
Title: Effects of stratification in spherical shell convection
Authors: Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2011AN....332..883K Altcode: 2011arXiv1109.4625K
We report on simulations of mildly turbulent convection in spherical
wedge geometry with varying density stratification. We vary the density
contrast within the convection zone by a factor of 20 and study the
influence of rotation on the solutions. We demonstrate that the size of
convective cells decreases and the anisotropy of turbulence increases
as the stratification is increased. Differential rotation is found to
change from anti-solar (slow equator) to solar-like (fast equator) at
roughly the same Coriolis number for all stratifications. The largest
stratification runs, however, are sensitive to changes of the Reynolds
number. Evidence for a near-surface shear layer is found in runs with
strong stratification and large Reynolds numbers.

---------------------------------------------------------
Title: Pumping velocity in homogeneous helical turbulence with shear
Authors: Rogachevskii, Igor; Kleeorin, Nathan; Käpylä, Petri J.;
Brandenburg, Axel
2011PhRvE..84e6314R Altcode: 2011arXiv1105.5785R
Using different analytical methods (the quasilinear approach, the
path-integral technique, and the tau-relaxation approximation) we
develop a comprehensive mean-field theory for a pumping effect of the
mean magnetic field in homogeneous nonrotating helical turbulence
with imposed large-scale shear. The effective pumping velocity is
proportional to the product of α effect and large-scale vorticity
associated with the shear, and causes a separation of the toroidal and
poloidal components of the mean magnetic field along the direction of
the mean vorticity. We also perform direct numerical simulations of
sheared turbulence in different ranges of hydrodynamic and magnetic
Reynolds numbers and use a kinematic test-field method to determine the
effective pumping velocity. The results of the numerical simulations
are in agreement with the theoretical predictions.

---------------------------------------------------------
Title: Nonlinear Small-scale Dynamos at Low Magnetic Prandtl Numbers
Authors: Brandenburg, Axel
2011ApJ...741...92B Altcode: 2011arXiv1106.5777B
Saturated small-scale dynamo solutions driven by isotropic non-helical
turbulence are presented at low magnetic Prandtl numbers Pr
M down to 0.01. For Pr M &lt; 0.1, most of the
energy is dissipated via Joule heat and, in agreement with earlier
results for helical large-scale dynamos, kinetic energy dissipation
is shown to diminish proportional to Pr1/2 M 
down to values of 0.1. In agreement with earlier work, there is,
in addition to a short Golitsyn k -11/3 spectrum near
the resistive scale, also some evidence for a short k -1
spectrum on larger scales. The rms magnetic field strength of the
small-scale dynamo is found to depend only weakly on the value of
Pr M and decreases by about a factor of two as Pr M
 is decreased from 1 to 0.01. The possibility of dynamo action
at Pr M = 0.1 in the nonlinear regime is argued to be a
consequence of a suppression of the bottleneck seen in the kinetic
energy spectrum in the absence of a dynamo and, more generally,
a suppression of kinetic energy near the dissipation wavenumber.

---------------------------------------------------------
Title: The fratricide of αΩ dynamos by their α2 siblings
Authors: Hubbard, A.; Rheinhardt, M.; Brandenburg, A.
2011A&A...535A..48H Altcode: 2011arXiv1102.2617H
Context. Helically forced magneto-hydrodynamic shearing-sheet turbulence
can support different large-scale dynamo modes, although the αΩ mode
is generally expected to dominate because it is the fastest growing
one. In an αΩ dynamo, most of the field amplification is produced by
the shear. As differential rotation is an ubiquitous source of shear
in astrophysics, such dynamos are believed to be the source of most
astrophysical large-scale magnetic fields. Aims: We study the
stability of oscillatory migratory αΩ type dynamos in turbulence
simulations. Methods: We use shearing-sheet simulations of
hydromagnetic turbulence that is helically forced at a wavenumber that
is about three times larger than the lowest wavenumber in the domain
so that both αΩ and α2 dynamo action is possible. 
Results: After initial dominance and saturation, the αΩ mode is found
to be destroyed by an orthogonal α2 mode sustained by the
helical turbulence alone. We show that there are at least two processes
through which this transition can occur. Conclusions: The
fratricide of αΩ dynamos by its α2 sibling is discussed
in the context of grand minima of stellar activity. However, the genesis
of αΩ dynamos from an α2 dynamo has not yet been found.

---------------------------------------------------------
Title: Model of driven and decaying magnetic turbulence in a cylinder
Authors: Kemel, Koen; Brandenburg, Axel; Ji, Hantao
2011PhRvE..84e6407K Altcode: 2011arXiv1106.1129K
Using mean-field theory, we compute the evolution of the magnetic
field in a cylinder with outer perfectly conducting boundaries and
imposed axial magnetic and electric fields. The thus injected magnetic
helicity in the system can be redistributed by magnetic helicity fluxes
down the gradient of the local current helicity of the small-scale
magnetic field. A weak reversal of the axial magnetic field is found
to be a consequence of the magnetic helicity flux in the system. Such
fluxes are known to alleviate so-called catastrophic quenching of the α
effect in astrophysical applications. A stronger field reversal can be
obtained if there is also a significant kinetic α effect. Application
to the reversed field pinch in plasma confinement devices is discussed.

---------------------------------------------------------
Title: Detection of Negative Effective Magnetic Pressure Instability
in Turbulence Simulations
Authors: Brandenburg, Axel; Kemel, Koen; Kleeorin, Nathan; Mitra,
Dhrubaditya; Rogachevskii, Igor
2011ApJ...740L..50B Altcode: 2011arXiv1109.1270B
We present the first numerical demonstration of the negative effective
magnetic pressure instability in direct numerical simulations of stably
stratified, externally forced, isothermal hydromagnetic turbulence in
the regime of large plasma beta. By the action of this instability,
initially uniform horizontal magnetic field forms flux concentrations
whose scale is large compared to the turbulent scale. We further
show that the magnetic energy of these large-scale structures is only
weakly dependent on the magnetic Reynolds number. Our results support
earlier mean-field calculations and analytic work that identified this
instability. Applications to the formation of active regions in the
Sun are discussed.

---------------------------------------------------------
Title: Dynamo-driven plasmoid ejections above a spherical surface
Authors: Warnecke, J.; Brandenburg, A.; Mitra, D.
2011A&A...534A..11W Altcode: 2011arXiv1104.0664W
 Aims: We extend earlier models of turbulent dynamos with an
upper, nearly force-free exterior to spherical geometry, and study how
flux emerges from lower layers to the upper ones without being driven
by magnetic buoyancy. We also study how this affects the possibility
of plasmoid ejection. Methods: A spherical wedge is used that
includes northern and southern hemispheres up to mid-latitudes and a
certain range in longitude of the Sun. In radius, we cover both the
region that corresponds to the convection zone in the Sun and the
immediate exterior up to twice the radius of the Sun. Turbulence
is driven with a helical forcing function in the interior, where
the sign changes at the equator between the two hemispheres. 
Results: An oscillatory large-scale dynamo with equatorward migration
is found to operate in the turbulence zone. Plasmoid ejections occur
in regular intervals, similar to what is seen in earlier Cartesian
models. These plasmoid ejections are tentatively associated with coronal
mass ejections (CMEs). The magnetic helicity is found to change sign
outside the turbulence zone, which is in agreement with recent findings
for the solar wind. Movie is available in electronic form at <A
href="http://www.aanda.org">http://www.aanda.org</A>

---------------------------------------------------------
Title: Theoretical comparison of plasma flow and magnetic feature
tracking speeds in the Sun
Authors: Guerrero, G.; Rheinhardt, M.; Brandenburg, A.; Dikpati, M.
2011sdmi.confE..94G Altcode:
Doppler measurements of the poleward flow speed at the solar
surface reveal a systematic difference from the speed inferred from
magnetic feature-tracking (MFT). In order to understand the reason
for this difference we simulate the magnetic feature tracking (MFT)
speed using advective-diffusive transport models in both one and
two dimensions. By depositing magnetic bipolar regions at different
latitudes at the Sun's surface and following their evolution for a
prescribed meridional circulation and magnetic diffusivity profiles,
we derive the MFT speed as a function of latitude. We find that in a
one dimensional surface-transport model the simulated MFT speed at the
surface is always the same as the meridional flow-speed used as input
to the model, but is different in a two-dimensional transport model
in the meridional (r, theta) plane. The difference depends on the
value of the magnetic diffusivity and on the radial gradient of the
latitudinal velocity. We have confirmed our results with two different
codes in spherical and Cartesian coordinates.

---------------------------------------------------------
Title: Active regions from near-surface dynamics
Authors: Brandenburg, Axel; Kemel, Koen; Kleeorin, Nathan; Mitra,
Dhrubaditya; Rogachevskii, Igor
2011sdmi.confE..38B Altcode:
We present the first numerical demonstration of the negative effective
magnetic pressure instability in direct numerical simulations
of stably-stratified, externally-forced, isothermal hydromagnetic
turbulence in the regime of large plasma beta. By the action of this
instability, initially uniform horizontal magnetic field forms flux
concentrations whose scale is large compared to the turbulent scale. We
further show that the magnetic energy of these large-scale structures
is only weakly dependent on the magnetic Reynolds number. Our results
support earlier mean-field calculations and analytic work which
identified this instability. Applications to the formation of active
regions in the Sun are discussed.

---------------------------------------------------------
Title: Mean-field diffusivities in passive scalar and magnetic
transport in irrotational flows
Authors: Rädler, Karl-Heinz; Brandenburg, Axel; Del Sordo, Fabio;
Rheinhardt, Matthias
2011PhRvE..84d6321R Altcode: 2011arXiv1104.1613R
Certain aspects of the mean-field theory of turbulent passive
scalar transport and of mean-field electrodynamics are considered
with particular emphasis on aspects of compressible fluids. It
is demonstrated that the total mean-field diffusivity for passive
scalar transport in a compressible flow may well be smaller than the
molecular diffusivity. This is in full analogy to an old finding
regarding the magnetic mean-field diffusivity in an electrically
conducting turbulently moving compressible fluid. These phenomena
occur if the irrotational part of the motion dominates the vortical
part, the Péclet or magnetic Reynolds number is not too large, and,
in addition, the variation of the flow pattern is slow. For both
the passive scalar and the magnetic cases several further analytical
results on mean-field diffusivities and related quantities found within
the second-order correlation approximation are presented, as well as
numerical results obtained by the test-field method, which applies
independently of this approximation. Particular attention is paid to
nonlocal and noninstantaneous connections between the turbulence-caused
terms and the mean fields. Two examples of irrotational flows, in
which interesting phenomena in the above sense occur, are investigated
in detail. In particular, it is demonstrated that the decay of a mean
scalar in a compressible fluid under the influence of these flows can
be much slower than without any flow, and can be strongly influenced
by the so-called memory effect, that is, the fact that the relevant
mean-field coefficients depend on the decay rates themselves.

---------------------------------------------------------
Title: Alpha effect due to buoyancy instability of a magnetic layer
Authors: Chatterjee, P.; Mitra, D.; Rheinhardt, M.; Brandenburg, A.
2011A&A...534A..46C Altcode: 2010arXiv1011.1218C
Context. A strong toroidal field can exist in form of a magnetic
layer in the overshoot region below the solar convection zone. This
motivates a more detailed study of the magnetic buoyancy instability
with rotation. Aims: We calculate the α effect due to
helical motions caused by an unstable magnetic layer in a rotating
density-stratified system with angular velocity Ω making an angle
θ with the vertical. We also study the dependence of the α effect
on θ and the strength of the initial magnetic field. Methods:
We carry out three-dimensional hydromagnetic simulations in Cartesian
geometry. A turbulent electromotive force (EMF) due to the correlations
of the small scale velocity and magnetic field is generated. We use
the test-field method to calculate the transport coefficients of
the inhomogeneous turbulence produced by the layer. Results:
We show that the growth rate of the instability and the twist of the
magnetic field vary monotonically with the ratio of thermal conductivity
to magnetic diffusivity. The resulting α effect is non-uniform and
increases with the strength of the initial magnetic field. It is thus
an example of an "anti-quenched" α effect. The α effect is also
nonlocal, i.e. scale dependent, requiring around 8-16 Fourier modes
to reconstruct the actual mean EMF based on the actual mean field.

---------------------------------------------------------
Title: Shear-driven Instabilities in Hall-magnetohydrodynamic Plasmas
Authors: Bejarano, Cecilia; Gómez, Daniel O.; Brandenburg, Axel
2011ApJ...737...62B Altcode: 2010arXiv1012.5284B
The large-scale dynamics of plasmas is well described within the
framework of magnetohydrodynamics (MHD). However, whenever the ion
density of the plasma becomes sufficiently low, the Hall effect is
likely to become important. The role of the Hall effect has been
studied in several astrophysical plasma processes, such as magnetic
reconnection, magnetic dynamo, MHD turbulence, or MHD instabilities. In
particular, the development of small-scale instabilities is essential
to understand the transport properties in a number of astrophysical
plasmas. The magneto-rotational instability (MRI), which takes place
in differentially rotating accretion disks embedded in relatively weak
magnetic fields, is just one example. The influence of the large-scale
velocity flows on small-scale instabilities is often approximated by a
linear shear flow. In this paper, we quantitatively study the role of
the Hall effect on plasmas embedded in large-scale shear flows. More
precisely, we show that an instability develops when the Hall
effect is present, which we therefore term as the Hall magneto-shear
instability. As a particular case, we recover the so-called MRI and
quantitatively assess the role of the Hall effect on its development
and evolution.

---------------------------------------------------------
Title: The negative magnetic pressure effect in stratified turbulence
Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2011IAUS..273...83K Altcode: 2010arXiv1010.1659K
While the rising flux tube paradigm is an elegant theory, its basic
assumptions, thin flux tubes at the bottom of the convection zone with
field strengths two orders of magnitude above equipartition, remain
numerically unverified at best. As such, in recent years the idea of a
formation of sunspots near the top of the convection zone has generated
some interest. The presence of turbulence can strongly enhance diffusive
transport mechanisms, leading to an effective transport coefficient
formalism in the mean-field formulation. The question is what happens
to these coefficients when the turbulence becomes anisotropic due to a
strong large-scale mean magnetic field. It has been noted in the past
that this anisotropy can also lead to highly non-diffusive behavior. In
the present work we investigate the formation of large-scale magnetic
structures as a result of a negative contribution of turbulence
to the large-scale effective magnetic pressure in the presence of
stratification. In direct numerical simulations of forced turbulence
in a stratified box, we verify the existence of this effect. This
phenomenon can cause formation of large-scale magnetic structures even
from initially uniform large-scale magnetic field.

---------------------------------------------------------
Title: Recurrent flux emergence from dynamo-generated fields
Authors: Warnecke, Jörn; Brandenburg, Axel
2011IAUS..271..407W Altcode: 2010arXiv1008.5278W
we investigate the emergence of a large-scale magnetic field. This
field is dynamo-generated by turbulence driven with a helical forcing
function. Twisted arcade-like field structures are found to emerge in
the exterior above the turbulence zone. Time series of the magnetic
field structure show recurrent plasmoid ejections.

---------------------------------------------------------
Title: Vorticity from irrotationally forced flow
Authors: Del Sordo, Fabio; Brandenburg, Axel
2011IAUS..271..375D Altcode: 2010arXiv1009.0147D; 2011IAUS..271..375S
In the interstellar medium the turbulence is believed to be forced
mostly through supernova explosions. In a first approximation these
flows can be written as a gradient of a potential being thus devoid of
vorticity. There are several mechanisms that could lead to vorticity
generation, like viscosity and baroclinic terms, rotation, shear and
magnetic fields, but it is not clear how effective they are, neither
is it clear whether the vorticity is essential in determining the
turbulent diffusion acting in the ISM. Here we present a study of
the role of rotation, shear and baroclinicity in the generation of
vorticity in the ISM.

---------------------------------------------------------
Title: Dynamo generated field emergence through recurrent plasmoid
ejections
Authors: Warnecke, Jörn; Brandenburg, Axel
2011IAUS..273..256W Altcode: 2010arXiv1010.0218W
Magnetic buoyancy is believed to drive the transport of magnetic flux
tubes from the convection zone to the surface of the Sun. The magnetic
fields form twisted loop-like structures in the solar atmosphere. In
this paper we use helical forcing to produce a large-scale
dynamo-generated magnetic field, which rises even without magnetic
buoyancy. A two layer system is used as computational domain where the
upper part represents the solar atmosphere. Here, the evolution of the
magnetic field is solved with the stress-and-relax method. Below this
region a magnetic field is produced by a helical forcing function in
the momentum equation, which leads to dynamo action. We find twisted
magnetic fields emerging frequently to the outer layer, forming
arch-like structures. In addition, recurrent plasmoid ejections can be
found by looking at space-time diagrams of the magnetic field. Recent
simulations in spherical coordinates show similar results.

---------------------------------------------------------
Title: Turbulence and magnetic spots at the surface of hot massive
stars
Authors: Cantiello, Matteo; Braithwaite, Jonathan; Brandenburg, Axel;
Del Sordo, Fabio; Käpylä, Petri; Langer, Norbert
2011IAUS..273..200C Altcode: 2010arXiv1010.2498C
Hot luminous stars show a variety of phenomena in their photospheres
and in their winds which still lack clear physical explanations at
this time. Among these phenomena are non-thermal line broadening, line
profile variability (LPVs), discrete absorption components (DACs), wind
clumping and stochastically excited pulsations. Cantiello et al. (2009)
argued that a convection zone close to the surface of hot, massive
stars, could be responsible for some of these phenomena. This convective
zone is caused by a peak in the opacity due to iron recombination
and for this reason is referred to as the “iron convection zone”
(FeCZ). 3D MHD simulations are used to explore the possible effects of
such subsurface convection on the surface properties of hot, massive
stars. We argue that turbulence and localized magnetic spots at the
surface are the likely consequence of subsurface convection in early
type stars.

---------------------------------------------------------
Title: Influence of Magnetic Helicity in MHD
Authors: Candelaresi, Simon; Del Sordo, Fabio; Brandenburg, Axel
2011IAUS..271..369C Altcode: 2010arXiv1008.5235C
Observations have shown that the Sun's magnetic field has helical
structures. The helicity content in magnetic field configurations is
a crucial constraint on the dynamical evolution of the system. Since
helicity is connected with the number of links we investigate
configurations with interlocked magnetic flux rings and one with
unlinked rings. It turns out that it is not the linking of the tubes
which affects the magnetic field decay, but the content of magnetic
helicity.

---------------------------------------------------------
Title: Spontaneous chiral symmetry breaking by hydromagnetic buoyancy
Authors: Chatterjee, Piyali; Mitra, Dhrubaditya; Brandenburg, Axel;
Rheinhardt, Matthias
2011PhRvE..84b5403C Altcode: 2010arXiv1011.1251C
Evidence for the parity-breaking nature of the magnetic buoyancy
instability in a stably stratified gas is reported. In the absence
of rotation, no helicity is produced, but the nonhelical state
is found to be unstable to small helical perturbations during the
development of the instability. The parity-breaking nature of this
magnetohydrodynamic instability appears to be the first of its kind
and has properties similar to those in chiral symmetry breaking in
biochemistry. Applications to the production of mean fields in galaxy
clusters are discussed.

---------------------------------------------------------
Title: From convective to stellar dynamos
Authors: Brandenburg, Axel; Käpylä, Petri J.; Korpi, Maarit J.
2011IAUS..271..279B Altcode: 2011arXiv1103.5475B
Convectively driven dynamos with rotation generating magnetic fields
on scales large compared with the scale of the turbulent eddies are
being reviewed. It is argued that such fields can be understood as
the result of an α effect. Simulations in Cartesian domains show that
such large-scale magnetic fields saturate on a time scale compatible
with the resistive one, suggesting that the magnitude of the α
effect is here still constrained by approximate magnetic helicity
conservation. It is argued that, in the absence of shear and/or any
other known large-scale dynamo effects, these simulations prove the
existence of turbulent α2-type dynamos. Finally, recent
results are discussed in the context of solar and stellar dynamos.

---------------------------------------------------------
Title: 3D MHD simulations of subsurface convection in OB stars
Authors: Cantiello, Matteo; Braithwaite, Jonathan; Brandenburg, Axel;
Del Sordo, Fabio; Käpylä, Petri; Langer, Norbert
2011IAUS..272...32C Altcode: 2010arXiv1009.4462C
During their main sequence evolution, massive stars can develop
convective regions very close to their surface. These regions are
caused by an opacity peak associated with iron ionization. Cantiello
et al. (2009) found a possible connection between the presence
of sub-photospheric convective motions and small scale stochastic
velocities in the photosphere of early-type stars. This supports
a physical mechanism where microturbulence is caused by waves that
are triggered by subsurface convection zones. They further suggest
that clumping in the inner parts of the winds of OB stars could be
related to subsurface convection, and that the convective layers
may also be responsible for stochastic excitation of non-radial
pulsations. Furthermore, magnetic fields produced in the iron convection
zone could appear at the surface of such massive stars. Therefore
subsurface convection could be responsible for the occurrence of
observable phenomena such as line profile variability and discrete
absorption components. These phenomena have been observed for decades,
but still evade a clear theoretical explanation. Here we present
preliminary results from 3D MHD simulations of such subsurface
convection.

---------------------------------------------------------
Title: Lagrangian Coherent Structures in Nonlinear Dynamos
Authors: Rempel, E. L.; Chian, A. C. -L.; Brandenburg, A.
2011ApJ...735L...9R Altcode: 2010arXiv1011.6327R
Turbulence and chaos play a fundamental role in stellar convective
zones through the transport of particles, energy, and momentum, and in
fast dynamos, through the stretching, twisting, and folding of magnetic
flux tubes. A particularly revealing way to describe turbulent motions
is through the analysis of Lagrangian coherent structures (LCSs),
which are material lines or surfaces that act as transport barriers
in the fluid. We report the detection of LCSs in helical MHD dynamo
simulations with scale separation. In an Arnold-Beltrami-Childress
flow, two dynamo regimes, a propagating coherent mean-field regime and
an intermittent regime, are identified as the magnetic diffusivity is
varied. The sharp contrast between the chaotic tangle of attracting and
repelling LCSs in both regimes permits a unique analysis of the impact
of the magnetic field on the velocity field. In a second example, LCSs
reveal the link between the level of chaotic mixing of the velocity
field and the saturation of a large-scale dynamo when the magnetic
field exceeds the equipartition value.

---------------------------------------------------------
Title: Chandrasekhar-Kendall functions in astrophysical dynamos
Authors: Brandenburg, Axel
2011Prama..77...67B Altcode: 2011arXiv1103.4976B
Some of the contributions of Chandrasekhar to the field of
magnetohydrodynamics are highlighted. Particular emphasis is placed
on the Chandrasekhar-Kendall functions that allow a decomposition of
a vector field into right- and left-handed contributions. Magnetic
energy spectra of both contributions are shown for a new set of
helically forced simulations at resolutions higher than what has been
available so far. For a forcing function with positive helicity, these
simulations show a forward cascade of the right-handed contributions
to the magnetic field and nonlocal inverse transfer for the left-handed
contributions. The speed of inverse transfer is shown to decrease with
increasing value of the magnetic Reynolds number.

---------------------------------------------------------
Title: Decay of helical and nonhelical magnetic knots
Authors: Candelaresi, Simon; Brandenburg, Axel
2011PhRvE..84a6406C Altcode: 2011arXiv1103.3518C
We present calculations of the relaxation of magnetic field structures
that have the shape of particular knots and links. A set of helical
magnetic flux configurations is considered, which we call n-foil
knots of which the trefoil knot is the most primitive member. We also
consider two nonhelical knots; namely, the Borromean rings as well
as a single interlocked flux rope that also serves as the logo of
the Inter-University Centre for Astronomy and Astrophysics in Pune,
India. The field decay characteristics of both configurations is
investigated and compared with previous calculations of helical and
nonhelical triple-ring configurations. Unlike earlier nonhelical
configurations, the present ones cannot trivially be reduced
via flux annihilation to a single ring. For the n-foil knots the
decay is described by power laws that range form t-2/3 to
t-1/3, which can be as slow as the t-1/3 behavior
for helical triple-ring structures that were seen in earlier work. The
two nonhelical configurations decay like t-1, which is
somewhat slower than the previously obtained t-3/2 behavior
in the decay of interlocked rings with zero magnetic helicity. We
attribute the difference to the creation of local structures that
contain magnetic helicity which inhibits the field decay due to the
existence of a lower bound imposed by the realizability condition. We
show that net magnetic helicity can be produced resistively as
a result of a slight imbalance between mutually canceling helical
pieces as they are being driven apart. We speculate that higher order
topological invariants beyond magnetic helicity may also be responsible
for slowing down the decay of the two more complicated nonhelical
structures mentioned above.

---------------------------------------------------------
Title: Reynolds stress and heat flux in spherical shell convection
Authors: Käpylä, P. J.; Mantere, M. J.; Guerrero, G.; Brandenburg,
A.; Chatterjee, P.
2011A&A...531A.162K Altcode: 2010arXiv1010.1250K
Context. Turbulent fluxes of angular momentum and enthalpy or heat due
to rotationally affected convection play a key role in determining
differential rotation of stars. Their dependence on latitude and
depth has been determined in the past from convection simulations
in Cartesian or spherical simulations. Here we perform a systematic
comparison between the two geometries as a function of the rotation
rate. Aims: Here we want to extend the earlier studies by
using spherical wedges to obtain turbulent angular momentum and
heat transport as functions of the rotation rate from stratified
convection. We compare results from spherical and Cartesian models
in the same parameter regime in order to study whether restricted
geometry introduces artefacts into the results. In particular,
we want to clarify whether the sharp equatorial profile of the
horizontal Reynolds stress found in earlier Cartesian models is
also reproduced in spherical geometry. Methods: We employ
direct numerical simulations of turbulent convection in spherical
and Cartesian geometries. In order to alleviate the computational
cost in the spherical runs, and to reach as high spatial resolution
as possible, we model only parts of the latitude and longitude. The
rotational influence, measured by the Coriolis number or inverse Rossby
number, is varied from zero to roughly seven, which is the regime
that is likely to be realised in the solar convection zone. Cartesian
simulations are performed in overlapping parameter regimes. 
Results: For slow rotation we find that the radial and latitudinal
turbulent angular momentum fluxes are directed inward and equatorward,
respectively. In the rapid rotation regime the radial flux changes sign
in accordance with earlier numerical results, but in contradiction with
theory. The latitudinal flux remains mostly equatorward and develops
a maximum close to the equator. In Cartesian simulations this peak
can be explained by the strong "banana cells". Their effect in the
spherical case does not appear to be as large. The latitudinal heat
flux is mostly equatorward for slow rotation but changes sign for
rapid rotation. Longitudinal heat flux is always in the retrograde
direction. The rotation profiles vary from anti-solar (slow equator) for
slow and intermediate rotation to solar-like (fast equator) for rapid
rotation. The solar-like profiles are dominated by the Taylor-Proudman
balance. Movies and Appendix A are available in electronic form
at <A href="http://www.aanda.org">http://www.aanda.org</A>

---------------------------------------------------------
Title: How can vorticity be produced in irrotationally forced flows?
Authors: Sordo, Fabio Del; Brandenburg, Axel
2011IAUS..274..373S Altcode: 2010arXiv1012.4772D
A spherical hydrodynamical expansion flow can be described as the
gradient of a potential. In that case no vorticity should be produced,
but several additional mechanisms can drive its production. Here we
analyze the effects of baroclinicity, rotation and shear in the case of
a viscous fluid. Those flows resemble what happens in the interstellar
medium. In fact in this astrophysical environment supernovae explosion
are the dominant flows and, in a first approximation, they can be seen
as spherical. One of the main difference is that in our numerical study
we examine only weakly supersonic flows, while supernovae explosions
are strongly supersonic.

---------------------------------------------------------
Title: Magnetic helicity fluxes in αΩ dynamos
Authors: Candelaresi, Simon; Brandenburg, Axel
2011IAUS..274..464C Altcode: 2010arXiv1012.4354C
In turbulent dynamos the production of large-scale magnetic fields is
accompanied by a separation of magnetic helicity in scale. The large-
and small-scale parts increase in magnitude. The small-scale part can
eventually work against the dynamo and quench it, especially at high
magnetic Reynolds numbers. A one-dimensional mean-field model of a
dynamo is presented where diffusive magnetic helicity fluxes within
the domain are important. It turns out that this effect helps to
alleviate the quenching. Here we show that internal magnetic helicity
fluxes, even within one hemisphere, can be important for alleviating
catastrophic quenching.

---------------------------------------------------------
Title: Plasmoid ejections driven by dynamo action underneath a
spherical surface
Authors: Warnecke, Jörn; Brandenburg, Axel; Mitra, Dhrubaditya
2011IAUS..274..306W Altcode: 2010arXiv1011.4299W
We present a unified three-dimensional model of the convection
zone and upper atmosphere of the Sun in spherical geometry. In
this model, magnetic fields, generated by a helically forced dynamo
in the convection zone, emerge without the assistance of magnetic
buoyancy. We use an isothermal equation of state with gravity and
density stratification. Recurrent plasmoid ejections, which rise
through the outer atmosphere, is observed. In addition, the current
helicity of the small-scale field is transported outwards and form
large structures like magnetic clouds.

---------------------------------------------------------
Title: Decay of trefoil and other magnetic knots
Authors: Candelaresi, Simon; Del Sordo, Fabio; Brandenburg, Axel
2011IAUS..274..461C Altcode: 2010arXiv1011.0417C
Two setups with interlocked magnetic flux tubes are used to study the
evolution of magnetic energy and helicity on magnetohydrodynamical
(MHD) systems like plasmas. In one setup the initial helicity is zero
while in the other it is finite. To see if it is the actual linking
or merely the helicity content that influences the dynamics of the
system we also consider a setup with unlinked field lines as well
as a field configuration in the shape of a trefoil knot. For helical
systems the decay of magnetic energy is slowed down by the helicity
which decays slowly. It turns out that it is the helicity content,
rather than the actual linking, that is significant for the dynamics.

---------------------------------------------------------
Title: Simulations of astrophysical dynamos
Authors: Brandenburg, Axel
2011IAUS..274..402B Altcode: 2010arXiv1012.5079B
Numerical aspects of dynamos in periodic domains are
discussed. Modifications of the solutions by numerically motivated
alterations of the equations are being reviewed using the examples of
magnetic hyperdiffusion and artificial diffusion when advancing the
magnetic field in its Euler potential representation. The importance
of using integral kernel formulations in mean-field dynamo theory is
emphasized in cases where the dynamo growth rate becomes comparable with
the inverse turnover time. Finally, the significance of microscopic
magnetic Prandtl number in controlling the conversion from kinetic to
magnetic energy is highlighted.

---------------------------------------------------------
Title: Scale Dependence of Magnetic Helicity in the Solar Wind
Authors: Brandenburg, Axel; Subramanian, Kandaswamy; Balogh, André;
Goldstein, Melvyn L.
2011ApJ...734....9B Altcode: 2011arXiv1101.1709B
We determine the magnetic helicity, along with the magnetic energy,
at high latitudes using data from the Ulysses mission. The data set
spans the time period from 1993 to 1996. The basic assumption of the
analysis is that the solar wind is homogeneous. Because the solar wind
speed is high, we follow the approach first pioneered by Matthaeus
et al. by which, under the assumption of spatial homogeneity, one can
use Fourier transforms of the magnetic field time series to construct
one-dimensional spectra of the magnetic energy and magnetic helicity
under the assumption that the Taylor frozen-in-flow hypothesis is
valid. That is a well-satisfied assumption for the data used in
this study. The magnetic helicity derives from the skew-symmetric
terms of the three-dimensional magnetic correlation tensor, while
the symmetric terms of the tensor are used to determine the magnetic
energy spectrum. Our results show a sign change of magnetic helicity
at wavenumber k ≈ 2 AU-1 (or frequency ν ≈ 2 μHz)
at distances below 2.8 AU and at k ≈ 30 AU-1 (or ν ≈
25 μHz) at larger distances. At small scales the magnetic helicity is
positive at northern heliographic latitudes and negative at southern
latitudes. The positive magnetic helicity at small scales is argued
to be the result of turbulent diffusion reversing the sign relative
to what is seen at small scales at the solar surface. Furthermore,
the magnetic helicity declines toward solar minimum in 1996. The
magnetic helicity flux integrated separately over one hemisphere
amounts to about 1045 Mx2 cycle-1
at large scales and to a three times lower value at smaller scales.

---------------------------------------------------------
Title: Turbulent magnetic pressure instability in stratified
turbulence
Authors: Kemel, K.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2011IAUS..274..473K Altcode: 2010arXiv1012.4360K
A reduction of total mean turbulent pressure due to the presence of
magnetic fields was previously shown to be a measurable effect in
direct numerical simulations. However, in the studied parameter regime
the formation of large-scale structures, as anticipated from earlier
mean-field simulations, was not found. An analysis of the relevant
mean-field parameter dependency and the parameter domain of interest
is conducted in order to clarify this apparent discrepancy.

---------------------------------------------------------
Title: Vorticity production through rotation, shear, and baroclinicity
Authors: Del Sordo, F.; Brandenburg, A.
2011A&A...528A.145D Altcode: 2010arXiv1008.5281D
Context. In the absence of rotation and shear, and under the assumption
of constant temperature or specific entropy, purely potential forcing
by localized expansion waves is known to produce irrotational flows
that have no vorticity. Aims: Here we study the production of
vorticity under idealized conditions when there is rotation, shear,
or baroclinicity, to address the problem of vorticity generation in
the interstellar medium in a systematic fashion. Methods:
We use three-dimensional periodic box numerical simulations to
investigate the various effects in isolation. Results: We find
that for slow rotation, vorticity production in an isothermal gas is
small in the sense that the ratio of the root-mean-square values of
vorticity and velocity is small compared with the wavenumber of the
energy-carrying motions. For Coriolis numbers above a certain level,
vorticity production saturates at a value where the aforementioned
ratio becomes comparable with the wavenumber of the energy-carrying
motions. Shear also raises the vorticity production, but no saturation
is found. When the assumption of isothermality is dropped, there
is significant vorticity production by the baroclinic term once
the turbulence becomes supersonic. In galaxies, shear and rotation
are estimated to be insufficient to produce significant amounts of
vorticity, leaving therefore only the baroclinic term as the most
favorable candidate. We also demonstrate vorticity production visually
as a result of colliding shock fronts.

---------------------------------------------------------
Title: Astrophysical turbulence modeling
Authors: Brandenburg, Axel; Nordlund, Åke
2011RPPh...74d6901B Altcode: 2009arXiv0912.1340B
The role of turbulence in various astrophysical settings
is reviewed. Among the differences to laboratory and atmospheric
turbulence we highlight the ubiquitous presence of magnetic fields that
are generally produced and maintained by dynamo action. The extreme
temperature and density contrasts and stratifications are emphasized
in connection with turbulence in the interstellar medium and in stars
with outer convection zones, respectively. In many cases turbulence
plays an essential role in facilitating enhanced transport of mass,
momentum, energy and magnetic fields in terms of the corresponding
coarse-grained mean fields. Those transport properties are usually
strongly modified by anisotropies and often completely new effects
emerge in such a description that have no correspondence in terms of
the original (non-coarse-grained) fields.

---------------------------------------------------------
Title: Cross Helicity and Turbulent Magnetic Diffusivity in the
Solar Convection Zone
Authors: Rüdiger, G.; Kitchatinov, L. L.; Brandenburg, A.
2011SoPh..269....3R Altcode: 2010arXiv1004.4881R; 2010SoPh..tmp..241R
In a density-stratified turbulent medium, the cross helicity
«u'⋅B'» is considered as a result of the interaction of the
velocity fluctuations and a large-scale magnetic field. By means of
a quasilinear theory and by numerical simulations, we find the cross
helicity and the mean vertical magnetic field to be anti-correlated. In
the high-conductivity limit the ratio of the helicity and the mean
magnetic field equals the ratio of the magnetic eddy diffusivity and
the (known) density scale height. The result can be used to predict
that the cross helicity at the solar surface will exceed the value of
1 gauss km s−1. Its sign is anti-correlated to that of
the radial mean magnetic field. Alternatively, we can use our result
to determine the value of the turbulent magnetic diffusivity from
observations of the cross helicity.

---------------------------------------------------------
Title: Turbulence Tutorial and Q&amp;A Joint Discussion of
Turbulence11 and GGlusters11 Programs
Authors: Brandenburg, Axel; Falkovich, Gregory; Kerr, Robert
2011gcca.progE..12B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Alleviating α quenching by solar wind and meridional flows
Authors: Mitra, D.; Moss, D.; Tavakol, R.; Brandenburg, A.
2011A&A...526A.138M Altcode: 2010arXiv1008.4226M
 Aims: We study the ability of magnetic helicity expulsion
to alleviate catastrophic α-quenching in mean field dynamos in
two-dimensional spherical wedge domains. Methods: Motivated
by the physical state of the outer regions of the Sun, we consider
α^2Ω mean field models with a dynamical α quenching. We include
two mechanisms which have the potential to facilitate helicity
expulsion, namely advection by a mean flow ("solar wind") and
meridional circulation. Results: We find that a wind alone can
prevent catastrophic quenching, with the field saturating at finite
amplitude. In certain parameter ranges, the presence of a large-scale
meridional circulation can reinforce this alleviation. However,
the saturated field strengths are typically below the equipartition
field strength. We discuss possible mechanisms that might increase
the saturated field.

---------------------------------------------------------
Title: Magnetic helicity fluxes in interface and flux transport
dynamos
Authors: Chatterjee, P.; Guerrero, G.; Brandenburg, A.
2011A&A...525A...5C Altcode: 2010arXiv1005.5335C
Context. Dynamos in the Sun and other bodies tend to produce magnetic
fields that possess magnetic helicity of opposite sign at large
and small scales, respectively. The build-up of magnetic helicity
at small scales provides an important saturation mechanism. 
Aims: In order to understand the nature of the solar dynamo we need
to understand the details of the saturation mechanism in spherical
geometry. In particular, we aim to understand the effects of magnetic
helicity fluxes from turbulence and meridional circulation. 
Methods: We consider a model with only radial shear confined to a
thin layer (tachocline) at the bottom of the convection zone. The
kinetic α owing to helical turbulence is assumed to be localized in a
region above the convection zone. The dynamical quenching formalism is
used to describe the build-up of mean magnetic helicity in the model,
which results in a magnetic α effect that feeds back on the kinetic α
effect. In some cases we compare these results with those obtained from
a model with a simple algebraic α quenching formula. Results: In
agreement with earlier findings, the magnetic α effect has the opposite
sign compared with the kinetic α effect and leads to a catastrophic
decrease of the saturation field strength proportional to the inverse
magnetic Reynolds number. At high latitudes this quenching effect
can lead to secondary dynamo waves that propagate poleward because
of the opposite sign of α. These secondary dynamo waves are driven
by small-scale magnetic helicity instead of the small-scale kinetic
helicity. Magnetic helicity fluxes both from turbulent mixing and from
meridional circulation alleviate catastrophic quenching. Interestingly,
supercritical diffusive helicity fluxes also give rise to secondary
dynamo waves and grand minima-like episodes.

---------------------------------------------------------
Title: Magnetic helicity transport in the advective gauge family
Authors: Candelaresi, Simon; Hubbard, Alexander; Brandenburg, Axel;
Mitra, Dhrubaditya
2011PhPl...18a2903C Altcode: 2010arXiv1010.6177C
Magnetic helicity fluxes are investigated in a family of gauges in which
the contribution from ideal magnetohydrodynamics takes the form of a
purely advective flux. Numerical simulations of magnetohydrodynamic
turbulence in this advective gauge family exhibit instabilities
triggered by the build-up of unphysical irrotational contributions to
the magnetic vector potential. As a remedy, the vector potential is
evolved in a numerically well behaved gauge, from which the advective
vector potential is obtained by a gauge transformation. In the kinematic
regime, the magnetic helicity density evolves similarly to a passive
scalar when resistivity is small and turbulent mixing is mild, i.e.,
when the fluid Reynolds number is not too large. In the dynamical
regime, resistive contributions to the magnetic helicity flux in the
advective gauge are found to be significant owing to the development
of small length scales in the irrotational part of the magnetic vector
potential.

---------------------------------------------------------
Title: A high-order public domain code for direct numerical
simulations of turbulent combustion
Authors: Babkovskaia, N.; Haugen, N. E. L.; Brandenburg, A.
2011JCoPh.230....1B Altcode: 2010arXiv1005.5301B
A high-order scheme for direct numerical simulations of turbulent
combustion is discussed. Its implementation in the massively parallel
and publicly available PENCIL CODE is validated with the focus on
hydrogen combustion. This is the first open source DNS code with
detailed chemistry available. An attempt has been made to present,
for the first time, the full set of evolution and auxiliary equations
required for a complete description of single phase non-isothermal fluid
dynamics with detailed chemical reactions. Ignition delay times (0D) and
laminar flame velocities (1D) are calculated and compared with results
from the commercially available Chemkin code. The scheme is verified
to be fifth order in space. Upon doubling the resolution, a 32-fold
increase in the accuracy of the flame front is demonstrated. Finally,
also turbulent and spherical flame front velocities are calculated
and the implementation of the non-reflecting so-called Navier-Stokes
Characteristic Boundary Condition is validated in all three directions.

---------------------------------------------------------
Title: Dissipation in dynamos at low and high magnetic Prandtl numbers
Authors: Brandenburg, A.
2011AN....332...51B Altcode: 2010arXiv1010.4805B
Using simulations of helically driven turbulence, it is shown that the
ratio of kinetic to magnetic energy dissipation scales with the magnetic
Prandtl number in power law fashion with an exponent of approximately
0.6. Over six orders of magnitude in the magnetic Prandtl number
the magnetic field is found to be sustained by large-scale dynamo
action of alpha-squared type. This work extends a similar finding
for small magnetic Prandtl numbers to the regime of large magnetic
Prandtl numbers. At large magnetic Prandtl numbers, most of the energy
is dissipated viscously, lowering thus the amount of magnetic energy
dissipation, which means that simulations can be performed at magnetic
Reynolds numbers that are large compared to the usual limits imposed
by a given resolution. This is analogous to an earlier finding that
at small magnetic Prandtl numbers, most of the energy is dissipated
resistively, lowering the amount of kinetic energy dissipation, so
simulations can then be performed at much larger fluid Reynolds numbers
than otherwise. The decrease in magnetic energy dissipation at large
magnetic Prandtl numbers is discussed in the context of underluminous
accretion found in some strut{quasars}.

---------------------------------------------------------
Title: Turbulent front speed in the Fisher equation: Dependence on
Damköhler number
Authors: Brandenburg, Axel; Haugen, Nils Erland L.; Babkovskaia,
Natalia
2011PhRvE..83a6304B Altcode: 2010arXiv1008.5145B
Direct numerical simulations and mean-field theory are used to model
reactive front propagation in a turbulent medium. In the mean-field
approach, memory effects of turbulent diffusion are taken into account
to estimate the front speed in cases in which the Damköhler number
is large. This effect is found to saturate the front speed to values
comparable with the speed of the turbulent motions. By comparing with
direct numerical simulations, it is found that the effective correlation
time is much shorter than for nonreacting flows. The nonlinearity of
the reaction term is found to make the front speed slightly faster.

---------------------------------------------------------
Title: Magnetic Helicity Flux in the Presence of Shear
Authors: Hubbard, Alexander; Brandenburg, Axel
2011ApJ...727...11H Altcode: 2010arXiv1006.3549H
Magnetic helicity has risen to be a major player in dynamo theory,
with the helicity of the small-scale field being linked to the dynamo
saturation process for the large-scale field. It is a nearly conserved
quantity, which allows its evolution equation to be written in terms of
production and flux terms. The flux term can be decomposed in a variety
of fashions. One particular contribution that has been expected to play
a significant role in dynamos in the presence of mean shear was isolated
by Vishniac &amp; Cho. Magnetic helicity fluxes are explicitly gauge
dependent however, and the correlations that have come to be called
the Vishniac-Cho flux were determined in the Coulomb gauge, which
turns out to be fraught with complications in shearing systems. While
the fluxes of small-scale helicity are explicitly gauge dependent,
their divergences can be gauge independent. We use this property to
investigate magnetic helicity fluxes of the small-scale field through
direct numerical simulations in a shearing-box system and find that in
a numerically usable gauge the divergence of the small-scale helicity
flux vanishes, while the divergence of the Vishniac-Cho flux remains
finite. We attribute this seeming contradiction to the existence
of horizontal fluxes of small-scale magnetic helicity with finite
divergences.

---------------------------------------------------------
Title: Turbulent transport in hydromagnetic flows
Authors: Brandenburg, A.; Chatterjee, P.; Del Sordo, F.; Hubbard,
A.; Käpylä, P. J.; Rheinhardt, M.
2010PhST..142a4028B Altcode: 2010arXiv1004.5380B
The predictive power of mean-field theory is emphasized by comparing
theory with simulations under controlled conditions. The recently
developed test-field method is used to extract turbulent transport
coefficients both in the kinematic and the nonlinear or quasi-kinematic
cases. A striking example of the quasi-kinematic method is provided by
magnetic buoyancy-driven flows that produce an α effect and turbulent
diffusion.

---------------------------------------------------------
Title: Shear-driven and diffusive helicity fluxes in αΩ dynamos
Authors: Guerrero, G.; Chatterjee, P.; Brandenburg, A.
2010MNRAS.409.1619G Altcode: 2010MNRAS.tmp.1434G; 2010arXiv1005.4818G; 2010MNRAS.tmp.1451G
We present non-linear mean-field αΩ dynamo simulations in spherical
geometry with simplified profiles of kinetic α effect and shear. We
take magnetic helicity evolution into account by solving a dynamical
equation for the magnetic α effect. This gives a consistent description
of the quenching mechanism in mean-field dynamo models. The main goal
of this work is to explore the effects of this quenching mechanism
in solar-like geometry, and in particular to investigate the role of
magnetic helicity fluxes, specifically diffusive and Vishniac-Cho (VC)
fluxes, at large magnetic Reynolds numbers (Rm). For models
with negative radial shear or positive latitudinal shear, the magnetic
α effect has predominantly negative (positive) sign in the Northern
(Southern) hemisphere. In the absence of fluxes, we find that the
magnetic energy follows an R-1m dependence, as
found in previous works. This catastrophic quenching is alleviated in
models with diffusive magnetic helicity fluxes resulting in magnetic
fields comparable to the equipartition value even for Rm=
107. On the other hand, models with a shear-driven
Vishniac-Cho flux show an increase in the amplitude of the magnetic
field with respect to models without fluxes, but only for Rm
&lt; 104. This is partly a consequence of assuming a
vacuum outside the Sun which cannot support a significant VC flux
across the boundary. However, in contrast to the diffusive flux, the
VC flux modifies the distribution of the magnetic field. In addition,
if an ill-determined scaling factor in the expression for the VC flux
is large enough, subcritical dynamo action is possible that is driven
by the action of shear and the divergence of magnetic helicity flux.

---------------------------------------------------------
Title: Turbulent diffusion and galactic magnetism
Authors: Brandenburg, Axel; Del Sordo, Fabio
2010HiA....15..432B Altcode: 2009arXiv0910.0072B
Using the test-field method for nearly irrotational turbulence driven
by spherical expansion waves it is shown that the turbulent magnetic
diffusivity increases with magnetic Reynolds numbers. Its value levels
off at several times the rms velocity of the turbulence multiplied by
the typical radius of the expansion waves. This result is discussed
in the context of the galactic mean-field dynamo.

---------------------------------------------------------
Title: Surface appearance of dynamo-generated large-scale fields
Authors: Warnecke, J.; Brandenburg, A.
2010A&A...523A..19W Altcode: 2010arXiv1002.3620W
 Aims: Twisted magnetic fields are frequently seen to emerge
above the visible surface of the Sun. This emergence is usually
associated with the rise of buoyant magnetic flux structures. Here
we ask how magnetic fields from a turbulent large-scale dynamo appear
above the surface if there is no magnetic buoyancy. Methods: The
computational domain is split into two parts. In the lower part, which
we refer to as the turbulence zone, the flow is driven by an assumed
helical forcing function leading to dynamo action. Above this region,
which we refer to as the exterior, a nearly force-free magnetic field
is computed at each time step using the stress-and-relax method. 
Results: Twisted arcade-like field structures are found to emerge in
the exterior above the turbulence zone. Strong current sheets tend
to form above the neutral line, where the vertical field component
vanishes. Time series of the magnetic field structure show recurrent
plasmoid ejections. The degree to which the exterior field is force
free is estimated as the ratio of the dot product of current density
and magnetic field strength to their respective rms values. This ratio
reaches values of up to 95% in the exterior. A weak outward flow is
driven by the residual Lorentz force.

---------------------------------------------------------
Title: Magnetic helicity fluxes in an α2 dynamo embedded in a halo
Authors: Hubbard, Alexander; Brandenburg, Axel
2010GApFD.104..577H Altcode: 2010arXiv1004.4591H
We present the results of simulations of forced turbulence in a slab
where the mean kinetic helicity has a maximum near the mid-plane,
generating gradients of magnetic helicity of both large and small-scale
fields. We also study systems that have poorly conducting buffer zones
away from the midplane in order to assess the effects of boundaries. The
dynamical α quenching phenomenology requires that the magnetic helicity
in the small-scale fields approaches a nearly static, gauge independent
state. To stress-test this steady state condition we choose a system
with a uniform sign of kinetic helicity, so that the total magnetic
helicity can reach a steady state value only through fluxes through
the boundary, which are themselves suppressed by the velocity boundary
conditions. Even with such a set up, the small-scale magnetic helicity
is found to reach a steady state. In agreement with the earlier work,
the magnetic helicity fluxes of small-scale fields are found to be
turbulently diffusive. By comparing results with and without halos,
we show that artificial constraints on magnetic helicity at the
boundary do not have a significant impact on the evolution of the
magnetic helicity, except that "softer" (halo) boundary conditions
give a lower energy of the saturated mean magnetic field.

---------------------------------------------------------
Title: Can catastrophic quenching be alleviated by separating shear
and α effect?
Authors: Chatterjee, Piyali; Brandenburg, Axel; Guerrero, Gustavo
2010GApFD.104..591C Altcode: 2010arXiv1005.5708C
The small-scale magnetic helicity produced as a by-product of
the large-scale dynamo is believed to play a major role in dynamo
saturation. In a mean-field model the generation of small-scale
magnetic helicity can be modelled by using the dynamical quenching
formalism. Catastrophic quenching refers to a decrease of the
saturation field strength with increasing Reynolds number. It has
been suggested that catastrophic quenching only affects the region of
non-zero helical turbulence (i.e. where the kinematic α operates) and
that it is possible to alleviate catastrophic quenching by separating
the region of strong shear from the α layer. We perform a systematic
study of a simple axisymmetric two-layer αΩ dynamo in a spherical
shell for Reynolds numbers in the range 1 ≤ R m ≤
105. In the framework of dynamical quenching we show that
this may not be the case, suggesting that magnetic helicity fluxes
would be necessary.

---------------------------------------------------------
Title: Pencil: Finite-difference Code for Compressible Hydrodynamic
Flows
Authors: Brandenburg, Axel; Dobler, Wolfgang
2010ascl.soft10060B Altcode:
The Pencil code is a high-order finite-difference code for
compressible hydrodynamic flows with magnetic fields. It is highly
modular and can easily be adapted to different types of problems. The
code runs efficiently under MPI on massively parallel shared- or
distributed-memory computers, like e.g. large Beowulf clusters. The
Pencil code is primarily designed to deal with weakly compressible
turbulent flows. To achieve good parallelization, explicit (as opposed
to compact) finite differences are used. Typical scientific targets
include driven MHD turbulence in a periodic box, convection in a slab
with non-periodic upper and lower boundaries, a convective star embedded
in a fully nonperiodic box, accretion disc turbulence in the shearing
sheet approximation, self-gravity, non-local radiation transfer, dust
particle evolution with feedback on the gas, etc. A range of artificial
viscosity and diffusion schemes can be invoked to deal with supersonic
flows. For direct simulations regular viscosity and diffusion is being
used. The code is written in well-commented Fortran90.

---------------------------------------------------------
Title: Test-field method for mean-field coefficients with MHD
background
Authors: Rheinhardt, M.; Brandenburg, A.
2010A&A...520A..28R Altcode: 2010arXiv1004.0689R
 Aims: The test-field method for computing turbulent transport
coefficients from simulations of hydromagnetic flows is extended
to the regime with a magnetohydrodynamic (MHD) background. 
Methods: A generalized set of test equations is derived using both
the induction equation and a modified momentum equation. By employing
an additional set of auxiliary equations, we obtain linear equations
describing the response of the system to a set of prescribed test
fields. Purely magnetic and MHD backgrounds are emulated by applying
an electromotive force in the induction equation analogously to the
ponderomotive force in the momentum equation. Both forces are chosen
to have Roberts-flow like geometry. Results: Examples with
purely magnetic as well as MHD backgrounds are studied where the
previously used quasi-kinematic test-field method breaks down. In
cases with homogeneous mean fields it is shown that the generalized
test-field method produces the same results as the imposed-field method,
where the field-aligned component of the actual electromotive force
from the simulation is used. Furthermore, results for the turbulent
diffusivity are given, which are inaccessible to the imposed-field
method. For MHD backgrounds, new mean-field effects are found that
depend on the occurrence of cross-correlations between magnetic and
velocity fluctuations. In particular, there is a contribution to the
mean Lorentz force that is linear in the mean field and hence reverses
sign upon a reversal of the mean field. For strong mean fields, α
is found to be quenched proportional to the fourth power of the field
strength, regardless of the type of background studied.

---------------------------------------------------------
Title: Oscillatory Migrating Magnetic Fields in Helical Turbulence
in Spherical Domains
Authors: Mitra, Dhrubaditya; Tavakol, Reza; Käpylä, Petri J.;
Brandenburg, Axel
2010ApJ...719L...1M Altcode: 2009arXiv0901.2364M
We present direct numerical simulations of the equations of compressible
magnetohydrodynamics in a wedge-shaped spherical shell, without
shear, but with random helical forcing which has negative (positive)
helicity in the northern (southern) hemisphere. We find a large-scale
magnetic field that is nearly uniform in the azimuthal direction
and approximately antisymmetric about the equator. Furthermore,
the large-scale field in each hemisphere oscillates on nearly
dynamical timescales with reversals of polarity and equatorward
migration. Corresponding mean-field models also show similar migratory
oscillations with a frequency that is nearly independent of the magnetic
Reynolds number. This mechanism may be relevant for understanding
equatorward migration seen in the solar dynamo.

---------------------------------------------------------
Title: Angular Momentum Transport in Convectively Unstable Shear Flows
Authors: Käpylä, Petri J.; Brandenburg, Axel; Korpi, Maarit J.;
Snellman, Jan E.; Narayan, Ramesh
2010ApJ...719...67K Altcode: 2010arXiv1003.0900K
Angular momentum transport due to hydrodynamic turbulent convection
is studied using local three-dimensional numerical simulations
employing the shearing box approximation. We determine the turbulent
viscosity from non-rotating runs over a range of values of the shear
parameter and use a simple analytical model in order to extract the
non-diffusive contribution (Λ-effect) to the stress in runs where
rotation is included. Our results suggest that the turbulent viscosity
is on the order of the mixing length estimate and weakly affected by
rotation. The Λ-effect is non-zero and a factor of 2-4 smaller than
the turbulent viscosity in the slow rotation regime. We demonstrate that
for Keplerian shear, the angular momentum transport can change sign and
be outward when the rotation period is greater than the turnover time,
i.e., when the Coriolis number is below unity. This result seems to
be relatively independent of the value of the Rayleigh number.

---------------------------------------------------------
Title: Disc turbulence and viscosity
Authors: Brandenburg, A.
2010tbha.book...61B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Open and closed boundaries in large-scale convective dynamos
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2010A&A...518A..22K Altcode: 2009arXiv0911.4120K
Context. Earlier work has suggested that large-scale dynamos can reach
and maintain equipartition field strengths on a dynamical time scale
only if magnetic helicity of the fluctuating field can be shed from
the domain through open boundaries. Aims: Our aim is to test
this scenario in convection-driven dynamos by comparing results for
open and closed boundary conditions. Methods: Three-dimensional
numerical simulations of turbulent compressible convection with shear
and rotation are used to study the effects of boundary conditions on the
excitation and saturation of large-scale dynamos. Open (vertical-field)
and closed (perfect- conductor) boundary conditions are used for
the magnetic field. The shear flow is such that the contours of
shear are vertical, crossing the outer surface, and are thus ideally
suited for driving a shear-induced magnetic helicity flux. 
Results: We find that for given shear and rotation rate, the growth
rate of the magnetic field is larger if open boundary conditions are
used. The growth rate first increases for small magnetic Reynolds
number, Rm, but then levels off at an approximately constant value for
intermediate values of Rm. For large enough Rm, a small-scale dynamo
is excited and the growth rate of the field in this regime increases
as Rm1/2. Regarding the nonlinear regime, the saturation
level of the energy of the total magnetic field is independent of
Rm when open boundaries are used. In the case of perfect-conductor
boundaries, the saturation level first increases as a function of Rm,
but then decreases proportional to Rm-1 for Rm ⪆ 30,
indicative of catastrophic quenching. These results suggest that
the shear-induced magnetic helicity flux is efficient in alleviating
catastrophic quenching when open boundaries are used. The horizontally
averaged mean field is still weakly decreasing as a function of Rm
even for open boundaries.

---------------------------------------------------------
Title: Calibrating passive scalar transport in shear-flow turbulence
Authors: Madarassy, Enikő J. M.; Brandenburg, Axel
2010PhRvE..82a6304M Altcode: 2009arXiv0906.3314M
The turbulent diffusivity tensor is determined for linear shear-flow
turbulence using numerical simulations. For moderately strong shear,
the diagonal components are found to increase quadratically with Peclet
and Reynolds numbers below about 10 and then become constant. The
diffusivity tensor is found to have components proportional to the
symmetric and antisymmetric parts of the velocity gradient matrix,
as well as products of these. All components decrease with the wave
number of the mean field in a Lorentzian fashion. The components of
the diffusivity tensor are found not to depend significantly on the
presence of helicity in the turbulence. The signs of the leading terms
in the expression for the diffusion tensor are found to be in good
agreement with estimates based on a simple closure assumption.

---------------------------------------------------------
Title: Numerical simulations of the decay of primordial magnetic
turbulence
Authors: Kahniashvili, Tina; Brandenburg, Axel; Tevzadze, Alexander
G.; Ratra, Bharat
2010PhRvD..81l3002K Altcode: 2010arXiv1004.3084K
We perform direct numerical simulations of forced and freely
decaying 3D magnetohydrodynamic turbulence in order to model magnetic
field evolution during cosmological phase transitions in the early
Universe. Our approach assumes the existence of a magnetic field
generated either by a process during inflation or shortly thereafter, or
by bubble collisions during a phase transition. We show that the final
configuration of the magnetic field depends on the initial conditions,
while the velocity field is nearly independent of initial conditions.

---------------------------------------------------------
Title: The α effect in rotating convection with sinusoidal shear
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2010MNRAS.402.1458K Altcode: 2009arXiv0908.2423K; 2009MNRAS.tmp.1866K
Using three-dimensional convection simulations, it is shown that a
sinusoidal variation of horizontal shear leads to a kinematic α effect
with a similar sinusoidal variation. The effect exists even for weak
stratification and arises owing to the inhomogeneity of turbulence and
the presence of impenetrable vertical boundaries. This system produces
large-scale magnetic fields that also show a sinusoidal variation in
the cross-stream direction. It is argued that earlier investigations
overlooked these phenomena partly because of the use of horizontal
averaging and also because measurements of α using an imposed
field combined with long time averages give erroneous results. It
is demonstrated that in such cases the actual horizontally averaged
mean field becomes non-uniform. The turbulent magnetic diffusion term
resulting from such non-uniform fields can then no longer be neglected
and begins to balance the α effect.

---------------------------------------------------------
Title: Magnetic-field decay of three interlocked flux rings with
zero linking number
Authors: Del Sordo, Fabio; Candelaresi, Simon; Brandenburg, Axel
2010PhRvE..81c6401D Altcode: 2009arXiv0910.3948D
The resistive decay of chains of three interlocked magnetic flux rings
is considered. Depending on the relative orientation of the magnetic
field in the three rings, the late-time decay can be either fast or
slow. Thus, the qualitative degree of tangledness is less important
than the actual value of the linking number or, equivalently, the
net magnetic helicity. Our results do not suggest that invariants of
higher order than that of the magnetic helicity need to be considered
to characterize the decay of the field.

---------------------------------------------------------
Title: Homochirality and the Need for Energy
Authors: Plasson, Raphaël; Brandenburg, Axel
2010OLEB...40...93P Altcode: 2009OLEB..tmp...26P; 2009arXiv0908.0658P
The mechanisms for explaining how a stable asymmetric chemical system
can be formed from a symmetric chemical system, in the absence of any
asymmetric influence other than statistical fluctuations, have been
developed during the last decades, focusing on the non-linear kinetic
aspects. Besides the absolute necessity of self-amplification processes,
the importance of energetic aspects is often underestimated. Going
down to the most fundamental aspects, the distinction between a single
object—that can be intrinsically asymmetric—and a collection
of objects—whose racemic state is the more stable one—must be
emphasized. A system of strongly interacting objects can be described as
one single object retaining its individuality and a single asymmetry;
weakly or non-interacting objects keep their own individuality,
and are prone to racemize towards the equilibrium state. In the
presence of energy fluxes, systems can be maintained in an asymmetric
non-equilibrium steady-state. Such dynamical systems can retain their
asymmetry for times longer than their racemization time.

---------------------------------------------------------
Title: Oscillatory migratory large-scale fields in mean-field and
direct simulations
Authors: Mitra, Dhrubaditya; Tavakol, Reza; Brandenburg, Axel;
Käpylä, Petri J.
2010IAUS..264..197M Altcode:
We summarise recent results form direct numerical simulations of
both non-rotating helically forced and rotating convection driven
MHD equations in spherical wedge-shape domains. In the former, using
perfect-conductor boundary conditions along the latitudinal boundaries
we observe oscillations, polarity reversals and equatorward migration
of the large-scale magnetic fields. In the latter we obtain angular
velocity with cylindrical contours and large-scale magnetic field which
shows oscillations, polarity reversals but poleward migration. The
occurrence of these behviours in direct numerical simulations is
clearly of interest. However the present models as they stand are
not directly applicable to the solar dynamo problem. Nevertheless,
they provide general insights into the operation of turbulent dynamos.

---------------------------------------------------------
Title: Mean electromotive force proportional to mean flow in MHD
turbulence
Authors: Rädler, K. -H.; Brandenburg, A.
2010AN....331...14R Altcode: 2009arXiv0910.0071R
In mean-field magnetohydrodynamics the mean electromotive force due
to velocity and magnetic-field fluctuations plays a crucial role. In
general it consists of two parts, one independent of and another one
proportional to the mean magnetic field. The first part may be nonzero
only in the presence of mhd turbulence, maintained, e.g., by small-scale
dynamo action. It corresponds to a battery, which lets a mean magnetic
field grow from zero to a finite value. The second part, which covers,
e.g., the \alpha effect, is important for large-scale dynamos. Only a
few examples of the aforementioned first part of the mean electromotive
force have been discussed so far. It is shown that a mean electromotive
force proportional to the mean fluid velocity, but independent of the
mean magnetic field, may occur in an originally homogeneous isotropic
mhd turbulence if there are nonzero correlations of velocity and
electric current fluctuations or, what is equivalent, of vorticity
and magnetic field fluctuations. This goes beyond the Yoshizawa
effect, which consists in the occurrence of mean electromotive forces
proportional to the mean vorticity or to the angular velocity defining
the Coriolis force in a rotating frame and depends on the cross-helicity
defined by the velocity and magnetic field fluctuations. Contributions
to the mean electromotive force due to inhomogeneity of the turbulence
are also considered. Possible consequences of the above findings for
the generation of magnetic fields in cosmic bodies are discussed.

---------------------------------------------------------
Title: Magnetic field evolution in simulations with Euler potentials
Authors: Brandenburg, Axel
2010MNRAS.401..347B Altcode: 2009arXiv0907.1906B; 2009MNRAS.tmp.1492B
Using two- and three-dimensional hydromagnetic simulations for a
range of different flows, including laminar and turbulent ones,
it is shown that solutions expressing the field in terms of Euler
potentials (EP) are in general incorrect if the EP are evolved with
an artificial diffusion term. In three dimensions, standard methods
using the magnetic vector potential are found to permit dynamo
action when the EP give decaying solutions. With an imposed field,
the EP method yields excessive power at small scales. This effect is
more exaggerated in the dynamic case, suggesting an unrealistically
reduced feedback from the Lorentz force. The EP approach agrees with
standard methods only at early times when magnetic diffusivity did not
have time to act. It is demonstrated that the usage of EP with even
a small artificial magnetic diffusivity does not converge to a proper
solution of hydromagnetic turbulence. The source of this disagreement
is not connected with magnetic helicity or the three-dimensionality of
the magnetic field, but is simply due to the fact that the non-linear
representation of the magnetic field in terms of EP that depend on the
same coordinates is incompatible with the linear diffusion operator
in the induction equation.

---------------------------------------------------------
Title: Equatorial magnetic helicity flux in simulations with
different gauges
Authors: Mitra, D.; Candelaresi, S.; Chatterjee, P.; Tavakol, R.;
Brandenburg, A.
2010AN....331..130M Altcode: 2009arXiv0911.0969M
We use direct numerical simulations of forced MHD turbulence with a
forcing function that produces two different signs of kinetic helicity
in the upper and lower parts of the domain. We show that the mean
flux of magnetic helicity from the small-scale field between the
two parts of the domain can be described by a Fickian diffusion law
with a diffusion coefficient that is approximately independent of the
magnetic Reynolds number and about one third of the estimated turbulent
magnetic diffusivity. The data suggest that the turbulent diffusive
magnetic helicity flux can only be expected to alleviate catastrophic
quenching at Reynolds numbers of more than several thousands. We
further calculate the magnetic helicity density and its flux in the
domain for three different gauges. We consider the Weyl gauge, in which
the electrostatic potential vanishes, the pseudo-Lorenz gauge, where
the speed of light is replaced by the sound speed, and the `resistive
gauge' in which the Laplacian of the magnetic vector potential acts
as a resistive term. We find that, in the statistically steady state,
the time-averaged magnetic helicity density and the magnetic helicity
flux are the same in all three gauges.

---------------------------------------------------------
Title: Convective dynamos in spherical wedge geometry
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.; Mitra, D.;
Tavakol, R.
2010AN....331...73K Altcode: 2009arXiv0909.1330K
Self-consistent convective dynamo simulations in wedge-shaped
spherical shells are presented. Differential rotation is generated
by the interaction of convection with rotation. Equatorward
acceleration and dynamo action are obtained only for sufficiently
rapid rotation. The angular velocity tends to be constant along
cylinders. Oscillatory large-scale fields are found to migrate in
the poleward direction. Comparison with earlier simulations in full
spherical shells and Cartesian domains is made.

---------------------------------------------------------
Title: Surface appearance of dynamo-generated large-scale fields
Authors: Brandenburg, Axel
2010cosp...38.2826B Altcode: 2010cosp.meet.2826B
Twisted magnetic fields are frequently seen to emerge above the visible
surface of the Sun. This emergence is usually associated with the rise
of buoyant magnetic flux structures. Here we address the question about
magnetic field structures that are generated by a turbulent large-scale
dynamo just beneath the surface. The computational domain is split into
two parts. In the lower part, which we refer to as the turbulence zone,
the flow is driven by an adopted helical forcing function leading to
dynamo action. Above this region, which we refer to as the exterior,
a nearly force-free magnetic field is computed at each time step using
the stress-and-relax method. A twisted arcade-like field structure
is found to emerge in the exterior above the turbulence zone. Strong
current sheets tend to be formed above the neutral line, where the
vertical field component vanishes. The degree to which the exterior
field is force-free is estimated as the ratio of the dot product of
current density and field strength to their respective rms values. This
ratio reaches values of up to 95driven by the residual Lorentz force.

---------------------------------------------------------
Title: Large-scale magnetic flux concentrations from turbulent
stresses
Authors: Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2010AN....331....5B Altcode: 2009arXiv0910.1835B
% In this study we provide the first numerical demonstration of the
effects of turbulence on the mean Lorentz force and the resulting
formation of large-scale magnetic structures. Using three-dimensional
direct numerical simulations (DNS) of forced turbulence we show that
an imposed mean magnetic field leads to a decrease of the turbulent
hydromagnetic pressure and tension. This phenomenon is quantified
by determining the relevant functions that relate the sum of the
turbulent Reynolds and Maxwell stresses with the Maxwell stress of
the mean magnetic field. Using such a parameterization, we show by
means of two-dimensional and three-dimensional mean-field numerical
modelling that an isentropic density stratified layer becomes unstable
in the presence of a uniform imposed magnetic field. This large-scale
instability results in the formation of loop-like magnetic structures
which are concentrated at the top of the stratified layer. In three
dimensions these structures resemble the appearance of bipolar magnetic
regions in the Sun. The results of DNS and mean-field numerical
modelling are in good agreement with theoretical predictions. We
discuss our model in the context of a distributed solar dynamo where
active regions and sunspots might be rather shallow phenomena.}
\begin{document

---------------------------------------------------------
Title: From Fibril to Diffuse Fields During Dynamo Saturation
Authors: Brandenburg, A.
2009ASPC..416..433B Altcode: 2009arXiv0904.2842B
The degree of intermittency of the magnetic field of a large-scale
dynamo is considered. Based on simulations it is argued that there is
a tendency for the field to become more diffuse and non-intermittent
as the dynamo saturates. The simulations are idealized in that the
turbulence is strongly helical and shear is strong, so the tendency
for the field to become more diffuse is somewhat exaggerated. Earlier
results concerning the effects of magnetic buoyancy are discussed. It
is emphasized that the resulting magnetic buoyancy is weak compared
with the stronger effects of simultaneous downward pumping. These
findings are used to support the notion that the solar dynamo might
operate in a distributed fashion where the near-surface shear layer
could play an important role.

---------------------------------------------------------
Title: The critical role of magnetic helicity in astrophysical
large-scale dynamos
Authors: Brandenburg, Axel
2009PPCF...51l4043B Altcode: 2009arXiv0909.4377B
The role of magnetic helicity in astrophysical large-scale dynamos
is reviewed and compared with cases where there is no energy supply
and an initial magnetic field can only decay. In both cases magnetic
energy tends to get redistributed to larger scales. Depending on the
efficiency of magnetic helicity fluxes the decay of a helical field
can speed up. Likewise, the saturation of a helical dynamo can speed
up through magnetic helicity fluxes. The astrophysical importance of
these processes is reviewed in the context of the solar dynamo and an
estimated upper limit for the magnetic helicity flux of 1046
Mx2/cycle is given.

---------------------------------------------------------
Title: Memory Effects in Turbulent Transport
Authors: Hubbard, Alexander; Brandenburg, Axel
2009ApJ...706..712H Altcode: 2008arXiv0811.2561H
In the mean-field theory of magnetic fields, turbulent transport, i.e.,
the turbulent electromotive force is described by a combination of the
α effect and turbulent magnetic diffusion, which are usually assumed
to be proportional, respectively, to the mean field and its spatial
derivatives. For a passive scalar, there is just turbulent diffusion,
where the mean flux of concentration depends on the gradient of the mean
concentration. However, these proportionalities are approximations that
are valid only if the mean field or the mean concentration vary slowly
in time. Examples are presented where turbulent transport possesses
memory, i.e., where it depends crucially on the past history of the
mean field. Such effects are captured by replacing turbulent transport
coefficients with time integral kernels, resulting in transport
coefficients that depend effectively on the frequency or the growth
rate of the mean field itself. In this paper, we perform numerical
experiments to find the characteristic timescale (or memory length) of
this effect as well as simple analytical models of the integral kernels
in the case of passive scalar concentrations and kinematic dynamos. The
integral kernels can then be used to find self-consistent growth or
decay rates of the mean fields. In mean-field dynamos, the growth
rates and cycle periods based on steady state values of α effect,
and turbulent diffusivity can be quite different from the actual values.

---------------------------------------------------------
Title: The role of the Yoshizawa effect in the Archontis dynamo
Authors: Sur, Sharanya; Brandenburg, Axel
2009MNRAS.399..273S Altcode: 2009MNRAS.tmp.1087S; 2009arXiv0902.2394S
The generation of mean magnetic fields is studied for a simple
non-helical flow where a net cross-helicity of either sign can
emerge. This flow, which is also known as the Archontis flow, is
a generalization of the Arnold-Beltrami-Childress flow, but with
the cosine terms omitted. The presence of cross-helicity leads to a
mean-field dynamo effect that is known as the Yoshizawa effect. Direct
numerical simulations of such flows demonstrate the presence of magnetic
fields on scales larger than the scale of the flow. Contrary to earlier
expectations, the Yoshizawa effect is found to be proportional to
the mean magnetic field and can therefore lead to its exponential
instead of just linear amplification for magnetic Reynolds numbers
that exceed a certain critical value. Unlike α effect dynamos, it
is found that the Yoshizawa effect is not notably constrained by the
presence of a conservation law. It is argued that this is due to the
presence of a forcing term in the momentum equation, which leads to a
non-zero correlation with the magnetic field. Finally, the application
to energy convergence in solar wind turbulence is discussed.

---------------------------------------------------------
Title: The α effect with imposed and dynamo-generated magnetic fields
Authors: Hubbard, A.; Del Sordo, F.; Käpylä, P. J.; Brandenburg, A.
2009MNRAS.398.1891H Altcode: 2009MNRAS.tmp.1219H; 2009arXiv0904.2773H
Estimates for the non-linear α effect in helical turbulence
with an applied magnetic field are presented using two different
approaches: the imposed-field method where the electromotive force
owing to the applied field is used, and the test-field method where
separate evolution equations are solved for a set of different test
fields. Both approaches agree for stronger fields, but there are
apparent discrepancies for weaker fields that can be explained by
the influence of dynamo-generated magnetic fields on the scale of the
domain that are referred to as meso-scale magnetic fields. Examples are
discussed where these meso-scale fields can lead to both drastically
overestimated and underestimated values of α compared with the
kinematic case. It is demonstrated that the kinematic value can be
recovered by resetting the fluctuating magnetic field to zero in
regular time intervals. It is concluded that this is the preferred
technique both for the imposed-field and the test-field methods.

---------------------------------------------------------
Title: Small-scale magnetic helicity losses from a mean-field dynamo
Authors: Brandenburg, Axel; Candelaresi, Simon; Chatterjee, Piyali
2009MNRAS.398.1414B Altcode: 2009MNRAS.tmp..979B; 2009arXiv0905.0242B
Using mean-field models with a dynamical quenching formalism, we
show that in finite domains magnetic helicity fluxes associated
with small-scale magnetic fields are able to alleviate catastrophic
quenching. We consider fluxes that result from advection by a mean flow,
the turbulent mixing down the gradient of mean small-scale magnetic
helicity density or the explicit removal which may be associated with
the effects of coronal mass ejections in the Sun. In the absence of
shear, all the small-scale magnetic helicity fluxes are found to be
equally strong for both large- and small-scale fields. In the presence
of shear, there is also an additional magnetic helicity flux associated
with the mean field, but this flux does not alleviate catastrophic
quenching. Outside the dynamo-active region, there are neither sources
nor sinks of magnetic helicity, so in a steady state this flux must
be constant. It is shown that unphysical behaviour emerges if the
small-scale magnetic helicity flux is forced to vanish within the
computational domain.

---------------------------------------------------------
Title: Shear-driven magnetic buoyancy oscillations
Authors: Vermersch, V.; Brandenburg, A.
2009AN....330..797V Altcode: 2009arXiv0909.0324V
The effects of uniform horizontal shear on a stably stratified layer of
gas is studied. The system is initially destabilized by a magnetically
buoyant flux tube pointing in the cross-stream direction. The shear
amplifies the initial field to Lundquist numbers of about 200-400, but
then its value drops to about 100-300, depending on the value of the
sub-adiabatic gradient. The larger values correspond to cases where the
stratification is strongly stable and nearly isothermal. At the end of
the runs the magnetic field is nearly axisymmetric, i.e. uniform in the
streamwise direction. In view of Cowling's theorem the sustainment of
the field remains a puzzle and may be due to subtle numerical effects
that have not yet been identified in detail. In the final state the
strength of the magnetic field decreases with height in such a way
that the field is expected to be unstable. Low amplitude oscillations
are seen in the vertical velocity even at late times, suggesting that
they might be persistent.

---------------------------------------------------------
Title: Turbulent Dynamos with Shear and Fractional Helicity
Authors: Käpylä, Petri J.; Brandenburg, Axel
2009ApJ...699.1059K Altcode: 2008arXiv0810.2298K
Dynamo action owing to helically forced turbulence and large-scale shear
is studied using direct numerical simulations. The resulting magnetic
field displays propagating wave-like behavior. This behavior can be
modeled in terms of an αΩ dynamo. In most cases super-equipartition
fields are generated. By varying the fraction of helicity of the
turbulence the regeneration of poloidal fields via the helicity effect
(corresponding to the α-effect) is regulated. The saturation level of
the magnetic field in the numerical models is consistent with a linear
dependence on the ratio of the fractional helicities of the small
and large-scale fields, as predicted by a simple nonlinear mean-field
model. As the magnetic Reynolds number (Re M ) based on the
wavenumber of the energy-carrying eddies is increased from 1 to 180,
the cycle frequency of the large-scale field is found to decrease by a
factor of about 6 in cases where the turbulence is fully helical. This
is interpreted in terms of the turbulent magnetic diffusivity, which
is found to be only weakly dependent on the Re M .

---------------------------------------------------------
Title: Large-scale Dynamos in Rigidly Rotating Turbulent Convection
Authors: Käpylä, Petri J.; Korpi, Maarit J.; Brandenburg, Axel
2009ApJ...697.1153K Altcode: 2008arXiv0812.3958K
The existence of large-scale dynamos in rigidly rotating turbulent
convection without shear is studied using three-dimensional numerical
simulations of penetrative rotating compressible convection. We
demonstrate that rotating convection in a Cartesian domain can drive a
large-scale dynamo even in the absence of shear. The large-scale field
contains a significant fraction of the total field in the saturated
state. The simulation results are compared with one-dimensional
mean-field dynamo models where turbulent transport coefficients,
as determined using the test field method, are used. The reason for
the absence of large-scale dynamo action in earlier studies is shown
to be due to the rotation being too slow: whereas the α-effect can
change sign, its magnitude stays approximately constant as a function
of rotation, and the turbulent diffusivity decreases monotonically with
increasing rotation. Only when rotation is rapid enough a large-scale
dynamo can be excited. The one-dimensional mean-field model with dynamo
coefficients from the test-field results predicts reasonably well
the dynamo excitation in the direct simulations. This result further
validates the test field procedure and reinforces the interpretation
that the observed dynamo is driven by a turbulent α-effect. This result
demonstrates the existence of an α-effect and an α2-dynamo
with natural forcing.

---------------------------------------------------------
Title: Large-scale Dynamos at Low Magnetic Prandtl Numbers
Authors: Brandenburg, Axel
2009ApJ...697.1206B Altcode: 2008arXiv0808.0961B
Using direct simulations of hydromagnetic turbulence driven by
random polarized waves it is shown that dynamo action is possible
over a wide range of magnetic Prandtl numbers from 10-3
to 1. Triply periodic boundary conditions are being used. In the
final saturated state the resulting magnetic field has a large-scale
component of Beltrami type. For the kinematic phase, growth rates
have been determined for magnetic Prandtl numbers between 0.01
and 1, but only the case with the smallest magnetic Prandtl number
shows large-scale magnetic fields. It is less organized than in the
nonlinear stage. For small magnetic Prandtl numbers the growth rates
are comparable to those calculated from an alpha squared mean-field
dynamo. In the linear regime the magnetic helicity spectrum has
a short inertial range compatible with a -5/3 power law, while in
the nonlinear regime it is the current helicity whose spectrum may
be compatible with such a law. In the saturated case, the spectral
magnetic energy in the inertial range is in slight excess over the
spectral kinetic energy, although for small magnetic Prandtl numbers
the magnetic energy spectrum reaches its resistive cut off wavenumber
more quickly. The viscous energy dissipation declines with the square
root of the magnetic Prandtl number, which implies that most of the
energy is dissipated via Joule heat.

---------------------------------------------------------
Title: Alpha effect and turbulent diffusion from convection
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2009A&A...500..633K Altcode: 2008arXiv0812.1792K
Aims: We study turbulent transport coefficients that describe the
evolution of large-scale magnetic fields in turbulent convection. Methods: We use the test field method, together with three-dimensional
numerical simulations of turbulent convection with shear and rotation,
to compute turbulent transport coefficients describing the evolution
of large-scale magnetic fields in mean-field theory in the kinematic
regime. We employ one-dimensional mean-field models with the derived
turbulent transport coefficients to examine whether they give results
that are compatible with direct simulations. Results: The results
for the α-effect as a function of rotation rate are consistent with
earlier numerical studies, i.e. increasing magnitude as rotation
increases and approximately cos θ latitude profile for moderate
rotation. Turbulent diffusivity, η_t, is proportional to the square of
the turbulent vertical velocity in all cases. Whereas ηt
decreases approximately inversely proportional to the wavenumber of
the field, the α-effect and turbulent pumping show a more complex
behaviour with partial or full sign changes and the magnitude staying
roughly constant. In the presence of shear and no rotation, a weak
α-effect is induced which does not seem to show any consistent trend
as a function of shear rate. Provided that the shear is large enough,
this small α-effect is able to excite a dynamo in the mean-field
model. The coefficient responsible for driving the shear-current
effect shows several sign changes as a function of depth but is also
able to contribute to dynamo action in the mean-field model. The
growth rates in these cases are, however, well below those in direct
simulations, suggesting that an incoherent α-shear dynamo may also
act in the simulations. If both rotation and shear are present, the
α-effect is more pronounced. At the same time, the combination of the
shear-current and Ω×{ J}-effects is also stronger than in the case
of shear alone, but subdominant to the α-shear dynamo. The results
of direct simulations are consistent with mean-field models where all
of these effects are taken into account without the need to invoke
incoherent effects.

---------------------------------------------------------
Title: Emergence of Protometabolisms and the Self-Organization of
Non-equilibrium Reaction Networks
Authors: Plasson, Raphael; Bersini, Hugues; Brandenburg, Axel
2009OLEB...39..263P Altcode:
The debate between Metabolism first and Replication first theories
is shaping the discussion about how life originated (Pross, 2004),
emphasizing either the necessity of a structured reaction network to
maintain information, or the necessity of information to shape the
reaction network. In order to solve this apparent paradox, a general
approach comes down to understanding how protometabolisms can lead
to the emergence of the first template replicators (Shapiro, 2006;
de Duve, 2007), from which open-ended evolutive systems can develop
(Ruiz-Mirazo et al., 2008). On the one hand, replication systems must
maintain their informational integrity, characterized by a specific
topology of the reaction network, implying the necessity of a continuous
consumption and use of energy. On the other hand, the presence of a
source of free energy should have lead to the self-organization of
reaction networks (Plasson and Bersini, submitted), that is to the
emergence and maintenance of protometabolisms. Such reservoirs of energy
(originating from several external energy sources, like sun light,
reduced material from Earth crust, meteorites entering the atmosphere,
etc.) generate both linear fluxes of reaction and reaction loops, as
attractors of the network (Plasson et al. submitted). This implies
the spontaneous generation of network catalysis and autocatalysis,
which introduces positive and negative feedbacks inside the system. In
such dynamical reaction networks, bifurcation mechanisms leads to the
extinction of some pathways, favoring the persistence of other. The
topology of the reaction network is subjected to a spontaneous
evolution, driven by free energy transfers. Rather than the increase
of complexity, this process can be better described as a change in
the nature of the complexity, from horizontal complexity (i.e. a large
number of simple molecules reacting non-selectively with each other)
to vertical complexity (i.e. a large number of complex molecules,
built on a limited number of building blocks, engaged in autocatalytic
cycles). Such self-organization phenomenoncanbelinked toanevolution
of the logical depthas described by Bennett (1986). A model of dynamic
polymerization of amino acids will be described as a simple example of
such self-organization of reaction network by bifurcation mechanisms
(Plasson et al. 2007). In this scope, the gap separating prebiotic
systems from the first reproductive systems can be described as
evolutive protometabolisms. The bifurcations, driven by the fighting
mechanisms between the network sub-elements, are sources of topological
changes inside the reaction networks, from randomness to structures
organized around some central compounds. This may have constituted the
first replicators, not as template replicators of similar molecules,
bu as network replicators of similar reaction cycles, competing with
each others.

---------------------------------------------------------
Title: Turbulent diffusion with rotation or magnetic fields
Authors: Brandenburg, Axel; Svedin, Andreas; Vasil, Geoffrey M.
2009MNRAS.395.1599B Altcode: 2009MNRAS.tmp..519B; 2009arXiv0901.2112B
The turbulent diffusion tensor describing the evolution of the mean
concentration of a passive scalar is investigated for non-helically
forced turbulence in the presence of rotation or a magnetic field. With
rotation, the Coriolis force causes a sideways deflection of the flux
of mean concentration. Within the magnetohydrodynamics approximation
there is no analogous effect from the magnetic field because the
effects on the flow do not depend on the sign of the field. Both
rotation and magnetic fields tend to suppress turbulent transport,
but this suppression is weaker in the direction along the magnetic
field. Turbulent transport along the rotation axis is not strongly
affected by rotation, except on shorter length-scales, i.e. when the
scale of the variation of the mean field becomes comparable with the
scale of the energy-carrying eddies. These results are discussed in
the context of anisotropic convective energy transport in the Sun.

---------------------------------------------------------
Title: Turbulent Dynamos in Spherical Shell Segments of Varying
Geometrical Extent
Authors: Mitra, Dhrubaditya; Tavakol, Reza; Brandenburg, Axel;
Moss, David
2009ApJ...697..923M Altcode: 2008arXiv0812.3106M
We use three-dimensional direct numerical simulations of the helically
forced magnetohydrodynamic equations in spherical shell segments
in order to study the effects of changes in the geometrical shape
and size of the domain on the growth and saturation of large-scale
magnetic fields. We inject kinetic energy along with kinetic helicity
in spherical domains via helical forcing using Chandrasekhar-Kendall
functions. We take perfect conductor boundary conditions for the
magnetic field to ensure that no magnetic helicity escapes the domain
boundaries. We find dynamo action giving rise to magnetic fields at
scales larger than the characteristic scale of the forcing. The magnetic
energy exceeds the kinetic energy over dissipative timescales, similar
to that seen earlier in Cartesian simulations in periodic boxes. As
we increase the size of the domain in the azimuthal direction,
we find that the nonlinearly saturated magnetic field organizes
itself in long-lived cellular structures with aspect ratios close to
unity. These structures tile the domain along the azimuthal direction,
thus resulting in very small longitudinally averaged magnetic fields
for large domain sizes. The scales of these structures are determined by
the smallest scales of the domain, which in our simulations is usually
the radial scale. We also find that increasing the meridional extent
of the domains produces little qualitative change, except a marginal
increase in the large-scale field. We obtain qualitatively similar
results in Cartesian domains with similar aspect ratios.

---------------------------------------------------------
Title: Advances in Theory and Simulations of Large-Scale Dynamos
Authors: Brandenburg, Axel
2009SSRv..144...87B Altcode: 2009arXiv0901.0329B
Recent analytical and computational advances in the theory of
large-scale dynamos are reviewed. The importance of the magnetic
helicity constraint is apparent even without invoking mean-field
theory. The tau approximation yields expressions that show how the
magnetic helicity gets incorporated into mean-field theory. The
test-field method allows an accurate numerical determination
of turbulent transport coefficients in linear and nonlinear
regimes. Finally, some critical views on the solar dynamo are being
offered and targets for future research are highlighted.

---------------------------------------------------------
Title: Paradigm shifts in solar dynamo modeling
Authors: Brandenburg, Axel
2009IAUS..259..159B Altcode: 2009arXiv0901.3789B
Selected topics in solar dynamo theory are being highlighted. The
possible relevance of the near-surface shear layer is discussed. The
role of turbulent downward pumping is mentioned in connection with
earlier concerns that a dynamo-generated magnetic field would be
rapidly lost from the convection zone by magnetic buoyancy. It is
argued that shear-mediated small-scale magnetic helicity fluxes are
responsible for the success of some of the recent large-scale dynamo
simulations. These fluxes help in disposing of excess small-scale
magnetic helicity. This small-scale magnetic helicity, in turn, is
generated in response to the production of an overall tilt in each
Parker loop. Some preliminary calculations of this helicity flux are
presented for a system with uniform shear. In the Sun the effects of
magnetic helicity fluxes may be seen in coronal mass ejections shedding
large amounts of magnetic helicity.

---------------------------------------------------------
Title: Alpha effect and diffusivity in helical turbulence with shear
Authors: Mitra, D.; Käpylä, P. J.; Tavakol, R.; Brandenburg, A.
2009A&A...495....1M Altcode: 2008arXiv0806.1608M
Aims: We study the dependence of turbulent transport coefficients, such
as the components of the α tensor (αij) and the turbulent
magnetic diffusivity tensor (ηij), on shear and magnetic
Reynolds number in the presence of helical forcing. Methods:
We use three-dimensional direct numerical simulations with periodic
boundary conditions and measure the turbulent transport coefficients
using the kinematic test field method. In all cases the magnetic Prandtl
number is taken as unity. Results: We find that with increasing
shear the diagonal components of αij quench, whereas those
of ηij increase. The antisymmetric parts of both tensors
increase with increasing shear. We also propose a simple expression for
the turbulent pumping velocity (or γ effect). This pumping velocity is
proportional to the kinetic helicity of the turbulence and the vorticity
of the mean flow. For negative helicity, i.e. for a positive trace of
αij, it points in the direction of the mean vorticity,
i.e. perpendicular to the plane of the shear flow. Our simulations
support this expression for low shear and magnetic Reynolds number. The
transport coefficients depend on the wavenumber of the mean flow in
a Lorentzian fashion, just as for non-shearing turbulence.

---------------------------------------------------------
Title: Mean-field effects in the Galloway-Proctor flow
Authors: Rädler, Karl-Heinz; Brandenburg, Axel
2009MNRAS.393..113R Altcode: 2008arXiv0809.0851R
In the framework of mean-field electrodynamics the coefficients
defining the mean electromotive force in Galloway-Proctor flows
are determined. These flows show a two-dimensional pattern and are
helical. The pattern wobbles in its plane. Apart from one exception a
circularly polarized Galloway-Proctor flow, i.e. a circular motion
of the flow pattern is assumed. This corresponds to one of the
cases considered recently by Courvoisier, Hughes &amp; Tobias. An
analytic theory of the α effect and related effects in this flow
is developed within the second-order correlation approximation and
a corresponding fourth-order approximation. In the validity range of
these approximations there is an α effect but no γ effect, or pumping
effect. Numerical results obtained with the test-field method, which
are independent of these approximations, confirm the results for α
and show that γ is in general non-zero. Both α and γ show a complex
dependency on the magnetic Reynolds number and other parameters that
define the flow, that is, amplitude and frequency of the circular
motion. Some results for the magnetic diffusivity ηt
and a related quantity are given, too. Finally, a result for α in
the case of a randomly varying linearly polarized Galloway-Proctor
flow, without the aforementioned circular motion, is presented. The
flows investigated show quite interesting effects. There is, however,
no straightforward way to relate these flows to turbulence and to use
them for studying properties of the α effect and associated effects
under realistic conditions.

---------------------------------------------------------
Title: Turbulent stresses as a function of shear rate in a local
disk model
Authors: Liljeström, A. J.; Korpi, M. J.; Käpylä, P. J.;
Brandenburg, A.; Lyra, W.
2009AN....330...92L Altcode: 2008arXiv0811.2341L
We present local numerical models of accretion disk turbulence driven
by the magnetorotational instability with varying shear rate. The
resulting turbulent stresses are compared with predictions of a closure
model in which triple correlations are modelled in terms of quadratic
correlations. This local model uses five nondimensional parameters to
describe the properties of the flow. We attempt to determine these
closure parameters for our simulations and find that the model does
produce qualitatively correct behaviour. In addition, we present results
concerning the shear rate dependency of the magnetic to kinetic energy
ratio. We find both the turbulent stress ratio and the total stress
to be strongly dependent on the shear rate.

---------------------------------------------------------
Title: Numerical study of large-scale vorticity generation in
shear-flow turbulence
Authors: Käpylä, Petri J.; Mitra, Dhrubaditya; Brandenburg, Axel
2009PhRvE..79a6302K Altcode: 2008arXiv0810.0833K
Simulations of stochastically forced shear-flow turbulence in a
shearing-periodic domain are used to study the spontaneous generation of
large-scale flow patterns in the direction perpendicular to the plane of
the shear. Based on an analysis of the resulting large-scale velocity
correlations it is argued that the mechanism behind this phenomenon
could be the mean-vorticity dynamo effect pioneered by Elperin,
Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This
effect is based on the anisotropy of the eddy viscosity tensor. One
of its components may be able to replenish cross-stream mean flows by
acting upon the streamwise component of the mean flow. Shear, in turn,
closes the loop by acting upon the cross-stream mean flow to produce
stronger streamwise mean flows. The diagonal component of the eddy
viscosity is found to be of the order of the rms turbulent velocity
divided by the wave number of the energy-carrying eddies.

---------------------------------------------------------
Title: Solar Dynamo and Magnetic Self-Organization
Authors: Kosovichev, A. G.; Arlt, R.; Bonanno, A.; Brandenburg,
A.; Brun, A. S.; Busse, F.; Dikpati, M.; Hill, F.; Gilman, P. A.;
Nordlund, A.; Ruediger, G.; Stein, R. F.; Sekii, T.; Stenflo, J. O.;
Ulrich, R. K.; Zhao, J.
2009astro2010S.160K Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Advances in Theory and Simulations of Large-Scale Dynamos
Authors: Brandenburg, Axel
2009odsm.book...87B Altcode:
Recent analytical and computational advances in the theory of
large-scale dynamos are reviewed. The importance of the magnetic
helicity constraint is apparent even without invoking mean-field
theory. The tau approximation yields expressions that show how the
magnetic helicity gets incorporated into mean-field theory. The
test-field method allows an accurate numerical determination
of turbulent transport coefficients in linear and nonlinear
regimes. Finally, some critical views on the solar dynamo are being
offered and targets for future research are highlighted.

---------------------------------------------------------
Title: A growing dynamo from a saturated Roberts flow dynamo
Authors: Tilgner, Andreas; Brandenburg, Axel
2008MNRAS.391.1477T Altcode: 2008arXiv0808.2141T
Using direct simulations, weakly non-linear theory and non-linear
mean-field theory, it is shown that the quenched velocity field
of a saturated non-linear dynamo can itself act as a kinematic
dynamo. The flow is driven by a forcing function that would produce
a Roberts flow in the absence of a magnetic field. This result
confirms an analogous finding by Cattaneo &amp; Tobias for the
more complicated case of turbulent convection, suggesting that
this may be a common property of non-linear dynamos; see also the
talk given online at the Kavli Institute for Theoretical Physics
(http://online.kitp.ucsb.edu/online/dynamo_c08/cattaneo). It is argued
that this property can be used to test non-linear mean-field dynamo
theories.

---------------------------------------------------------
Title: Large-scale dynamos in turbulent convection with shear
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2008A&A...491..353K Altcode: 2008arXiv0806.0375K
Aims: To study the existence of large-scale convective dynamos under
the influence of shear and rotation. Methods: Three-dimensional
numerical simulations of penetrative compressible convection with
uniform horizontal shear are used to study dynamo action and the
generation of large-scale magnetic fields. We consider cases where the
magnetic Reynolds number is either marginal or moderately supercritical
with respect to small-scale dynamo action in the absence of shear and
rotation. Our magnetic Reynolds number is based on the wavenumber of
the depth of the convectively unstable layer. The effects of magnetic
helicity fluxes are studied by comparing results for the magnetic
field with open and closed boundaries. Results: Without shear
no large-scale dynamos are found even if the ingredients necessary
for the α-effect (rotation and stratification) are present in the
system. When uniform horizontal shear is added, a large-scale magnetic
field develops, provided the boundaries are open. In this case the mean
magnetic field contains a significant fraction of the total field. For
those runs where the magnetic Reynolds number is between 60 and 250, an
additional small-scale dynamo is expected to be excited, but the field
distribution is found to be similar to cases with smaller magnetic
Reynolds number where the small-scale dynamo is not excited. In the
case of closed (perfectly conducting) boundaries, magnetic helicity
fluxes are suppressed and no large-scale fields are found. Similarly,
poor large-scale field development is seen when vertical shear is used
in combination with periodic boundary conditions in the horizontal
directions. If, however, open (normal-field) boundary conditions are
used in the x-direction, a large-scale field develops. These results
support the notion that shear not only helps to generate the field,
but it also plays a crucial role in driving magnetic helicity fluxes
out of the system along the isocontours of shear, thereby allowing
efficient dynamo action.

---------------------------------------------------------
Title: Magnetic Quenching of α and Diffusivity Tensors in Helical
Turbulence
Authors: Brandenburg, Axel; Rädler, Karl-Heinz; Rheinhardt, Matthias;
Subramanian, Kandaswamy
2008ApJ...687L..49B Altcode: 2008arXiv0805.1287B
The effect of a dynamo-generated mean magnetic field of Beltrami
type on the mean electromotive force is studied. In the absence of
the mean magnetic field the turbulence is assumed to be homogeneous
and isotropic, but it becomes inhomogeneous and anisotropic with
this field. Using the test-field method the dependence of the α
and turbulent diffusivity tensors on the magnetic Reynolds number
ReM is determined for magnetic fields that have reached
approximate equipartition with the velocity field. The tensor components
are characterized by a pseudoscalar α and a scalar turbulent magnetic
diffusivity ηt. Increasing ReM from 2 to
600 reduces ηt by a factor ≈5, suggesting that the
quenching of ηt is, in contrast to the two-dimensional
case, only weakly dependent on ReM. Over the same range of
ReM, however, α is reduced by a factor ≈14, which can
be explained by a corresponding increase of a magnetic contribution
to the α-effect with opposite sign. Within this framework, the
corresponding kinetic contribution to the α-effect turns out to
be independent of ReM for 2 &lt;= ReM &lt;=
600. The level of fluctuations of α and ηt is only 10%
and 20% of the respective kinematic reference values.

---------------------------------------------------------
Title: Nonlinear aspects of astrobiological research
Authors: Brandenburg, Axel
2008arXiv0809.0261B Altcode:
Several aspects of mathematical astrobiology are discussed. It
is argued that around the time of the origin of life the
handedness of biomolecules must have established itself through an
instability. Possible pathways of producing a certain handedness
include mechanisms involving either autocatalysis or, alternatively,
epimerization as governing effects. Concepts for establishing
hereditary information are discussed in terms of the theory of
hypercycles. Instabilities toward parasites and possible remedies
by invoking spatial extent are reviewed. Finally, some effects of
early life are discussed that contributed to modifying and regulating
atmosphere and climate of the Earth, and that could have contributed
to the highly oxidized state of its crust.

---------------------------------------------------------
Title: The dual role of shear in large-scale dynamos
Authors: Brandenburg, A.
2008AN....329..725B Altcode: 2008arXiv0808.0959B
The role of shear in alleviating catastrophic quenching by shedding
small-scale magnetic helicity through fluxes along contours of constant
shear is discussed. The level of quenching of the dynamo effect depends
on the quenched value of the turbulent magnetic diffusivity. Earlier
estimates that might have suffered from the force-free degeneracy of
Beltrami fields are now confirmed for shear flows where this degeneracy
is lifted. For a dynamo that is saturated near equipartition field
strength those estimates result in a 5-fold decrease of the magnetic
diffusivity as the magnetic Reynolds number based on the wavenumber
of the energy-carrying eddies is increased from 2 to 600. Finally,
the role of shear in driving turbulence and large-scale fields by the
magneto-rotational instability is emphasized. New simulations are
presented and the 3\pi/4 phase shift between poloidal and toroidal
fields is confirmed. It is suggested that this phase shift might be
a useful diagnostic tool in identifying mean-field dynamo action in
simulations and to distinguish this from other scenarios invoking
magnetic buoyancy as a means to explain migration away from the
midplane.

---------------------------------------------------------
Title: Lambda effect from forced turbulence simulations
Authors: Käpylä, P. J.; Brandenburg, A.
2008A&A...488....9K Altcode: 2008arXiv0806.3751K
Aims: We determine the components of the Λ-effect tensor that
quantifies the contributions to the turbulent momentum transport even
for uniform rotation. Methods: Three-dimensional numerical
simulations are used to study turbulent transport in triply
periodic cubes under the influence of rotation and anisotropic
forcing. Comparison is made with analytical results obtained via
the so-called minimal tau-approximation. Results: In the case
where the turbulence intensity in the vertical direction dominates,
the vertical stress is always negative. This situation is expected
to occur in stellar convection zones. The horizontal component of the
stress is weaker and exhibits a maximum at latitude 30° - regardless
of how rapid the rotation is. The minimal tau-approximation captures
many of the qualitative features of the numerical results, provided the
relaxation time tau is close to the turnover time, i.e. the Strouhal
number is of order unity. Tables [see full textsee full textsee
full text]-[see full textsee full textsee full text] are only available
in electronic form at http.//www.aanda.org

---------------------------------------------------------
Title: Turbulent protostellar discs
Authors: Brandenburg, A.
2008PhST..130a4016B Altcode: 2008arXiv0808.0960B
Aspects of turbulence in protostellar accretion discs are being
reviewed. The emergence of dead zones due to poor ionization and
alternatives to the magneto-rotational instability are discussed. The
coupling between dust and gas in protostellar accretion discs is
explained and the turbulent drag is compared with laminar drag in the
Stokes and Epstein regimes. Finally, the significance of magnetic-field
generation in turbulent discs is emphasized in connection with driving
outflows and with star disc coupling.

---------------------------------------------------------
Title: A solar mean field dynamo benchmark
Authors: Jouve, L.; Brun, A. S.; Arlt, R.; Brandenburg, A.; Dikpati,
M.; Bonanno, A.; Käpylä, P. J.; Moss, D.; Rempel, M.; Gilman, P.;
Korpi, M. J.; Kosovichev, A. G.
2008A&A...483..949J Altcode:
Context: The solar magnetic activity and cycle are linked to an
internal dynamo. Numerical simulations are an efficient and accurate
tool to investigate such intricate dynamical processes. Aims:
We present the results of an international numerical benchmark
study based on two-dimensional axisymmetric mean field solar dynamo
models in spherical geometry. The purpose of this work is to provide
reference cases that can be analyzed in detail and that can help in
further development and validation of numerical codes that solve such
kinematic problems. Methods: The results of eight numerical
codes solving the induction equation in the framework of mean field
theory are compared for three increasingly computationally intensive
models of the solar dynamo: an αΩ dynamo with constant magnetic
diffusivity, an αΩ dynamo with magnetic diffusivity sharply varying
with depth and an example of a flux-transport Babcock-Leighton dynamo
which includes a non-local source term and one large single cell of
meridional circulation per hemisphere. All cases include a realistic
profile of differential rotation and thus a sharp tachocline. Results: The most important finding of this study is that all codes
agree quantitatively to within less than a percent for the αΩ dynamo
cases and within a few percent for the flux-transport case. Both
the critical dynamo numbers for the onset of dynamo action and the
corresponding cycle periods are reasonably well recovered by all
codes. Detailed comparisons of butterfly diagrams and specific cuts of
both toroidal and poloidal fields at given latitude and radius confirm
the good quantitative agreement. Conclusions: We believe that
such a benchmark study will be a very useful tool since it provides
detailed standard cases for comparison and reference.

---------------------------------------------------------
Title: Scale dependence of alpha effect and turbulent diffusivity
Authors: Brandenburg, A.; Rädler, K. -H.; Schrinner, M.
2008A&A...482..739B Altcode: 2008arXiv0801.1320B
Aims: We determine the alpha effect and turbulent magnetic diffusivity
for mean magnetic fields with profiles of different length scales from
simulations of isotropic turbulence. We then relate these results
to nonlocal formulations in which alpha and the turbulent magnetic
diffusivity correspond to integral kernels. Methods: We solve
evolution equations for magnetic fields that give the response to
imposed test fields. These test fields correspond to mean fields
with various wavenumbers. Both an imposed fully helical steady
flow consisting of a pattern of screw-like motions (Roberts flow)
and time-dependent, statistically steady isotropic turbulence are
considered. In the latter case the evolution equations are solved
simultaneously with the momentum and continuity equations. The
corresponding results for the electromotive force are used to calculate
alpha and magnetic diffusivity tensors. Results: For both,
the Roberts flow under the second-order correlation approximation
and the isotropic turbulence alpha and turbulent magnetic diffusivity
are greatest on large scales and these values diminish toward smaller
scales. In both cases, the alpha effect and turbulent diffusion kernels
are approximated by exponentials, corresponding to Lorentzian profiles
in Fourier space. For isotropic turbulence, the turbulent diffusion
kernel is half as wide as the alpha effect kernel. For the Roberts
flow beyond the second-order correlation approximation, the turbulent
diffusion kernel becomes negative on large scales.

---------------------------------------------------------
Title: Boundary layer on the surface of a neutron star
Authors: Babkovskaia, N.; Brandenburg, A.; Poutanen, J.
2008MNRAS.386.1038B Altcode: 2008arXiv0802.1663B; 2008MNRAS.tmp..447B
In an attempt to model the accretion on to a neutron star in
low-mass X-ray binaries, we present 2D hydrodynamical models of
the gas flow in close vicinity of the stellar surface. First, we
consider a gas pressure-dominated case, assuming that the star is
non-rotating. For the stellar mass we take Mstar = 1.4
× 10-2Msolar and for the gas temperature T =
5 × 106 K. Our results are qualitatively different in the
case of a realistic neutron star mass and a realistic gas temperature
of T ~= 108 K, when the radiation pressure dominates. We
show that to get the stationary solution in a latter case, the star
most probably has to rotate with the considerable velocity.

---------------------------------------------------------
Title: Core Mass Function: The Role of Gravity
Authors: Dib, Sami; Brandenburg, Axel; Kim, Jongsoo; Gopinathan,
Maheswar; André, Philippe
2008ApJ...678L.105D Altcode: 2008arXiv0801.2257D
We analyze the mass distribution of cores formed in an isothermal,
magnetized, turbulent, and self-gravitating nearly critical molecular
cloud model. Cores are identified at two density threshold levels. Our
main results are that the presence of self-gravity modifies the
slopes of the core mass function (CMF) at the high-mass end. At low
thresholds, the slope is shallower than the one predicted by pure
turbulent fragmentation. The shallowness of the slope is due to the
effects of core coalescence and gas accretion. Most importantly, the
slope of the CMF at the high-mass end steepens when cores are selected
at higher density thresholds, or alternatively, if the CMF is fitted
with a lognormal function, the width of the lognormal distribution
decreases with increasing threshold. This is due to the fact that
gravity plays a more important role in denser structures selected at
higher density threshold and leads to the conclusion that the role of
gravity is essential in generating a CMF that bears more resemblance
to the IMF when cores are selected with an increasing density threshold
in the observations.

---------------------------------------------------------
Title: Modeling a Maunder minimum
Authors: Brandenburg, A.; Spiegel, E. A.
2008AN....329..351B Altcode: 2008arXiv0801.2156B
We introduce on/off intermittency into a mean field dynamo model by
imposing stochastic fluctuations in either the alpha effect or through
the inclusion of a fluctuating electromotive force. Sufficiently strong
small scale fluctuations with time scales of the order of 0.3-3 years
can produce long term variations in the system on time scales of the
order of hundreds of years. However, global suppression of magnetic
activity in both hemispheres at once was not observed. The variation of
the magnetic field does not resemble that of the sunspot number, but
is more reminiscent of the 10Be record. The interpretation
of our results focuses attention on the connection between the level
of magnetic activity and the sunspot number, an issue that must be
elucidated if long term solar effects are to be well understood.

---------------------------------------------------------
Title: Magnetic Diffusivity Tensor and Dynamo Effects in Rotating
and Shearing Turbulence
Authors: Brandenburg, A.; Rädler, K. -H.; Rheinhardt, M.; Käpylä,
P. J.
2008ApJ...676..740B Altcode: 2007arXiv0710.4059B
The turbulent magnetic diffusivity tensor is determined in the presence
of rotation or shear. The question is addressed whether dynamo action
from the shear-current effect can explain large-scale magnetic field
generation found in simulations with shear. For this purpose a set
of evolution equations for the response to imposed test fields is
solved with turbulent and mean motions calculated from the momentum and
continuity equations. The corresponding results for the electromotive
force are used to calculate turbulent transport coefficients. The
diagonal components of the turbulent magnetic diffusivity tensor are
found to be very close together, but their values increase slightly
with increasing shear and decrease with increasing rotation rate. In
the presence of shear, the sign of the two off-diagonal components
of the turbulent magnetic diffusion tensor is the same and opposite
to the sign of the shear. This implies that dynamo action from the
shear-current effect is impossible, except perhaps for high magnetic
Reynolds numbers. However, even though there is no alpha effect on the
average, the components of the α tensor display Gaussian fluctuations
around zero. These fluctuations are strong enough to drive an incoherent
alpha-shear dynamo. The incoherent shear-current effect, on the other
hand, is found to be subdominant.

---------------------------------------------------------
Title: Kinematic α-effect in isotropic turbulence simulations
Authors: Sur, Sharanya; Brandenburg, Axel; Subramanian, Kandaswamy
2008MNRAS.385L..15S Altcode: 2008MNRAS.tmpL...7S; 2007arXiv0711.3789S
Using numerical simulations at moderate magnetic Reynolds numbers up
to 220, it is shown that in the kinematic regime, isotropic helical
turbulence leads to an α-effect and a turbulent diffusivity
whose values are independent of the magnetic Reynolds number,
Rm, provided Rm exceeds unity. These turbulent
coefficients are also consistent with expectations from the first-order
smoothing approximation. For small values of Rm, α and
turbulent diffusivity are proportional to Rm. Over finite
time-intervals, meaningful values of α and turbulent diffusivity can
be obtained even when there is small-scale dynamo action that produces
strong magnetic fluctuations. This suggests that the fields generated
by the small-scale dynamo do not make a correlated contribution to
the mean electromotive force.

---------------------------------------------------------
Title: α -effect dynamos with zero kinetic helicity
Authors: Rädler, Karl-Heinz; Brandenburg, Axel
2008PhRvE..77b6405R Altcode: 2008arXiv0801.0602R
A simple explicit example of a Roberts-type dynamo is given in which
the α effect of mean-field electrodynamics exists in spite of pointwise
vanishing kinetic helicity of the fluid flow. In this way, it is shown
that α -effect dynamos do not necessarily require nonzero kinetic
helicity. A mean-field theory of Roberts-type dynamos is established
within the framework of the second-order correlation approximation. In
addition, numerical solutions of the original dynamo equations are
given that are independent of any approximation of that kind. Both
theory and numerical results demonstrate the possibility of dynamo
action in the absence of kinetic helicity.

---------------------------------------------------------
Title: The helicity constraint in spherical shell dynamos
Authors: Brandenburg, A.; Käpylä, P. J.; Mitra, D.; Moss, D.;
Tavakol, R.
2007AN....328.1118B Altcode: 2007arXiv0711.3616B
The motivation for considering distributed large scale dynamos
in the solar context is reviewed in connection with the magnetic
helicity constraint. Preliminary accounts of 3-dimensional direct
numerical simulations (in spherical shell segments) and simulations
of 2-dimensional mean field models (in spherical shells) are
presented. Interesting similarities as well as some differences
are noted.

---------------------------------------------------------
Title: Turbulent viscosity and Λ-effect from numerical turbulence
models
Authors: Käpylä, P. J.; Brandenburg, A.
2007AN....328.1006K Altcode: 2007arXiv0710.5632K
Homogeneous anisotropic turbulence simulations are used to determine
off-diagonal components of the Reynolds stress tensor and its
parameterization in terms of turbulent viscosity and Λ-effect. The
turbulence is forced in an anisotropic fashion by enhancing the strength
of the forcing in the vertical direction. The Coriolis force is included
with a rotation axis inclined relative to the vertical direction. The
system studied here is significantly simpler than that of turbulent
stratified convection which has often been used to study Reynolds
stresses. Certain puzzling features of the results for convection,
such as sign changes or highly concentrated latitude distributions,
are not present in the simpler system considered here.

---------------------------------------------------------
Title: Homochirality in an Early Peptide World
Authors: Brandenburg, Axel; Lehto, Harry J.; Lehto, Kirsi M.
2007AsBio...7..725B Altcode: 2006q.bio....10051B
A recently proposed model of non-autocatalytic reactions in dipeptide
formation that leads to spontaneous symmetry breaking and homochirality
was examined. The model is governed by activation, polymerization,
epimerization, and depolymerization of amino acids. Symmetry
breaking was determined to result primarily from the different
rates of reactions that involve homodimers and heterodimers, i.e.,
stereoselective reactions, and the fact that epimerization can only
occur on the N-terminal residue and not on the C-terminal residue. This
corresponds to an auto-inductive cyclic process that works only in
one direction. It is argued that epimerization mimics autocatalytic
behavior as well as mutual antagonism, both of which are known to be
crucial for the production of full homochirality.

---------------------------------------------------------
Title: Magnetic helicity effects in astrophysical and laboratory
dynamos
Authors: Brandenburg, A.; Käpylä, P. J.
2007NJPh....9..305B Altcode: 2007arXiv0705.3507B
Magnetic helicity effects are discussed in laboratory and astro-physical
settings. Firstly, dynamo action in Taylor Green flows is discussed
for different boundary conditions. However, because of the lack of
scale separation with respect to the container, no large-scale field
is being produced and there is no resistively slow saturation phase as
otherwise expected. Secondly, the build-up of a large-scale field is
demonstrated in a simulation where a localized magnetic eddy produces
field on a larger scale if the eddy possesses a swirl. Such a set-up
might be realizable experimentally through coils. Finally, new emerging
issues regarding the connection between magnetic helicity and the solar
dynamo are discussed. It is demonstrated that dynamos with a nonlocal
(Babcock Leighton type) α effect can also be catastrophically quenched,
unless there are magnetic helicity fluxes.

---------------------------------------------------------
Title: Why coronal mass ejections are necessary for the dynamo
Authors: Brandenburg, Axel
2007HiA....14..291B Altcode: 2007astro.ph..1056B
Large scale dynamo-generated fields are a combination of interlocked
poloidal and toroidal fields. Such fields possess magnetic helicity
that needs to be regenerated and destroyed during each cycle. A
number of numerical experiments now suggests that stars may do this
by shedding magnetic helicity. In addition to plain bulk motions,
a favorite mechanism involves magnetic helicity flux along lines of
constant rotation. We also know that the sun does shed the required
amount of magnetic helicity mostly in the form of coronal mass
ejections. Solar-like stars without cycles do not face such strong
constraints imposed by magnetic helicity evolution and may not display
coronal activity to that same extent. I discuss the evidence leading to
this line of argument. In particular, I discuss simulations showing
the generation of strong mean toroidal fields provided the outer
boundary condition is left open so as to allow magnetic helicity to
escape. Control experiments with closed boundaries do not produce
strong mean fields.

---------------------------------------------------------
Title: Simulations of the anisotropic kinetic and magnetic alpha
effects
Authors: Brandenburg, A.; Subramanian, K.
2007AN....328..507B Altcode: 2007arXiv0705.3508B
Using simulations of isotropically forced helical turbulence the
contributions to kinetic and magnetic alpha effects are computed. It
is shown that for the parameter regimes considered in an earlier
publication (Brandenburg &amp; Subramanian 2005), the expressions for
isotropic and anisotropic alpha effects give quantitatively similar
results. Both kinetic and magnetic alpha effects are proportional to a
relaxation time whose value, in units of the turnover time, is shown to
be approximately unity and independent of the magnetic Reynolds number.

---------------------------------------------------------
Title: Near-surface shear layer dynamics
Authors: Brandenburg, Axel
2007IAUS..239..457B Altcode: 2007astro.ph..1057B
The outer surface layers of the sun show a clear deceleration
at low latitudes. This is generally thought to be the result of
a strong dominance of vertical turbulent motions associated with
strong downdrafts. This strong negative radial shear should not only
contribute to amplifying the toroidal field locally and to expelling
magnetic helicity, but it may also be responsible for producing a strong
prograde pattern speed in the supergranulation layer. Using simulations
of rotating stratified convection in cartesian boxes located at low
latitudes around the equator it is shown that in the surface layers
patterns move in the prograde direction on top of a retrograde mean
background flow. These patterns may also be associated with magnetic
tracers and even sunspot proper motions that are known to be prograde
relative to the much slower surface plasma.

---------------------------------------------------------
Title: Kinetic and magnetic α-effects in non-linear dynamo theory
Authors: Sur, Sharanya; Subramanian, Kandaswamy; Brandenburg, Axel
2007MNRAS.376.1238S Altcode: 2007MNRAS.tmp..151S; 2007astro.ph..1001S
The backreaction of the Lorentz force on the α-effect is studied
in the limit of small magnetic and fluid Reynolds numbers, using the
first-order smoothing approximation (FOSA) to solve both the induction
and momentum equations. Both steady and time-dependent forcings
are considered. In the low Reynolds number limit, the velocity and
magnetic fields can be expressed explicitly in terms of the forcing
function. The non-linear α-effect is then shown to be expressible
in several equivalent forms in agreement with formalisms that are
used in various closure schemes. On one hand, one can express α
completely in terms of the helical properties of the velocity field
as in traditional FOSA, or, alternatively, as the sum of two terms, a
so-called kinetic α-effect and an oppositely signed term proportional
to the helical part of the small-scale magnetic field. These results
hold for both steady and time-dependent forcing at arbitrary strength
of the mean field. In addition, the τ-approximation is considered in
the limit of small fluid and magnetic Reynolds numbers. In this limit,
the τ closure term is absent and the viscous and resistive terms
must be fully included. The underlying equations are then identical
to those used under FOSA, but they reveal interesting differences
between the steady and time-dependent forcing. For steady forcing, the
correlation between the forcing function and the small-scale magnetic
field turns out to contribute in a crucial manner to determine the net
α-effect. However for delta-correlated time-dependent forcing, this
force-field correlation vanishes, enabling one to write α exactly as
the sum of kinetic and magnetic α-effects, similar to what one obtains
also in the large Reynolds number regime in the τ-approximation closure
hypothesis. In the limit of strong imposed fields, B0,
we find α ~ B-20 for delta-correlated forcing,
in contrast to the well-known α ~ B-30 behaviour
for the case of a steady forcing. The analysis presented here is also
shown to be in agreement with numerical simulations of steady as well
as random helical flows.

---------------------------------------------------------
Title: Probing turbulence in OMC1 at the star forming scale:
observations and simulations
Authors: Gustafsson, Maiken; Brandenburg, Axel; Lemaire, Jean-Louis;
Field, David
2007IAUS..237..183G Altcode: 2006IAUS..237E..32G
A key to understanding the mechanism of star formation is to
characterise in detail the dynamics of the turbulent, highly perturbed
and magnetized plasma from which stars are forming. This can be
achieved by statistical analysis of the turbulent velocity structure
and should involve both observations and simulated data. To this purpose
we use high spatial resolution IR K-band observations of velocities of
vibrationally excited H2 in the Orion Molecular Cloud (OMC1). Data cover
scales of 70 AU to 30000 AU [1]. OMC1 is the archetypal massive star
forming region and is highly active. This is exemplified by the presence
of protostars and fast outflows. We compare the observational results
with numerical simulations of supersonic hydrodynamic turbulence. We
present the structure functions and the scaling of the structure
functions with their order. The structure functions for OMC1 show clear
deviations from power laws, that is, deviations from fractal scaling,
around 1000-2000 AU and around 300 AU. The scaling of the higher order
structure functions with order deviates from the standard scaling
for supersonic turbulence [1,2]. The unusual scaling is explained as
a selection effect of preferentially observing the shocked part of
the gas. The scaling can be reproduced using line-of-sight integrated
velocity data from subsets of simulations that select regions of strong
flow convergence associated with shock structure. The simulations, which
do not include self-gravity or magnetic fields, are unable to reproduce
the deviations from power laws of the structure functions. These
deviations could be ascribed to the presence of low mass protostars
and associated structures such as outflows and circumstellar disks
[4]. [1] Gustafsson et al. 2006a, A&amp;A, 445,601, [2] She &amp;
Leveque 1994, PRL, 72, 336, [3] Boldyrev 2002, ApJ, 569, 841, [4]
Gustafsson et al 2006b, A&amp;A in press, astro-ph/0512214

---------------------------------------------------------
Title: Thermal Instability in Shearing and Periodic Turbulence
Authors: Brandenburg, Axel; Korpi, Maarit J.; Mee, Antony J.
2007ApJ...654..945B Altcode: 2006astro.ph..4244B
The thermal instability with a piecewise power law cooling function is
investigated using one- and three-dimensional simulations with periodic
and shearing-periodic boundary conditions in the presence of constant
thermal diffusion and kinematic viscosity coefficients. Consistent with
earlier findings, the flow behavior depends on the average density,
&lt;ρ&gt;. When &lt;ρ&gt; is in the range (1-5)×10-24
g cm-3, the system is unstable and segregates into cool
and warm phases with temperatures of roughly 100 and 104 K,
respectively. However, in all cases the resulting average pressure is independent of &lt;ρ&gt; and just a little above the minimum
value. For a constant heating rate of 0.015 ergs g-1
s-1, the mean pressure is around 24×10-14
dyn (corresponding to p/kB~1750 K cm-3). Cool
patches tend to coalesce into bigger ones. In all cases investigated,
there is no sustained turbulence, which is in agreement with earlier
results. Simulations in which turbulence is driven by a body force
show that when rms velocities of between 10 and 30 km s-1
are obtained, the resulting dissipation rates are comparable to the
thermal energy input rate. The resulting mean pressures are then
about 30×10-14 dyn, corresponding to p/kB~2170
K cm-3. This is comparable to the value expected for the
Galaxy. Differential rotation tends to make the flow two-dimensional,
that is, uniform in the streamwise direction, but this does not lead
to instability.

---------------------------------------------------------
Title: Dynamos in accretion discs
Authors: Brandenburg, A.; von Rekowski, B.
2007MmSAI..78..374B Altcode: 2007astro.ph..2493B
It is argued that accretion discs in young stellar objects may have
hot coronae that are heated by magnetic reconnection. This is a
consequence of the magneto-rotational instability driving turbulence
in the disc. Magnetic reconnection away from the midplane leads to
heating of the corona which, in turn, contributes to driving disc winds.

---------------------------------------------------------
Title: Disk Winds, Jets, and Outflows: Theoretical and Computational
Foundations
Authors: Pudritz, R. E.; Ouyed, R.; Fendt, Ch.; Brandenburg, A.
2007prpl.conf..277P Altcode: 2006astro.ph..3592P
We review advances in the theoretical and computational studies of
disk winds, jets, and outflows, including the connection between
accretion and jets, the launch of jets from magnetized disks, the
coupled evolution of jets and disks, the interaction of magnetized
young stellar objects with their surrounding disks and the relevance to
outflows, and finally, the link between jet formation and gravitational
collapse. We also address the predictions the theory makes about jet
kinematics, collimation, and rotation that have recently been confirmed
by high-spatial- and high-spectral-resolution observations. Disk winds
have a universal character that may account for jets and outflows
during the formation of massive stars as well as brown dwarfs.

---------------------------------------------------------
Title: The Solar Interior-Radial Structure, Rotation, Solar Activity
Cycle
Authors: Brandenburg, A.
2007hste.book...28B Altcode: 2007astro.ph..3711B
Some basic properties of the solar convection zone are considered and
the use of helioseismology as an observational tool to determine its
depth and internal angular velocity is discussed. Aspects of solar
magnetism are described and explained in the framework of dynamo
theory. The main focus is on mean field theories for the Sun's magnetic
field and its differential rotation.

---------------------------------------------------------
Title: Location of the Solar Dynamo and Near-Surface Shear
Authors: Brandenburg, A.
2006ASPC..354..121B Altcode: 2005astro.ph.12637B
The location of the solar dynamo is discussed in the context of
new insights into the theory of nonlinear turbulent dynamos. It is
argued that, from a dynamo-theoretic point of view, the bottom of the
convection zone is not a likely location for the solar dynamo, but
that it may be distributed over the convection zone. The near surface
shear layer produces not only east-west field alignment, but it also
helps the dynamo to dispose of its excess small scale magnetic helicity.

---------------------------------------------------------
Title: Simulating field-aligned diffusion of a cosmic ray gas
Authors: Snodin, Andrew P.; Brandenburg, Axel; Mee, Antony J.;
Shukurov, Anvar
2006MNRAS.373..643S Altcode: 2006MNRAS.tmp.1221S; 2005astro.ph..7176S
The macroscopic behaviour of cosmic rays in turbulent magnetic
fields is discussed. An implementation of anisotropic diffusion of
cosmic rays with respect to the magnetic field in a non-conservative,
high-order, finite-difference magnetohydrodynamic code is discussed. It
is shown that the standard implementation fails near singular X-points
of the magnetic field, which are common if the field is random. A
modification to the diffusion model for cosmic rays is described and
the resulting telegraph equation (implemented by solving a dynamic
equation for the diffusive flux of cosmic rays) is used; it is argued
that this modification may better describe the physics of cosmic ray
diffusion. The present model reproduces several processes important
for the propagation and local confinement of cosmic rays, including
spreading perpendicular to the local large-scale magnetic field,
controlled by the random-to-total magnetic field ratio, and the balance
between cosmic ray pressure and magnetic tension. Cosmic ray diffusion
is discussed in the context of a random magnetic field produced
by turbulent dynamo action. It is argued that energy equipartition
between cosmic rays and other constituents of the interstellar medium
does not necessarily imply that cosmic rays play a significant role
in the balance of forces.

---------------------------------------------------------
Title: Magnetic Helicity Density and Its Flux in Weakly Inhomogeneous
Turbulence
Authors: Subramanian, Kandaswamy; Brandenburg, Axel
2006ApJ...648L..71S Altcode: 2005astro.ph..9392S
A gauge-invariant and hence physically meaningful definition of
magnetic helicity density for random fields is proposed, using the
Gauss linking formula, as the density of correlated field line
linkages. This definition is applied to the random small-scale
field in weakly inhomogeneous turbulence, whose correlation length
is small compared with the scale on which the turbulence varies. For
inhomogeneous systems, with or without boundaries, our technique then
allows one to study the local magnetic helicity density evolution in
a gauge-independent fashion, which was not possible earlier. This
evolution equation is governed by local sources (owing to the mean
field) and by the divergence of a magnetic helicity flux density. The
role of magnetic helicity fluxes in alleviating catastrophic quenching
of mean field dynamos is discussed.

---------------------------------------------------------
Title: The nature of turbulence in OMC1 at the scale of star
formation: observations and simulations
Authors: Gustafsson, M.; Brandenburg, A.; Lemaire, J. L.; Field, D.
2006A&A...454..815G Altcode: 2005astro.ph.12214G
Aims.To study turbulence in the Orion Molecular Cloud (OMC1)
by comparing observed and simulated characteristics of the gas
motions. Methods: Using a dataset of vibrationally excited H2 emission
in OMC1 containing radial velocity and brightness which covers scales
from 70 AU to 30 000 AU, we present the structure functions and the
scaling of the structure functions with their order. These are compared
with the predictions of two-dimensional projections of simulations of
supersonic hydrodynamic turbulence. Results: The structure functions of
OMC1 are not well represented by power laws, but show clear deviations
below 2000 AU. However, using the technique of extended self-similarity,
power laws are recovered at scales down to 160 AU. The scaling of the
higher order structure functions with order deviates from the standard
scaling for supersonic turbulence. This is explained as a selection
effect of preferentially observing the shocked part of the gas and the
scaling can be reproduced using line-of-sight integrated velocity data
from subsets of supersonic turbulence simulations. These subsets select
regions of strong flow convergence and high density associated with
shock structure. Deviations of the structure functions in OMC1 from
power laws cannot however be reproduced in simulations and remains an
outstanding issue.

---------------------------------------------------------
Title: Why coronal mass ejections are necessary for the dynamo
Authors: Brandenburg, A.
2006IAUJD...8E..62B Altcode:
Large scale dynamo-generated fields are a combination of interlocked
poloidal and toroidal fields. Such fields possess magnetic helicity
that needs to be regenerated and destroyed during each cycle. A
sequence of numerical experiments now suggests that stars may do this
by shedding magnetic helicity. In addition to plain bulk motions,
a favorite mechanism involves magnetic helicity flux along lines of
constant rotation. We also know that the sun does shed the required
amount of magnetic helicity mostly in the form of coronal mass
ejections. Solar-like stars without cycles do not face such strong
constraints imposed by magnetic helicity evolution and may not display
coronal activity to that same extent. In my talk I will discuss the
evidence leading to this line of argument. In particular, I will
discuss simulations showing the generation of strong mean toroidal
fields provided the outer boundary condition is left open so as to
allow magnetic helicity to escape. Control experiments with closed
boundaries do not produce strong mean fields.

---------------------------------------------------------
Title: Hydrodynamic and hydromagnetic energy spectra from large
eddy simulations
Authors: Haugen, Nils Erland L.; Brandenburg, Axel
2006PhFl...18g5106H Altcode: 2004astro.ph.12666H
Direct and large eddy simulations of hydrodynamic and hydromagnetic
turbulence have been performed in an attempt to isolate artifacts from
real and possibly asymptotic features in the energy spectra. It is shown
that in a hydrodynamic turbulence simulation with a Smagorinsky subgrid
scale model using 5123 mesh points, two important features
of the 40963 simulation on the Earth simulator [Y. Kaneda et
al., Phys. Fluids 15, L21 (2003)] are reproduced: a k-0.1
correction to the inertial range with a k-5/3 Kolmogorov
slope and the form of the bottleneck just before the dissipative
subrange. Furthermore, it is shown that, while a Smagorinsky-type
model for the induction equation causes an artificial and unacceptable
reduction in the dynamo efficiency, hyper-resistivity yields good
agreement with direct simulations. In the large-scale part of the
inertial range, an excess of the spectral magnetic energy over
the spectral kinetic energy is confirmed. However, a trend toward
spectral equipartition at smaller scales in the inertial range can be
identified. With magnetic fields, no explicit bottleneck effect is seen.

---------------------------------------------------------
Title: Turbulence from localized random expansion waves
Authors: Mee, Antony J.; Brandenburg, Axel
2006MNRAS.370..415M Altcode: 2006MNRAS.tmp..668M; 2006astro.ph..2057M
In an attempt to determine the outer scale of turbulence driven by
localized sources, such as supernova explosions in the interstellar
medium, we consider a forcing function given by the gradient of
Gaussian profiles localized at random positions. Different coherence
times of the forcing function are considered. In order to isolate the
effects specific to the nature of the forcing function, we consider
the case of a polytropic equation of state and restrict ourselves
to forcing amplitudes such that the flow remains subsonic. When the
coherence time is short, the outer scale agrees with the half-width
of the Gaussian. Longer coherence times can cause extra power
at large scales, but this would not yield power-law behaviour at
scales larger than that of the expansion waves. At scales smaller
than the scale of the expansion waves the spectrum is close to power
law with a spectral exponent of -2. The resulting flow is virtually
free of vorticity. Viscous driving of vorticity turns out to be weak
and self-amplification through the non-linear term is found to be
insignificant. No evidence for small-scale dynamo action is found in
cases where the magnetic induction equation is solved simultaneously
with the other equations.

---------------------------------------------------------
Title: Magnetic helicity in primordial and dynamo scenarios of
galaxies
Authors: Brandenburg, A.
2006AN....327..461B Altcode: 2006astro.ph..1496B
Some common properties of helical magnetic fields in decaying and driven
turbulence are discussed. These include mainly the inverse cascade that
produces fields on progressively larger scales. Magnetic helicity also
restricts the evolution of the large-scale field: the field decays less
rapidly than a non-helical field, but it also saturates more slowly,
i.e. on a resistive time scale if there are no magnetic helicity
fluxes. The former effect is utilized in primordial field scenarios,
while the latter is important for successfully explaining astrophysical
dynamos that saturate faster than resistively. Dynamo action is argued
to be important not only in the galactic dynamo, but also in accretion
discs in active galactic nuclei and around protostars, both of which
contribute to producing a strong enough seed magnetic field. Although
primordial magnetic fields may be too weak to compete with these
astrophysical mechanisms, such fields could perhaps still be important
in producing polarization effects in the cosmic background radiation.

---------------------------------------------------------
Title: Nonaxisymmetric stability in the shearing sheet approximation
Authors: Brandenburg, A.; Dintrans, B.
2006A&A...450..437B Altcode: 2001astro.ph.11313B
Aims.To quantify the transient growth of nonaxisymmetric perturbations
in unstratified magnetized and stratified non-magnetized rotating
linear shear flows in the shearing sheet approximation of accretion
disc flows. Methods: .The Rayleigh quotient in modal approaches
for the linearized equations (with time-dependent wavenumber) and
the amplitudes from direct shearing sheet simulations using a finite
difference code are compared. Results: .Both approaches agree in
their predicted growth behavior. The magneto-rotational instability
for axisymmetric and non-axisymmetric perturbations is shown to
have the same dependence of the (instantaneous) growth rate on the
wavenumber along the magnetic field, but in the nonaxisymmetric case
the growth is only transient. However, a meaningful dependence of the
Rayleigh quotient on the radial wavenumber is obtained. While in the
magnetized case the total amplification factor can be several orders
of magnitude, it is only of order ten or less in the nonmagnetic
case. Stratification is shown to have a stabilizing effect. In
the present case of shearing-periodic boundaries the (local)
strato-rotational instability seems to be absent.

---------------------------------------------------------
Title: Radiative transfer in decomposed domains
Authors: Heinemann, T.; Dobler, W.; Nordlund, Å.; Brandenburg, A.
2006A&A...448..731H Altcode: 2005astro.ph..3510H
Aims. An efficient algorithm for calculating radiative transfer
on massively parallel computers using domain decomposition is
presented. Methods. The integral formulation of the transfer equation
is used to divide the problem into a local but compute-intensive
part for calculating the intensity and optical depth integrals,
and a nonlocal part for communicating the intensity between adjacent
processors. Results. The waiting time of idle processors during the
nonlocal communication part does not have a severe impact on the
scaling. The wall clock time thus scales nearly linearly with the
inverse number of processors.

---------------------------------------------------------
Title: Galactic dynamo and helicity losses through fountain flow
Authors: Shukurov, A.; Sokoloff, D.; Subramanian, K.; Brandenburg, A.
2006A&A...448L..33S Altcode: 2005astro.ph.12592S
Aims. Nonlinear behaviour of galactic dynamos is studied, allowing
for magnetic helicity removal by the galactic fountain flow.Methods. A
suitable advection speed is estimated, and a one-dimensional mean-field
dynamo model with dynamic α-effect is explored. Results. It is shown
that the galactic fountain flow is efficient in removing magnetic
helicity from galactic discs. This alleviates the constraint on the
galactic mean-field dynamo resulting from magnetic helicity conservation
and thereby allows the mean magnetic field to saturate at a strength
comparable to equipartition with the turbulent kinetic energy.

---------------------------------------------------------
Title: Magnetic Field Generation in Fully Convective Rotating Spheres
Authors: Dobler, Wolfgang; Stix, Michael; Brandenburg, Axel
2006ApJ...638..336D Altcode: 2004astro.ph.10645D
Magnetohydrodynamic simulations of fully convective, rotating spheres
with volume heating near the center and cooling at the surface
are presented. The dynamo-generated magnetic field saturates at
equipartition field strength near the surface. In the interior, the
field is dominated by small-scale structures, but outside the sphere, by
the global scale. Azimuthal averages of the field reveal a large-scale
field of smaller amplitude also inside the star. The internal angular
velocity shows some tendency to be constant along cylinders and is
“antisolar” (fastest at the poles and slowest at the equator).

---------------------------------------------------------
Title: Stellar dynamo driven wind braking versus disc coupling
Authors: von Rekowski, B.; Brandenburg, A.
2006AN....327...53V Altcode: 2005astro.ph..4053V
Star-disc coupling is considered in numerical models where the stellar
field is not an imposed perfect dipole, but instead a more irregular
self-adjusting dynamo-generated field. Using axisymmetric simulations of
the hydromagnetic mean-field equations, it is shown that the resulting
stellar field configuration is more complex, but significantly better
suited for driving a stellar wind. In agreement with recent findings by
a number of people, star-disc coupling is less efficient in braking
the star than previously thought. Moreover, stellar wind braking
becomes equally important. In contrast to a perfect stellar dipole
field, dynamo-generated stellar fields favor field-aligned accretion
with considerably higher velocity at low latitudes, where the field
is weaker and originating in the disc. Accretion is no longer nearly
periodic (as it is in the case of a stellar dipole), but it is more
irregular and episodic.

---------------------------------------------------------
Title: The angular momentum transport by the strato-rotational
instability in simulated Taylor-Couette flows
Authors: Brandenburg, A.; Ruediger, G.
2005astro.ph.12409B Altcode:
Aims: To investigate the stability and angular momentum transport by
the strato-rotational instability in the nonlinear regime. Methods: The
hydrodynamic compressible equations are solved in a cartesian box in
which the outer cylinder is embedded. Gravity along the rotation axis
leads to density stratification. No-slip boundary conditions are used
in the radial direction, while free-slip conditions are used on the
two ends of the cylinders. Results: The strato-rotational instability
is confirmed and the Reynolds stress is shown to transport angular
momentum away from the axis. However, the growth rate decreases with
increasing Reynolds number. This, as well as the presence of boundaries
renders this instability less relevant for astrophysical applications.

---------------------------------------------------------
Title: Distributed versus tachocline dynamos
Authors: Brandenburg, Axel
2005astro.ph.12638B Altcode:
Arguments are presented in favor of the idea that the solar dynamo
may operate not just at the bottom of the convection zone, i.e. in
the tachocline, but it may operate in a more distributed fashion in
the entire convection zone. The near-surface shear layer is likely to
play an important role in this scenario.

---------------------------------------------------------
Title: Connection between active longitudes and magnetic helicity
Authors: Brandenburg, A.; Käpylä, P. J.
2005astro.ph.12639B Altcode:
A two-dimensional mean field dynamo model is solved where magnetic
helicity conservation is fully included. The model has a negative
radial velocity gradient giving rise to equatorward migration of
magnetic activity patterns. In addition the model develops longitudinal
variability with activity patches travelling in longitude. These
patches may be associated with active longitudes.

---------------------------------------------------------
Title: Dissociation in a Polymerization Model of Homochirality
Authors: Brandenburg, A.; Andersen, A. C.; Nilsson, M.
2005OLEB...35..507B Altcode: 2005q.bio.....2008B
A fully self-contained model of homochirality is presented that
contains the effects of both polymerization and dissociation. The
dissociation fragments are assumed to replenish the substrate from
which new monomers can grow and undergo new polymerization. The mean
length of isotactic polymers is found to grow slowly with the normalized
total number of corresponding building blocks. Alternatively, if one
assumes that the dissociation fragments themselves can polymerize
further, then this corresponds to a strong source of short polymers,
and an unrealistically short average length of only 3. By contrast,
without dissociation, isotactic polymers becomes infinitely long.

---------------------------------------------------------
Title: Turbulence and its parameterization in accretion discs
Authors: Brandenburg, A.
2005AN....326..787B Altcode: 2005astro.ph.10015B
Accretion disc turbulence is investigated in the framework of the
shearing box approximation. The turbulence is either driven by the
magneto-rotational instability or, in the non-magnetic case, by an
explicit and artificial forcing term in the momentum equation. Unlike
the magnetic case, where most of the dissipation occurs in the disc
corona, in the forced hydrodynamic case most of the dissipation occurs
near the midplane. In the hydrodynamic case evidence is presented for
the stochastic excitation of epicycles. When the vertical and radial
epicyclic frequencies are different (modeling the properties around
rotating black holes), the beat frequency between these two frequencies
appear to show up as a peak in the temporal power spectrum in some
cases. Finally, the full turbulent resistivity tensor is determined
and it is found that, if the turbulence is driven by a forcing term,
the signs of its off-diagonal components are such that this effect
would not be capable of dynamo action by the shear-current effect.

---------------------------------------------------------
Title: Effect of the radiative background flux in convection
Authors: Brandenburg, A.; Chan, K. L.; Nordlund, Å.; Stein, R. F.
2005AN....326..681B Altcode: 2005astro.ph..8404B
Numerical simulations of turbulent stratified convection are used
to study models with approximately the same convective flux, but
different radiative fluxes. As the radiative flux is decreased, for
constant convective flux: the entropy jump at the top of the convection
zone becomes steeper, the temperature fluctuations increase and the
velocity fluctuations decrease in magnitude, and the distance that
low entropy fluid from the surface can penetrate increases. Velocity
and temperature fluctuations follow mixing length scaling laws.

---------------------------------------------------------
Title: Unidirectional polymerization leading to homochirality in
the RNA world
Authors: Nilsson, M.; Brandenburg, A.; Andersen, A. C.; Höfner, S.
2005IJAsB...4..233N Altcode: 2005q.bio.....5041N
The differences between unidirectional and bidirectional polymerization
are considered. The unidirectional case is discussed in the framework
of the RNA world. Similar to earlier models of this type, where
polymerization was assumed to proceed in a bidirectional fashion
(presumed to be relevant to peptide nucleic acids), left- and
right-handed monomers are produced via an autocatalysis from an
achiral substrate. The details of the bifurcation from a racemic
solution to a homochiral state of either handedness is shown to be
remarkably independent of whether the polymerization is unidirectional
or bidirectional. Slightly larger differences are seen when dissociation
is allowed and the dissociation fragments are recycled into the
achiral substrate.

---------------------------------------------------------
Title: Astrophysical magnetic fields and nonlinear dynamo theory
Authors: Brandenburg, Axel; Subramanian, Kandaswamy
2005PhR...417....1B Altcode: 2004astro.ph..5052B
The current understanding of astrophysical magnetic fields is reviewed,
focusing on their generation and maintenance by turbulence. In the
astrophysical context this generation is usually explained by a
self-excited dynamo, which involves flows that can amplify a weak
‘seed’ magnetic field exponentially fast. Particular emphasis
is placed on the nonlinear saturation of the dynamo. Analytic and
numerical results are discussed both for small scale dynamos, which are
completely isotropic, and for large scale dynamos, where some form of
parity breaking is crucial. Central to the discussion of large scale
dynamos is the so-called alpha effect which explains the generation
of a mean field if the turbulence lacks mirror symmetry, i.e. if the
flow has kinetic helicity. Large scale dynamos produce small scale
helical fields as a waste product that quench the large scale dynamo
and hence the alpha effect. With this in mind, the microscopic theory
of the alpha effect is revisited in full detail and recent results
for the loss of helical magnetic fields are reviewed.

---------------------------------------------------------
Title: Minimal tau approximation and simulations of the alpha effect
Authors: Brandenburg, A.; Subramanian, K.
2005A&A...439..835B Altcode: 2005astro.ph..4222B
The validity of a closure called the minimal tau approximation (MTA),
is tested in the context of dynamo theory, wherein triple correlations
are assumed to provide relaxation of the turbulent electromotive
force. Under MTA, the alpha effect in mean field dynamo theory becomes
proportional to a relaxation time scale multiplied by the difference
between kinetic and current helicities. It is shown that the value
of the relaxation time is positive and, in units of the turnover
time at the forcing wavenumber, it is of the order of unity. It is
quenched by the magnetic field - roughly independently of the magnetic
Reynolds number. However, this independence becomes uncertain at large
magnetic Reynolds number. Kinetic and current helicities are shown to
be dominated by large scale properties of the flow.

---------------------------------------------------------
Title: Spectrum and amplitudes of internal gravity waves excited by
penetrative convection in solar-type stars
Authors: Dintrans, B.; Brandenburg, A.; Nordlund, Å.; Stein, R. F.
2005A&A...438..365D Altcode: 2005astro.ph..2138D
The excitation of internal gravity waves by penetrative convective
plumes is investigated using 2-D direct simulations of compressible
convection. The wave generation is quantitatively studied from the
linear response of the radiative zone to the plumes penetration,
using projections onto the g-modes solutions of the associated linear
eigenvalue problem for the perturbations. This allows an accurate
determination of both the spectrum and amplitudes of the stochastically
excited modes. Using time-frequency diagrams of the mode amplitudes,
we then show that the lifetime of a mode is around twice its period
and that during times of significant excitation up to 40% of the total
kinetic energy may be contained into g-modes.

---------------------------------------------------------
Title: Scaling laws in decaying helical hydromagnetic turbulence
Authors: Christensson, M.; Hindmarsh, M.; Brandenburg, A.
2005AN....326..393C Altcode: 2002astro.ph..9119C
We study the evolution of growth and decay laws for the magnetic field
coherence length ξ, energy E_M and magnetic helicity H in freely
decaying 3D MHD turbulence. We show that with certain assumptions,
self-similarity of the magnetic power spectrum alone implies that ξ σm
t1/2. This in turn implies that magnetic helicity decays as
Hσm t-2s, where s=(ξ_diff/ξH)2, in
terms of ξ_diff, the diffusion length scale, and ξ_H, a length scale
defined from the helicity power spectrum. The relative magnetic helicity
remains constant, implying that the magnetic energy decays as E_M σm
t-1/2-2s. The parameter s is inversely proportional to the
magnetic Reynolds number Re_M, which is constant in the self-similar
regime.

---------------------------------------------------------
Title: Strong mean field dynamos require supercritical helicity fluxes
Authors: Brandenburg, A.; Subramanian, K.
2005AN....326..400B Altcode: 2005astro.ph..5457B
Several one and two dimensional mean field models are analyzed where the
effects of current helicity fluxes and boundaries are included within
the framework of the dynamical quenching model. In contrast to the case
with periodic boundary conditions, the final saturation energy of the
mean field decreases inversely proportional to the magnetic Reynolds
number. If a nondimensional scaling factor in the current helicity flux
exceeds a certain critical value, the dynamo can operate even without
kinetic helicity, i.e. it is based only on shear and current helicity
fluxes, as first suggested by Vishniac &amp; Cho (2001, ApJ 550,
752). Only above this threshold is the current helicity flux also able
to alleviate catastrophic quenching. The fact that certain turbulence
simulations have now shown apparently non-resistively limited mean
field saturation amplitudes may be suggestive of the current helicity
flux having exceeded this critical value. Even below this critical
value the field still reaches appreciable strength at the end of the
kinematic phase, which is in qualitative agreement with dynamos in
periodic domains. However, for large magnetic Reynolds numbers the
field undergoes subsequent variations on a resistive time scale when,
for long periods, the field can be extremely weak.

---------------------------------------------------------
Title: Homochiral Growth Through Enantiomeric Cross-Inhibition
Authors: Brandenburg, A.; Andersen, A. C.; Höfner, S.; Nilsson, M.
2005OLEB...35..225B Altcode: 2004q.bio.....1036B
The stability and conservation properties of a recently proposed
polymerization model are studied. The achiral (racemic) solution
is linearly unstable once the relevant control parameter (here the
fidelity of the catalyst) exceeds a critical value. The growth rate
is calculated for different fidelity parameters and cross-inhibition
rates. A chirality parameter is defined and shown to be conserved by
the nonlinear terms of the model. Finally, a truncated version of the
model is used to derive a set of two ordinary differential equations
and it is argued that these equations are more realistic than those
used in earlier models of that form.

---------------------------------------------------------
Title: Nonhelical turbulent dynamos: shocks and shear
Authors: Brandenburg, A.; Haugen, N.; Mee, A.
2005mpge.conf..139B Altcode: 2005astro.ph..1006B
Small scale turbulent dynamo action in compressible transonic
turbulence is discussed. It is shown that the critical value of the
magnetic Reynolds number displays a bimodal behavior and changes from
a typical value of 35 for small Mach numbers to about 80 for larger
Mach numbers. The transition between the two regimes is relatively
sharp. The direct simulations are then compared with simulations
where shocks are captured using a shock viscosity that becomes large
at locations where there are shocks. In the presence of shear it is
shown that large scale dynamo action is possible.

---------------------------------------------------------
Title: Signatures of axinos and gravitinos at colliders
Authors: Brandenburg, A.; Covi, L.; Hamaguchi, K.; Roszkowski, L.;
Steffen, F. D.
2005PhLB..617...99B Altcode: 2005hep.ph....1287B
The axino and the gravitino are well-motivated candidates for the
lightest supersymmetric particle (LSP) and also for cold dark matter in
the Universe. Assuming that a charged slepton is the next-to-lightest
supersymmetric particle (NLSP), we show how the NLSP decays can
be used to probe the axino LSP scenario in hadronic axion models
as well as the gravitino LSP scenario at the Large Hadron Collider
and the International Linear Collider. We show how one can identify
experimentally the scenario realized in nature. In the case of the
axino LSP, the NLSP decays will allow one to estimate the value of
the axino mass and the Peccei Quinn scale.

---------------------------------------------------------
Title: The Onset of a Small-Scale Turbulent Dynamo at Low Magnetic
Prandtl Numbers
Authors: Schekochihin, A. A.; Haugen, N. E. L.; Brandenburg, A.;
Cowley, S. C.; Maron, J. L.; McWilliams, J. C.
2005ApJ...625L.115S Altcode: 2004astro.ph.12594S
We study numerically the dependence of the critical magnetic Reynolds
number Rmc for the turbulent small-scale dynamo on the
hydrodynamic Reynolds number Re. The turbulence is statistically
homogeneous, isotropic, and mirror-symmetric. We are interested
in the regime of low magnetic Prandtl number Pm=Rm/Re&lt;1, which
is relevant for stellar convective zones, protostellar disks, and
laboratory liquid-metal experiments. The two asymptotic possibilities
are Rmc--&gt;const as Re--&gt;∞ (a small-scale dynamo
exists at low Pm) or Rmc/Re=Pmc--&gt;const as
Re--&gt;∞ (no small-scale dynamo exists at low Pm). Results obtained
in two independent sets of simulations of MHD turbulence using grid and
spectral codes are brought together and found to be in quantitative
agreement. We find that at currently accessible resolutions,
Rmc grows with Re with no sign of approaching a constant
limit. We reach the maximum values of Rmc~500 for Re~3000. By
comparing simulations with Laplacian viscosity, fourth-, sixth-, and
eighth-order hyperviscosity, and Smagorinsky large-eddy viscosity, we
find that Rmc is not sensitive to the particular form of
the viscous cutoff. This work represents a significant extension of
the studies previously published by Schekochihin et al. (2004a) and
Haugen et al. (2004a) and the first detailed scan of the numerically
accessible part of the stability curve Rmc(Re).

---------------------------------------------------------
Title: The Case for a Distributed Solar Dynamo Shaped by Near-Surface
Shear
Authors: Brandenburg, Axel
2005ApJ...625..539B Altcode: 2005astro.ph..2275B
Arguments for and against the widely accepted picture of a solar
dynamo being seated in the tachocline are reviewed, and alternative
ideas concerning dynamos operating in the bulk of the convection zone,
or perhaps even in the near-surface shear layer, are discussed. Based
on the angular velocities of magnetic tracers, it is argued that the
observations are compatible with a distributed dynamo that may be
strongly shaped by the near-surface shear layer. Direct simulations
of dynamo action in a slab with turbulence and shear are presented
to discuss filling factor and tilt angles of bipolar regions in such
a model.

---------------------------------------------------------
Title: Investigation of Top Quark Spin Correlations at Hadron
Colliders
Authors: Bernreuther, W.; Brandenburg, A.; Si, Z. G.; Uwer, P.
2005iche.conf.1166B Altcode: 2004hep.ph...10197B; 2004iche.conf.1166B
We report on our results about hadronic tbar {t} production at NLO
QCD including t ,bar {t} spin effects, especially on tbar {t} spin
correlations.

---------------------------------------------------------
Title: The problem of small and large scale fields in the solar dynamo
Authors: Brandenburg, A.; Haugen, N. E. L.; Käpylä, P. J.; Sandin, C.
2005AN....326..174B Altcode: 2004astro.ph.12364B
Three closely related stumbling blocks of solar mean field dynamo
theory are discussed: how dominant are the small scale fields,
how is the alpha effect quenched, and whether magnetic and current
helicity fluxes alleviate the quenching? It is shown that even at the
largest currently available resolution there is no clear evidence
of power law scaling of the magnetic and kinetic energy spectra in
turbulence. However, using subgrid scale modeling, some indications
of asymptotic equipartition can be found. The frequently used first
order smoothing approach to calculate the alpha effect and other
transport coefficients is contrasted with the superior minimal tau
approximation. The possibility of catastrophic alpha quenching is
discussed as a result of magnetic helicity conservation. Magnetic and
current helicity fluxes are shown to alleviate catastrophic quenching
in the presence of shear. Evidence for strong large scale dynamo action,
even in the absence of helicity in the forcing, is presented.

---------------------------------------------------------
Title: Spatial dynamics of homochiralization
Authors: Multamäki, Tuomas; Brandenburg, Axel
2005IJAsB...4...75M Altcode: 2005q.bio.....5040M
The emergence and spread of chirality on the early Earth is
considered by studying a set of reaction-diffusion equations based
on a polymerization model. It is found that effective mixing of the
early oceans is necessary to reach the present homochiral state. The
possibility of introducing mass extinctions and modifying the emergence
rate of life are discussed.

---------------------------------------------------------
Title: Ejection of Bi-Helical Fields from the Sun
Authors: Brandenburg, Axel; Blackman, Eric G.
2005HiA....13..101B Altcode:
Over the past decade the measurement of magnetic and current helicity
at the solar surface has attracted significant interest. There is now
general consensus that the two helicities are negative in the north and
positive in the south. On the other hand the tilt of bipolar regions in
the clockwise direction in the north corresponds to a positive writhe
helicity. In the south the tilt is counterclockwise corresponding to
negative writhe helicity. These signs of writhe helicity which are thus
apposite to the twist helicity measured as current helicity are also
suggested by N-shaped sigmoids in the north and S-shaped sigmoids in
the south. We interpret these as bi-helical magnetic field structures
which have in the north negative magnetic helicity at smaller scales
and positive magnetic helicity at the largest scales and oppositely
in the south. This is also what is expected and required from dynamo
theory in order that the dynamo cycle is able to reverse the entire
field in a time as short as 11 years. The generation and evolution of
bi-helical fields is studied using hydromagnetic turbulence simulations
both for the convection zone and the solar wind.

---------------------------------------------------------
Title: Editorial
Authors: Anderson, Anja C.; Brandenburg, Axel
2005IJAsB...4....1A Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Thermal Production of Axinos in the Early Universe
Authors: Brandenburg, A.; Steffen, F. D.
2005sem..conf..271B Altcode: 2004hep.ph....7324B
We compute the thermal axino production rate in supersymmetric QCD to
leading order in the gauge coupling. Using hard thermal loop resummation
and the Braaten-Yuan prescription, we obtain a finite result in a
gauge-invariant way, which takes into account Debye screening in
the hot quark-gluon-squark-gluino plasma. The relic axino density
from thermal reactions in the early Universe is evaluated assuming
the axino is the lightest supersymmetric particle and stable due to
R-parity conservation. From the comparison with the WMAP results, we
find that axinos could provide the dominant part of cold dark matter,
for example, for an axino mass of 100 keV and a reheating temperature
of 106 GeV.

---------------------------------------------------------
Title: Importance of Magnetic Helicity in Dynamos
Authors: Brandenburg, Axel
2005LNP...664..219B Altcode: 2004astro.ph.12366B
Magnetic helicity is nearly conserved and its evolution equation
provides a dynamical feedback on the alpha effect that is distinct
from the conventional algebraic alpha quenching. The seriousness of
this dynamical alpha quenching is particularly evident in the case of
closed or periodic boxes. The explicit connection with catastrophic
alpha quenching is reviewed and the alleviating effects of magnetic
and current helicity fluxes are discussed.

---------------------------------------------------------
Title: Delayed correlation between turbulent energy injection and
dissipation
Authors: Pearson, Bruce R.; Yousef, Tarek A.; Haugen, Nils Erland L.;
Brandenburg, Axel; Krogstad, Per-Åge
2004PhRvE..70e6301P Altcode: 2004physics...4114P
The dimensionless kinetic energy dissipation rate Cɛ is
estimated from numerical simulations of statistically stationary
isotropic box turbulence that is slightly compressible. The
Taylor microscale Reynolds number (Reλ) range is
20≲Reλ≲220 and the statistical stationarity is
achieved with a random phase forcing method. The strong Reλ
dependence of Cɛ abates when Reλ≈100 after
which Cɛ slowly approaches ≈0.5 , a value slightly
different from previously reported simulations but in good agreement
with experimental results. If Cɛ is estimated at a
specific time step from the time series of the quantities involved
it is necessary to account for the time lag between energy injection
and energy dissipation. Also, the resulting value can differ from the
ensemble averaged value by up to ±30% . This may explain the spread
in results from previously published estimates of Cɛ .

---------------------------------------------------------
Title: Catastrophic alpha quenching alleviated by helicity flux
and shear
Authors: Brandenburg, A.; Sandin, C.
2004A&A...427...13B Altcode: 2004astro.ph..1267B
A new simulation set-up is proposed for studying mean field dynamo
action. The model combines the computational advantages of local
Cartesian geometry with the ability to include a shear profile that
resembles the sun's differential rotation at low latitudes. It is
shown that in a two-dimensional mean field model this geometry produces
cyclic solutions with dynamo waves traveling away from the equator -
as expected for a positive alpha effect in the northern hemisphere. In
three dimensions with turbulence driven by a helical forcing function,
an alpha effect is self-consistently generated in the presence of a
finite imposed toroidal magnetic field. The results suggest that, due
to a finite flux of current helicity out of the domain, alpha quenching
appears to be non-catastrophic - at least for intermediate values of the
magnetic Reynolds number. For larger values of the magnetic Reynolds
number, however, there is evidence for a reversal of the trend and
that α may decrease with increasing magnetic Reynolds number. Control
experiments with closed boundaries confirm that in the absence of a
current helicity flux, but with shear as before, alpha quenching is
always catastrophic and alpha decreases inversely proportional to the
magnetic Reynolds number. For solar parameters, our results suggest
a current helicity flux of about 0.001 Gtwopers. This corresponds to
a magnetic helicity flux, integrated over the northern hemisphere and
over the 11 year solar cycle, of about 1046 Mx2.

---------------------------------------------------------
Title: Nonlinear Current Helicity Fluxes in Turbulent Dynamos and
Alpha Quenching
Authors: Subramanian, Kandaswamy; Brandenburg, Axel
2004PhRvL..93t5001S Altcode: 2004astro.ph..8020S
Large scale dynamos produce small scale current helicity as a
waste product that quenches the large scale dynamo process (alpha
effect). This quenching can be catastrophic (i.e., intensify with
magnetic Reynolds number) unless one has fluxes of small scale magnetic
(or current) helicity out of the system. We derive the form of helicity
fluxes in turbulent dynamos, taking also into account the nonlinear
effects of Lorentz forces due to fluctuating fields. We confirm the
form of an earlier derived magnetic helicity flux term, and also show
that it is not renormalized by the small scale magnetic field, just
like turbulent diffusion. Additional nonlinear fluxes are identified,
which are driven by the anisotropic and antisymmetric parts of the
magnetic correlations. These could provide further ways for turbulent
dynamos to transport out small scale magnetic helicity, so as to avoid
catastrophic quenching.

---------------------------------------------------------
Title: Shearing and embedding box simulations of the magnetorotational
instability
Authors: Brandenburg, Axel; Dintrans, Boris; Haugen, Nils Erland L.
2004AIPC..733..122B Altcode: 2004astro.ph.12363B
Two different computational approaches to the magnetorotational
instability (MRI) are pursued: the shearing box approach which is suited
for local simulations and the embedding box approach whereby a Taylor
Couette flow is embedded in a box so that numerical problems with
the coordinate singularity are avoided. New shearing box simulations
are presented and differences between regular and hyperviscosity
are discussed. Preliminary simulations of spherical nonlinear Taylor
Couette flow in an embedding box are presented and the effects of an
axial field on the background flow are studied.

---------------------------------------------------------
Title: Suppression of small scale dynamo action by an imposed
magnetic field
Authors: Haugen, Nils Erland L.; Brandenburg, Axel
2004PhRvE..70c6408H Altcode: 2004astro.ph..2281H
Nonhelical hydromagnetic turbulence with an externally imposed magnetic
field is investigated using direct numerical simulations. It is shown
that the imposed magnetic field lowers the spectral magnetic energy in
the inertial range. This is explained by a suppression of the small
scale dynamo. At large scales, however, the spectral magnetic energy
increases with increasing imposed field strength for moderately strong
fields, and decreases only slightly for even stronger fields. The
presence of Alfvén waves is explicitly confirmed by monitoring the
evolution of magnetic field and velocity at one point. The frequency
ω agrees with vAk1 , where vA is the
Alfvén speed and k1 is the smallest wave number in the box.

---------------------------------------------------------
Title: Mach number dependence of the onset of dynamo action
Authors: Haugen, Nils Erland L.; Brandenburg, Axel; Mee, Antony J.
2004MNRAS.353..947H Altcode: 2004astro.ph..5453H
The effect of compressibility on the onset of non-helical turbulent
dynamo action is investigated using both direct simulations as well
as simulations with shock-capturing viscosities, keeping, however,
the regular magnetic diffusivity. It is found that the critical
magnetic Reynolds number increases from about 35 in the subsonic
regime to about 70 in the supersonic regime. Although the shock
structures are sharper in the high-resolution direct simulations
compared with the low-resolution shock-capturing simulations, the
magnetic field looks roughly similar in both cases and does not show
any shock structures. Similarly, the onset of dynamo action is not
significantly affected by the shock-capturing viscosity.

---------------------------------------------------------
Title: Inertial range scaling in numerical turbulence with
hyperviscosity
Authors: Haugen, Nils Erland L.; Brandenburg, Axel
2004PhRvE..70b6405H Altcode: 2004astro.ph..2301H
Numerical turbulence with hyperviscosity is studied and compared with
direct simulations using ordinary viscosity and data from wind tunnel
experiments. It is shown that the inertial range scaling is similar in
all three cases. Furthermore, the bottleneck effect is approximately
equally broad (about one order of magnitude) in these cases and only
its height is increased in the hyperviscous case—presumably as a
consequence of the steeper decent of the spectrum in the hyperviscous
subrange. The mean normalized dissipation rate is found to be in
agreement with both wind tunnel experiments and direct simulations. The
structure function exponents agree with the She-Leveque model. Decaying
turbulence with hyperviscosity still gives the usual t-1.25
decay law for the kinetic energy, and also the bottleneck effect is
still present and about equally strong.

---------------------------------------------------------
Title: Self-Regulating Supernova Heating in Interstellar Medium
Simulations
Authors: Sarson, Graeme R.; Shukurov, Anvar; Nordlund, Åke; Gudiksen,
Boris; Brandenburg, Axel
2004Ap&SS.292..267S Altcode: 2003astro.ph..7013S
Numerical simulations of the multi-phase interstellar medium have been
carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box
model, with random motions driven by supernova explosions. These
calculations incorporate the effects of magnetic fields and rotation
in 3D; these play important dynamical roles in the galaxy, but are
neglected in many other simulations. The supernovae driving the motions
are not arbitrarily imposed, but occur where gas accumulates into cold,
dense clouds; their implementation uses a physically motivated model
for the evolution of such clouds. The process is self-regulating, and
produces mean supernova rates as part of the solution. Simulations with
differing mean density show a power law relation between the supernova
rate and density, with exponent 1.7; this value is within the range
suggested from observations (taking star formation rate as a proxy for
supernova rate). The global structure of the supernova driven medium
is strongly affected by the presence of magnetic fields; e.g. for one
solution the filling factor of hot gas is found to vary from 0.19 (with
no field) to 0.12 (with initial mid-plane field B 0= 6 μG).

---------------------------------------------------------
Title: Outflows from Dynamo-Active Protostellar Accretion Discs
Authors: von Rekowski, Brigitta; Brandenburg, Axel; Dobler, Wolfgang;
Shukurov, Anvar
2004Ap&SS.292..493V Altcode: 2003astro.ph..6603V
An axisymmetric model of a cool, dynamo-active accretion disc is applied
to protostellar discs. Thermally and magnetically driven outflows
develop that are not collimated within 0.1 AU. In the presence of a
central magnetic field from the protostar, accretion onto the protostar
is highly episodic, which is in agreement with earlier work.

---------------------------------------------------------
Title: High-Resolution Simulations of Nonhelical MHD Turbulence
Authors: Haugen, N. E. L.; Brandenburg, A.; Dobler, W.
2004Ap&SS.292...53H Altcode: 2003astro.ph..6453H
According to the kinematic theory of nonhelical dynamo action, the
magnetic energy spectrum increases with wavenumber and peaks at the
resistive cutoff wavenumber. It has previously been argued that even
in the dynamical case, the magnetic energy peaks at the resistive
scale. Using high resolution simulations (up to 10243
meshpoints) with no large-scale imposed field, we show that the
magnetic energy peaks at a wavenumber that is independent of the
magnetic Reynolds number and about five times larger than the forcing
wavenumber. Throughout the inertial range, the spectral magnetic energy
exceeds the kinetic energy by a factor of two to three. Both spectra are
approximately parallel. The total energy spectrum seems to be close to k
-3/2, but there is a strong bottleneck effect and we suggest
that the asymptotic spectrum is instead k -5/3. This is
supported by the value of the second-order structure function exponent
that is found to be ζ2=0.70, suggesting a k -1.70
spectrum. The third-order structure function scaling exponent is very
close to unity,—in agreement with Goldreich Sridhar theory.

---------------------------------------------------------
Title: Identification of gravity waves in hydrodynamical simulations
Authors: Dintrans, B.; Brandenburg, A.
2004A&A...421..775D Altcode: 2003astro.ph.11094D
The excitation of internal gravity waves by an entropy bubble
oscillating in an isothermal atmosphere is investigated using direct
two-dimensional numerical simulations. The oscillation field is measured
by a projection of the simulated velocity field onto the anelastic
solutions of the linear eigenvalue problem for the perturbations. This
facilitates a quantitative study of both the spectrum and the amplitudes
of excited g-modes. Appendices are only available in electronic
form at http://www.edpsciences.org

---------------------------------------------------------
Title: Structured, Dynamo Driven Stellar and Disc Winds
Authors: von Rekowski, B.; Brandenburg, A.
2004ASPC..313..476V Altcode: 2004apnw.conf..476V; 2003astro.ph.10398V
Considerable progress has been made in understanding the hydrodynamics,
but only to a certain extent the magnetohydrodynamics, of shaping
bipolar outflows forming protoplanetary nebulae (PPNs) and planetary
nebulae (PNs). In particular, Blackman et al. (2001a, 2001b) point out
two problems related to the formation of PNs and PPNs, regarding the
formation of multipolar structures and the origin of the nebulae. They
propose a solution by giving a semi-quantitative physical model which
should be investigated by numerical simulations.

---------------------------------------------------------
Title: How long can left and right handed life forms coexist?
Authors: Brandenburg, Axel; Multamäki, Tuomas
2004IJAsB...3..209B Altcode: 2004q.bio.....7008B
Reaction-diffusion equations based on a polymerization model are solved
to simulate the spreading of hypothetic left and right-handed life
forms on the Earth's surface. The equations exhibit front-like behavior
as is familiar from the theory of the spreading of epidemics. It is
shown that the relevant time scale for achieving global homochirality
is not, however, the time scale of front propagation, but the much
longer global diffusion time. The process can be sped up by turbulence
and large scale flows. It is speculated that, if the deep layers of
the early ocean were sufficiently quiescent, there may have been the
possibility of competing early life forms with opposite handedness.

---------------------------------------------------------
Title: Simulations of nonhelical hydromagnetic turbulence
Authors: Haugen, Nils Erland; Brandenburg, Axel; Dobler, Wolfgang
2004PhRvE..70a6308H Altcode: 2003astro.ph..7059H
Nonhelical hydromagnetic forced turbulence is investigated using
large scale simulations on up to 256 processors and 10243
mesh points. The magnetic Prandtl number is varied between 1/8 and 30,
although in most cases it is unity. When the magnetic Reynolds number
is based on the inverse forcing wave number, the critical value for
dynamo action is shown to be around 35 for magnetic Prandtl number
of unity. For small magnetic Prandtl numbers we find the critical
magnetic Reynolds number to increase with decreasing magnetic Prandtl
number. The Kazantsev k3/2 spectrum for magnetic energy is
confirmed for the kinematic regime, i.e., when nonlinear effects are
still unimportant and when the magnetic Prandtl number is unity. In
the nonlinear regime, the energy budget converges for large Reynolds
numbers (around 1000) such that for our parameters about 70% is
in kinetic energy and about 30% is in magnetic energy. The energy
dissipation rates are converged to 30% viscous dissipation and 70%
resistive dissipation. Second-order structure functions of the Elsasser
variables give evidence for a k-5/3 spectrum. Nevertheless,
the three-dimensional spectrum is close to k-3/2 , but
we argue that this is due to the bottleneck effect. The bottleneck
effect is shown to be equally strong both for magnetic and nonmagnetic
turbulence, but it is far weaker in one-dimensional spectra that are
normally studied in laboratory turbulence. Structure function exponents
for other orders are well described by the She-Leveque formula, but
the velocity field is significantly less intermittent and the magnetic
field is more intermittent than the Elsasser variables.

---------------------------------------------------------
Title: Outflows and accretion in a star-disc system with stellar
magnetosphere and disc dynamo
Authors: von Rekowski, B.; Brandenburg, A.
2004A&A...420...17V Altcode: 2003astro.ph..7201V
The interaction between a protostellar magnetosphere and a surrounding
dynamo-active accretion disc is investigated using an axisymmetric
mean-field model. In all models investigated, the dynamo-generated
magnetic field in the disc arranges itself such that in the corona,
the field threading the disc is anti-aligned with the central dipole so
that no X-point forms. When the magnetospheric field is strong enough
(stellar surface field strength around 2 kG or larger), accretion
happens in a recurrent fashion with periods of around 15 to 30 days,
which is somewhat longer than the stellar rotation period of around 10
days. In the case of a stellar surface field strength of at least a few
100 G, the star is being spun up by the magnetic torque exerted on the
star. The stellar accretion rates are always reduced by the presence
of a magnetosphere which tends to divert a much larger fraction of the
disc material into the wind. Both, a pressure-driven stellar wind and
a disc wind form. In all our models with disc dynamo, the disc wind is
structured and driven by magneto-centrifugal as well as pressure forces.

---------------------------------------------------------
Title: New Algorithms for Magnetohydrodynamics and Gravity that
Emphasize Resolution and Speed.
Authors: Maron, J.; Dennis, T.; Howes, G.; Brandenburg, A.; Chandran,
B.; Blackman, E.
2004DDA....35.0407M Altcode: 2004BAAS...36..854M
The Gradient Particle Magnetohydrodynamics (GPM) algorithm combines
the strengths of an adaptive grid code (AMR) and a smoothed particle
code (SPH) by instilling grid-quality gradients into a Lagrangian
particle code. It is of particular utility for disk/jet systems. The hypergradient code uses high-precision tuned finite differences
to achieve spectral-quality resolution with 5 times the speed of a
spectral code. The finite differencing is not based on a high-order
polynomial fit. The polynomial scheme has supurb accuracy for
low-wavenumber gradients but fails at high wavenumbers. We instead
use a scheme tuned to enhance high-wavenumber accuracy at the expense
of low wavenumbers, although the loss of low-wavenumber accuracy
is negligibly slight. A tuned gradient is capable of capturing all
wavenumbers up to 80 percent of the Nyquist limit with an error of
no worse than 1 percent. The fact that gradients are based on finite
differences enables diverse geometries to be considered and eliminates
the parallel communications bottleneck. The gravity algorithm
is based on the Barnes-Hut tree. It evades the latencies associated
with memory accesses, divides, and square roots by grouping bundles of
particles together into a simultaneous treewalk and using a polynomial
series to approximate the divides and square roots. The algorithm runs
10 times faster than the standard tree codes with no loss of accuracy
and it works for individual timesteps.

---------------------------------------------------------
Title: Magnetic helicity evolution in a periodic domain with
imposed field
Authors: Brandenburg, Axel; Matthaeus, William H.
2004PhRvE..69e6407B Altcode: 2003astro.ph..5373B
In helical hydromagnetic turbulence with an imposed magnetic field
(which is constant in space and time) the magnetic helicity of the
field within a periodic domain is no longer an invariant of the ideal
equations. Alternatively, there is a generalized magnetic helicity
that is an invariant of the ideal equations. It is shown that this
quantity is not gauge invariant and that it can therefore not be used
in practice. Instead, the evolution equation of the magnetic helicity
of the field describing the deviation from the imposed field is shown
to be a useful tool. It is demonstrated that this tool can determine
steady state quenching of the alpha-effect. A simple three-scale model
is derived to describe the evolution of the magnetic helicity and
to predict its sign as a function of the imposed field strength. The
results of the model agree favorably with simulations.

---------------------------------------------------------
Title: Self-similar scaling in decaying numerical turbulence
Authors: Yousef, Tarek A.; Haugen, Nils Erland L.; Brandenburg, Axel
2004PhRvE..69e6303Y Altcode: 2003astro.ph.12505Y
Decaying turbulence is studied numerically using as initial condition
a random flow whose shell-integrated energy spectrum increases with
wave number k like kq . Alternatively, initial conditions
are generated from a driven turbulence simulation by simply stopping
the driving. It is known that the dependence of the decaying energy
spectrum on wave number, time, and viscosity can be collapsed onto a
unique scaling function that depends only on two parameters. This is
confirmed using three-dimensional simulations and the dependence of
the scaling function on its two arguments is determined.

---------------------------------------------------------
Title: Simulations of dust-trapping vortices in protoplanetary discs
Authors: Johansen, A.; Andersen, A. C.; Brandenburg, A.
2004A&A...417..361J Altcode: 2003astro.ph.10059J
Local three-dimensional shearing box simulations of the compressible
coupled dust-gas equations are used in the fluid approximation to
study the evolution of different initial vortex configurations in a
protoplanetary disc and their dust-trapping capabilities. The initial
conditions for the gas are derived from an analytic solution to the
compressible Euler equation and the continuity equation. The solution
is valid if there is a vacuum outside the vortex. In the simulations
the vortex is either embedded in a hot corona, or it is extended in
a cylindrical fashion in the vertical direction. Both configurations
are found to survive for at least one orbit and lead to accumulation
of dust inside the vortex. This confirms earlier findings that dust
accumulates in anticyclonic vortices, indicating that this is a viable
mechanism for planetesimal formation.

---------------------------------------------------------
Title: Non-Fickian diffusion and tau approximation from numerical
turbulence
Authors: Brandenburg, Axel; Käpylä, Petri J.; Mohammed, Amjed
2004PhFl...16.1020B Altcode: 2003astro.ph..6521B
Evidence for non-Fickian diffusion of a passive scalar is presented
using direct simulations of homogeneous isotropic turbulence. The
results compare favorably with an explicitly time-dependent closure
model based on the tau approximation. In the numerical experiments
three different cases are considered: (i) zero mean concentration
with finite initial concentration flux, (ii) an initial top hat
profile for the concentration, and (iii) an imposed background
concentration gradient. All cases agree in the resulting relaxation
time in the tau approximation relating the triple correlation to the
concentration flux. The first order smoothing approximation is shown
to be inapplicable.

---------------------------------------------------------
Title: Stochastic excitation of gravity waves by overshooting
convection in solar-type stars
Authors: Dintrans, Boris; Brandenburg, Axel; Nordlund, Ake; Stein,
R. F.
2004astro.ph..3093D Altcode:
The excitation of gravity waves by penetrative convective plumes is
investigated using 2D direct simulations of compressible convection. The
oscillation field is measured by a new technique based on the projection
of our simulation data onto the theoretical g-modes solutions of the
associated linear eigenvalue problem. This allows us to determine both
the excited modes and their corresponding amplitudes accurately.

---------------------------------------------------------
Title: The effects of spiral arms on the multi-phase ISM
Authors: Shukurov, Anvar; Sarson, Graeme R.; Nordlund, Åke; Gudiksen,
Boris; Brandenburg, Axel
2004Ap&SS.289..319S Altcode: 2002astro.ph.12260S
Statistical parameters of the ISM driven by thermal energy
injectionsfrom supernova explosions have been obtained from 3D,
nonlinear,magnetohydrodynamic, shearing-box simulations for spiral
arm andinterarm regions. The density scale height obtained for the
interarm regionsis 50% larger than within the spiral arms because
of thehigher gas temperature. The filling factorof the hot gas is
also significantly larger between the armsand depends sensitively on
magnetic field strength.

---------------------------------------------------------
Title: Helical coronal ejections and their role in the solar cycle
Authors: Brandenburg, Axel; Sandin, Christer; Käpylä, Petri J.
2004IAUS..223...57B Altcode: 2005IAUS..223...57B; 2004astro.ph..7598B
The standard theory of the solar cycle in terms of an alpha-Omega dynamo
hinges on a proper understanding of the nonlinear alpha effect. Boundary
conditions play a surprisingly important role in determining the
magnitude of alpha. For closed boundaries, the total magnetic helicity
is conserved, and since the alpha effect produces magnetic helicity
of one sign in the large scale field, it must simultaneously produce
magnetic helicity of the opposite sign. It is this secondary magnetic
helicity that suppresses the dynamo in a potentially catastrophic
fashion. Open boundaries allow magnetic helicity to be lost. Simulations
are presented that allow an estimate of alpha in the presence of open
or closed boundaries, either with or without solar-like differential
rotation. In all cases the sign of the magnetic helicity agrees with
that observed at the solar surface (negative in the north, positive
in the south), where significant amounts of magnetic helicity can be
ejected via coronal mass ejections. It is shown that open boundaries
tend to alleviate catastrophic alpha quenching. The importance of
looking at current helicity instead of magnetic helicity is emphasized
and the conceptual advantages are discussed.

---------------------------------------------------------
Title: Turbulent magnetic Prandtl number and magnetic diffusivity
quenching from simulations
Authors: Yousef, T. A.; Brandenburg, A.; Rüdiger, G.
2003A&A...411..321Y Altcode: 2003astro.ph..2425Y
Forced turbulence simulations are used to determine the turbulent
kinematic viscosity, nut , from the decay rate of a large
scale velocity field. Likewise, the turbulent magnetic diffusivity,
etat, is determined from the decay of a large scale magnetic
field. In the kinematic regime, when the field is weak, the turbulent
magnetic Prandtl number, nut/etat, is about
unity. When the field is nonhelical, etat is quenched
when magnetic and kinetic energies become comparable. For helical
fields the quenching is stronger and can be described by a dynamical
quenching formula.

---------------------------------------------------------
Title: Is Nonhelical Hydromagnetic Turbulence Peaked at Small Scales?
Authors: Haugen, Nils Erland L.; Brandenburg, Axel; Dobler, Wolfgang
2003ApJ...597L.141H Altcode: 2003astro.ph..3372H
Nonhelical hydromagnetic turbulence without an imposed magnetic field is
considered in the case where the magnetic Prandtl number is unity. The
magnetic field is entirely due to dynamo action. The magnetic energy
spectrum peaks at a wavenumber of about 5 times the minimum wavenumber
in the domain, and not at the resistive scale, as has previously
been argued. Throughout the inertial range, the spectral magnetic
energy exceeds the kinetic energy by a factor of about 2.5, and both
spectra are approximately parallel. At first glance, the total energy
spectrum seems to be close to k-3/2, but there is a strong
bottleneck effect and it is suggested that the asymptotic spectrum is
k-5/3. This is supported by the value of the second-order
structure function exponent that is found to be ζ2=0.70,
suggesting a k-1.70 spectrum.

---------------------------------------------------------
Title: Relaxation of writhe and twist of a bi-helical magnetic field
Authors: Yousef, T. A.; Brandenburg, A.
2003A&A...407....7Y Altcode: 2003astro.ph..3148Y
In the past few years suggestions have emerged that the solar magnetic
field might have a bi-helical contribution with oppositely polarized
magnetic fields at large and small scales, and that the shedding of
such fields may be crucial for the operation of the dynamo. It is shown
that, if a bi-helical field is shed into the solar wind, positive and
negative contributions of the magnetic helicity spectrum tend to mix and
decay. Even in the absence of turbulence, mixing and decay can occur
on a time scale faster than the resistive one provided the two signs
of magnetic helicity originate from a single tube. In the presence
of turbulence, positively and negatively polarized contributions mix
rapidly in such a way that the ratio of magnetic helicity to magnetic
energy is largest both at the largest scale and in the dissipation
range. In absolute units the small scale excess of helical fields is
however negligible.

---------------------------------------------------------
Title: Bottleneck effect in three-dimensional turbulence simulations
Authors: Dobler, Wolfgang; Haugen, Nils Erland; Yousef, Tarek A.;
Brandenburg, Axel
2003PhRvE..68b6304D Altcode: 2003astro.ph..3324D
At numerical resolutions around 5123 and above,
three-dimensional energy spectra from turbulence simulations begin
to show noticeably shallower spectra than k-5/3 near the
dissipation wave number (“bottleneck effect”). This effect is
shown to be significantly weaker in one-dimensional spectra such
as those obtained in wind tunnel turbulence. The difference can be
understood in terms of the transformation between the one-dimensional
and three-dimensional energy spectra under the assumption that the
turbulent velocity field is isotropic. Transversal and longitudinal
energy spectra are similar and can both accurately be computed from
the full three-dimensional spectra. Second-order structure functions
are less susceptible to the bottleneck effect and may be better suited
for inferring the scaling exponent from numerical simulation data.

---------------------------------------------------------
Title: Outflows and Accretion in a Protostellar Star-disc System
Authors: von Rekowski, Brigitta; Brandenburg, Axel
2003ANS...324...68V Altcode: 2003ANS...324..I10V
No abstract at ADS

---------------------------------------------------------
Title: Decay of Magnetic Fields in the Early Universe
Authors: Hindmarsh, Mark; Christensson, M.; Brandenburg, A.
2003sem..conf..482H Altcode: 2003astro.ph..2320H
We study the evolution of a stochastic helical magnetic field generated
in the early Universe after the electroweak phase transition, using
standard magnetohydrodynamics (MHD). We find how the coherence length
ξ, magnetic energy EM and magnetic helicity H evolve with
time. We show that the self-similarity of the magnetic power spectrum
alone implies that ξ ~ t1/2. This in turn implies that
magnetic helicity decays as H ~ t-2s, and that the magnetic
energy decays as EM ~ t-0.5-2s, where s inversely
proportional to the magnetic Reynolds number ReM. These
laws improve on several previous estimates.

---------------------------------------------------------
Title: Computational aspects of astrophysical MHD and turbulence
Authors: Brandenburg, Axel
2003and..book..269B Altcode: 2003eclm.book..269B; 2001astro.ph..9497B
The advantages of high-order finite difference scheme for
astrophysical MHD and turbulence simulations are highlighted. A
number of one-dimensional test cases are presented ranging from
various shock tests to Parker-type wind solutions. Applications
to magnetized accretion discs and their associated outflows are
discussed. Particular emphasis is placed on the possibility of dynamo
action in three-dimensional turbulent convection and shear flows,
which is relevant to stars and astrophysical discs. The generation
of large scale fields is discussed in terms of an inverse magnetic
cascade and the consequences imposed by magnetic helicity conservation
are reviewed with particular emphasis on the issue of alpha-quenching.

---------------------------------------------------------
Title: MHD simulations of small and large scale dynamos
Authors: Brandenburg, A.; Haugen, N. E. L.; Dobler, W.
2003astro.ph..3371B Altcode:
Isotropic homogeneous hydromagnetic turbulence is studied using
numerical simulations at resolutions of up to 1024^3 meshpoints. It is
argued that, in contrast to the kinematic regime, the nonlinear regime
is characterized by a spectral magnetic power that is decreasing with
increasing wavenumber, regardless of whether or not the turbulence has
helicity. This means that the root-mean-square field strength converges
to a limiting value at large magnetic Reynolds numbers. The total
(magnetic and kinetic) energy spectrum tends to be somewhat shallower
than k^{-5/3}, in agreement with the findings of other groups. In the
presence of helicity, an inverse cascade develops, provided the scale
separation between the size of the computational box and the scale of
the energy carrying eddies exceeds a ratio of at least two. Finally,
the constraints imposed by magnetic helicity conservation on mean-field
theory are reviewed and new results of simulations are presented.

---------------------------------------------------------
Title: Structured outflow from a dynamo active accretion disc
Authors: von Rekowski, B.; Brandenburg, A.; Dobler, W.; Dobler, W.;
Shukurov, A.
2003A&A...398..825V Altcode: 2000astro.ph..3174V
We present an axisymmetric numerical model of a dynamo active
accretion disc. If the dynamo-generated magnetic field in the disc
is sufficiently strong (close to equipartition with thermal energy),
a fast magneto-centrifugally driven outflow develops within a conical
shell near the rotation axis, together with a slower pressure driven
outflow from the outer parts of the disc as well as around the axis. Our
results show that a dynamo active accretion disc can contribute to
driving an outflow even without any external magnetic field. The fast
outflow in the conical shell is confined by the azimuthal field which is
produced by the dynamo in the disc and advected to the disc corona. This
part of the outflow has high angular momentum and is cooler and less
dense than its surroundings. The conical shell's half-opening angle
is typically about 30o near the disc and decreases slightly
with height. The slow outflow is hotter and denser.

---------------------------------------------------------
Title: Doubly Helical Coronal Ejections from Dynamos and Their Role
in Sustaining the Solar Cycle
Authors: Blackman, Eric G.; Brandenburg, Axel
2003ApJ...584L..99B Altcode: 2002astro.ph.12010B
Two questions about the solar magnetic field might be answered together
once their connection is identified. The first is important for
large-scale dynamo theory: what prevents the magnetic back-reaction
forces from shutting down the dynamo cycle? The second question is,
what determines the handedness of twist and writhe in magnetized coronal
ejecta? Magnetic helicity conservation is important for answering both
questions. Conservation implies that dynamo generation of large-scale
writhed structures is accompanied by the oppositely signed twist along
these structures. The latter is associated with the back-reaction
force. We suggest that coronal mass ejections simultaneously liberate
small-scale twist and large-scale writhe of opposite sign, helping
to prevent the cycle from quenching and enabling a net magnetic flux
change in each hemisphere. Solar observations and helicity spectrum
measurements from our simulation of a rising flux tube support this
idea. We show a new pictorial of dynamo flux generation that includes
the back-reaction and magnetic helicity conservation and represents
the field by a ribbon or tube rather than a line.

---------------------------------------------------------
Title: Contributions to the theory of a two-scale homogeneous dynamo
experiment
Authors: Rädler, Karl-Heinz; Brandenburg, Axel
2003PhRvE..67b6401R Altcode: 2002physics...8023R
The principle of the two-scale dynamo experiment at the
Forschungszentrum Karlsruhe is closely related to that of the Roberts
dynamo working with a simple fluid flow which is, with respect to proper
Cartesian coordinates x, y, and z, periodic in x and y and independent
of z. A modified Roberts dynamo problem is considered with a flow more
similar to that in the experimental device. Solutions are calculated
numerically, and on this basis an estimate of the excitation condition
of the experimental dynamo is given. The modified Roberts dynamo
problem is also considered in the framework of the mean-field dynamo
theory, in which the crucial induction effect of the fluid motion is an
anisotropic α effect. Numerical results are given for the dependence
of the mean-field coefficients on the fluid flow rates. The excitation
condition of the dynamo is also discussed within this framework. The
behavior of the dynamo in the nonlinear regime, i.e., with backreaction
of the magnetic field on the fluid flow, depends on the effect of the
Lorentz force on the flow rates. The quantities determining this effect
are calculated numerically. The results for the mean-field coefficients
and the quantities describing the backreaction provide corrections to
earlier results, which were obtained under simplifying assumptions.

---------------------------------------------------------
Title: The Helicity Issue in Large Scale Dynamos
Authors: Brandenburg, A.
2003LNP...614..402B Altcode: 2002astro.ph..7394B; 2003tmfa.conf..402B
The connection between helically isotropic MHD turbulence and mean-field
dynamo theory is reviewed. The nonlinearity in the mean-field theory
is not yet well established, but detailed comparison with simulations
begin to help select viable forms of the nonlinearity. The crucial
discriminant is the magnetic helicity, which is known to evolve only on
a slow resistive time scale in the limit of large magnetic Reynolds
number. Particular emphasis is put on the possibility of memory
effects, which means that an additional explicitly time-dependent
equation for the nonlinearity is solved simultaneously with the
mean-field equations. This approach leads to better agreement with
the simulations, while it would also produce more favorable agreement
between models and stellar dynamos.

---------------------------------------------------------
Title: Ejection of Bi-Helical Magnetic Fields from the Sun
Authors: Brandenburg, Axel; Blackman, Eric G.
2003IAUJD...3E..33B Altcode: 2003astro.ph.12543B
Over the past decade the measurement of magnetic and current helicity
at the solar surface has attracted significant interest. There is now
general consensus that the two helicities are negative in the north and
positive in the south. On the other hand the tilt of bipolar regions in
the clockwise direction in the north corresponds to a positive writhe
helicity. In the south the tilt is counterclockwise corresponding to
negative writhe helicity. These signs of writhe helicity which are thus
apposite to the twist helicity measured as current helicity are also
suggested by N-shaped sigmoids in the north and S-shaped sigmoids in
the south. We interpret these as bi-helical magnetic field structures
which have in the north negative magnetic helicity at smaller scales
and positive magnetic helicity at the largest scales and oppositely
in the south. This is also what is expected and required from dynamo
theory in order that the dynamo cycle is able to reverse the entire
field in a time as short as 11 years. The generation and evolution of
bi-helical fields is studied using hydromagnetic turbulence simulations
both for the convection zone and the solar wind.

---------------------------------------------------------
Title: On the generation of internal gravity waves by penetrative
convection
Authors: Dintrans, B.; Brandenburg, A.; Nordlund, Å.; Stein, R. F.
2003sf2a.conf..511D Altcode: 2003sf2a.confE.216D
Gravity waves propagating in the radiative zones of solar-type stars are
suspected to play a major role in the transport processes. However, the
problem of their excitation remains open as a simple kappa-mechanism
based on hydrogen and helium ionization zones is not applicable
here. One possibility concerns the excitation by overshooting convection
from neighboring convection zones. Strong downward plumes are known
to penetrate substantial distances into the adjacent stable zone so
that internal gravity waves can be randomly generated. We will present
results coming from 2D-simulations of overshooting convection, for
which a new detection method based on the anelastic subspace allows
us to precisely measure internal waves which are stochastically excited.

---------------------------------------------------------
Title: Stochastic Excitation of Gravity Waves by Overshooting
Convection in Solar-Type Stars
Authors: Dintrans, Boris; Brandenburg, Axel; Nordlund, Åke; Stein,
Robert F.
2003Ap&SS.284..237D Altcode:
The excitation of gravity waves by penetrative convective plumes is
investigated using 2D direct simulations of compressible convection. The
oscillation field is measured by a new technique based on the projection
of our simulation data onto the theoretical g-modes solutions of the
associated linear eigenvalue problem. This allows us to determine both
the excited modes and their corresponding amplitudes accurately.

---------------------------------------------------------
Title: How magnetic helicity ejection helps large scale dynamos
Authors: Brandenburg, A.; Blackman, E. G.; Sarson, G. R.
2003AdSpR..32.1835B Altcode: 2003astro.ph..5374B
There is mounting evidence that the ejection of magnetic helicity
from the solar surface is important for the solar dynamo. Observations
suggest that in the northern hemisphere the magnetic helicity flux is
negative. We propose that this magnetic helicity flux is mostly due to
small scale magnetic fields; in contrast to the more systematic large
scale field of the 11 year cycle, whose helicity flux may be of opposite
sign, and may be excluded from the observational interpretation. Using
idealized simulations of MHD turbulence as well as a simple two-scale
model, we show that shedding small scale (helical) field has two
important effects. (i) The strength of the large scale field reaches the
observed levels. (ii) The evolution of the large scale field proceeds on
time scales shorter than the resistive time scale, as would otherwise
be enforced by magnetic helicity conservation. In other words, the
losses ensure that the solar dynamo is always in the near-kinematic
regime. This requires, however, that the ratio of small scale to large
scale losses cannot be too small, for otherwise the large scale field
in the near-kinematic regime will not reach the observed values.

---------------------------------------------------------
Title: Helical Surface Structures
Authors: Brandenburg, A.; Blackman, E. G.
2003IAUS..210..233B Altcode: 2002astro.ph.12019B
Over the past few years there has been growing interest in helical
magnetic field structures seen at the solar surface, in coronal mass
ejections, as well as in the solar wind. Although there is a great
deal of randomness in the data, on average the extended structures are
mostly left-handed on the northern hemisphere and right-handed on the
southern. Surface field structures are also classified as dextral (=
right bearing) and sinistral (= left bearing) occurring preferentially
in the northern and southern hemispheres respectively. Of particular
interest here is a quantitative measurement of the associated emergence
rates of helical structures, which translate to magnetic helicity
fluxes. In this review, we give a brief survey of what has been found
so far and what is expected based on models. Particular emphasis is put
on the scale dependence of the associated fields and an attempt is made
to estimate the helicity flux of the mean field vs. fluctuating field.

---------------------------------------------------------
Title: Magnetic helicity and the solar dynamo
Authors: Brandenburg, Axel; Blackman, Eric G.
2002ESASP.506..805B Altcode: 2002ESPM...10..805B; 2002svco.conf..805B
Over the past few years there has been growing interest in helical
magnetic field structures seen at the solar surface, in coronal mass
ejections, as well as in the solar wind. Although there is a great
deal of randomness in the data, on average the extended structures
are mostly left-handed on the northern hemisphere and right-handed on
the southern. Surface field structures are also classified as dextral
(=right bearing) and sinistral (=left bearing) occurring preferentially
in the northern and southern hemispheres respectively. Of particular
interest here is a quantitative measurement of the associated emergence
rates of helical structures, which translate to magnetic helicity
fluxes. In this review, we give a brief survey of what has been found
so far and what is expected based on models. Particular emphasis is put
on the scale dependence of the associated fields and an attempt is made
to estimate the helicity flux of the mean field vs. fluctuating field.

---------------------------------------------------------
Title: Dynamic Nonlinearity in Large-Scale Dynamos with Shear
Authors: Blackman, Eric G.; Brandenburg, Axel
2002ApJ...579..359B Altcode: 2002astro.ph..4497B
We supplement the mean field dynamo growth equation with the total
magnetic helicity evolution equation. This provides an explicitly
time-dependent model for α-quenching in dynamo theory. For dynamos
without shear, this approach accounts for the observed large-scale
field growth and saturation in numerical simulations. After a
significant kinematic phase, the dynamo is resistively quenched, i.e.,
the saturation time depends on the microscopic resistivity. This is
independent of whether or not the turbulent diffusivity is resistively
quenched. We find that the approach is also successful for dynamos
that include shear and exhibit migratory waves (cycles). In this case,
however, whether or not the cycle period remains of the order of the
dynamical timescale at large magnetic Reynolds numbers does depend
on how the turbulent magnetic diffusivity quenches. Since this is
unconstrained by magnetic helicity conservation, the diffusivity
is currently an input parameter. Comparison with current numerical
experiments suggests a turbulent diffusivity that depends only weakly
on the magnetic Reynolds number, but higher resolution simulations
are needed.

---------------------------------------------------------
Title: Magnetoconvection and dynamo coefficients. II. Field-direction
dependent pumping of magnetic field
Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A.; Rüdiger, G.
2002A&A...394..735O Altcode: 2002astro.ph..2299O
We study the pumping of magnetic flux in three-dimensional compressible
magnetoconvection in the context of stellar dynamos. The simulation
domain represents a rectangular section from the lower part of
a stellar convection zone plus the underlying stably stratified
layer, with a total depth of up to five pressure scale heights. Once
convection has attained a statistically stationary state, a magnetic
field is introduced. The magnetic field is subsequently modified
by the convective motions, and the resulting pumping effects are
isolated by calculating various coefficients of the expansion of the
electromotive force, /line{u}x{b}, in terms of components of the mean
magnetic field. The dependence of the pumping effects on rotation,
latitude and other parameters is studied. First numerical evidence
is found for the existence of pumping effects in the horizontal
directions. Evidence is found that the pumping effects act differently
on different components of the mean magnetic field. Latitudinal pumping
is mainly equatorward for a toroidal field, and can be poleward for a
poloidal field. Longitudinal pumping is mainly retrograde for the radial
field but prograde for the latitudinal field. The pumping effect in the
vertical direction is found to be dominated by the diamagnetic effect,
equivalent to a predominating downward advection with a maximum speed in
the turbulent case of about 10% of the rms convective velocity. Where
possible, an attempt is made to identify the physical origin of the
effect. Finally, some consequences of the results for stellar dynamos
are discussed.

---------------------------------------------------------
Title: Hydromagnetic turbulence in computer simulations
Authors: Brandenburg, A.; Dobler, W.
2002CoPhC.147..471B Altcode: 2001astro.ph.11569B
The usefulness of high-order schemes in astrophysical MHD turbulence
simulations is discussed. Simple advection tests of hat profiles are
used to compare schemes of different order. Higher order schemes
generally need less explicit diffusion. In the case of a standing
Burgers shock it is shown that the overall accuracy improves as the
order of the scheme is increased. A memory efficient 3-step 2N-RK scheme
is used. For cache efficiency, the entire set of equations is solved
along pencils in the yz-plane. The advantage of solving for the magnetic
vector potential is highlighted. Finally, results from a simulation of
helical turbulence exhibiting large scale dynamo action are discussed.

---------------------------------------------------------
Title: Magnetic helicity in stellar dynamos: new numerical experiments
Authors: Brandenburg, A.; Dobler, W.; Subramanian, K.
2002AN....323...99B Altcode: 2001astro.ph.11567B
The theory of large scale dynamos is reviewed with particular emphasis
on the magnetic helicity constraint in the presence of closed and open
boundaries. In the presence of closed or periodic boundaries, helical
dynamos respond to the helicity constraint by developing small scale
separation in the kinematic regime, and by showing long time scales in
the nonlinear regime where the scale separation has grown to the maximum
possible value. A resistively limited evolution towards saturation
is also found at intermediate scales before the largest scale of the
system is reached. Larger aspect ratios can give rise to different
structures of the mean field which are obtained at early times, but the
final saturation field strength is still decreasing with decreasing
resistivity. In the presence of shear, cyclic magnetic fields are
found whose period is increasing with decreasing resistivity, but the
saturation energy of the mean field is in strong super-equipartition
with the turbulent energy. It is shown that artificially induced
losses of small scale field of opposite sign of magnetic helicity
as the large scale field can, at least in principle, accelerate the
production of large scale (poloidal) field. Based on mean field models
with an outer potential field boundary condition in spherical geometry,
we verify that the sign of the magnetic helicity flux from the large
scale field agrees with the sign of alpha. For solar parameters,
typical magnetic helicity fluxes lie around 1047 Mx2 per cycle.

---------------------------------------------------------
Title: A new look at dynamo cycle amplitudes
Authors: Saar, S. H.; Brandenburg, A.
2002AN....323..357S Altcode: 2002astro.ph..7392S
We explore the dependence of the amplitude of stellar dynamo cycle
variability (as seen in the Mount Wilson Ca II HK timeseries data) on
other stellar parameters. We find that the fractional cycle amplitude
A_cyc (i.e. the ratio of the peak-to-peak variation to the average)
decreases somewhat with mean activity, increases with decreasing
effective temperature, but is not correlated with inverse Rossby
number Ro-1. We find that A_cyc increases with the ratio
of cycle and rotational frequencies omega_cyc /Omega along two, nearly
parallel branches.

---------------------------------------------------------
Title: Solar and stellar dynamos - latest developments
Authors: Brandenburg, A.; Dobler, W.
2002AN....323..411B Altcode: 2002astro.ph..7393B
Recent progress in the theory of solar and stellar dynamos is
reviewed. Particular emphasis is placed on the mean-field theory which
tries to describe the collective behavior of the magnetic field. In
order to understand solar and stellar activity, a quantitatively
reliable theory is necessary. Much of the new developments center
around magnetic helicity conservation which is seen to be important
in numerical simulations. Only a dynamical, explicitly time dependent
theory of alpha -quenching is able to describe this behavior correctly.

---------------------------------------------------------
Title: Local and Nonlocal Magnetic Diffusion and Alpha-Effect Tensors
in Shear Flow Turbulence
Authors: Brandenburg, Axel; Sokoloff, Dmitry
2002GApFD..96..319B Altcode: 2001astro.ph.11568B
Various approaches to estimate turbulent transport coefficients from
numerical simulations of hydromagnetic turbulence are discussed. A
quantitative comparison between the averaged magnetic field obtained
from a specific three-dimensional simulation of a rotating turbulent
shear flow in a slab and a simple one-dimensional alpha-omega dynamo
model is given. A direct determination of transport coefficients is
attempted by calculating the correlation matrix of different components
of the field and its derivatives. This matrix relates the electromotive
force to physically relevant parameters like the tensor components of
the f-effect and the turbulent diffusivity. The f-effect operating on
the toroidal field is found to be negative and of similar magnitude as
the value obtained in previous work by correlating the electromotive
force with the mean magnetic field. The turbulent diffusion of the
toroidal field is comparable to the kinematic viscosity that was
determined earlier by comparing the stress with the shear. However,
the turbulent diffusion of the radial field component is smaller and
can even be formally negative. The method is then modified to obtain
the spectral dependence of the turbulent transport coefficients on the
wavenumber. There is evidence for nonlocal behaviour in that most of
the response comes from the smallest wavenumbers corresponding to the
largest scale possible in the simulation. Again, the turbulent diffusion
coefficient for the radial field component is small, or even negative,
which is considered unphysical. However, when the diffusion tensor is
assumed to be diagonal the radial component of the diffusion tensor is
positive, supporting thus the relevance of a nonlocal approach. Finally,
model calculations are presented using nonlocal prescriptions of the
f-effect and the turbulent diffusion. We emphasize that in all cases
the electromotive force exhibits a strong stochastic component which
make the f-effect and the turbulent diffusion intrinsically noisy.

---------------------------------------------------------
Title: Nonlinear states of the screw dynamo
Authors: Dobler, Wolfgang; Shukurov, Anvar; Brandenburg, Axel
2002PhRvE..65c6311D Altcode: 2001astro.ph..5484D
The self-excitation of magnetic field by a spiral Couette flow between
two coaxial cylinders is considered. We solve numerically the fully
nonlinear, three-dimensional magnetohydrodynamic (MHD) equations for
magnetic Prandtl numbers Pm (ratio of kinematic viscosity
to magnetic diffusivity) between 0.14 and 10 and kinematic and magnetic
Reynolds numbers up to about 2000. In the initial stage of exponential
field growth (kinematic dynamo regime), we find that the dynamo switches
from one distinct regime to another as the radial width δrB
of the magnetic field distribution becomes smaller than the separation
of the field maximum from the flow boundary. The saturation of
magnetic field growth is due to a reduction in the velocity shear
resulting mainly from the azimuthally and axially averaged part of the
Lorentz force, which agrees with an asymptotic result for the limit of
Pm&lt;&lt;1. In the parameter regime considered, the magnetic
energy decreases with kinematic Reynolds number as Re-0.84,
which is approximately as predicted by the nonlinear asymptotic theory
(~Re-1). However, when the velocity field is maintained
by a volume force (rather than by viscous stress) the dependence of
magnetic energy on the kinematic Reynolds number is much weaker.

---------------------------------------------------------
Title: The Nonlinearity of Large Scale Dynamos
Authors: Brandenburg, Axel
2002smra.progE...2B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Effect of Hyperdiffusivity on Turbulent Dynamos with Helicity
Authors: Brandenburg, Axel; Sarson, Graeme R.
2002PhRvL..88e5003B Altcode: 2001astro.ph.10171B
In numerical studies of turbulence, hyperviscosity is often used as
a tool to extend the inertial subrange and to reduce the dissipative
subrange. By analogy, hyperdiffusivity (or hyperresistivity) is
sometimes used in magnetohydrodynamics. The underlying assumption is
that only the small scales are affected by this manipulation. In the
present paper, possible side effects on the evolution of the large-scale
magnetic field are investigated. It is found that for turbulent flows
with helicity, hyperdiffusivity causes the dynamo-generated magnetic
field to saturate at a higher level than normal diffusivity. This result
is successfully interpreted in terms of magnetic helicity conservation,
which also predicts that full saturation is reached only after a time
comparable to the large-scale magnetic (hyper)diffusion time.

---------------------------------------------------------
Title: Global hydromagnetic non-adiabatic disc simulations
Authors: von Rekowski, B.; Brandenburg, A.; Dobler, W.; Shukurov, A.
2002bhty.confE..23V Altcode: 2002bhty.confE..23R
No abstract at ADS

---------------------------------------------------------
Title: The solar dynamo: worrying about magnetic helicity
Authors: Brandenburg, A.
2002ocnd.confE..23B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: MHD inverse cascade in the early Universe
Authors: Hindmarsh, Mark; Christensson, M.; Brandenburg, A.
2002astro.ph..1466H Altcode:
We have carried out numerical simulations of freely decaying
magnetohydrodynamic (MHD) turbulence in three dimensions, which can be
applied to the evolution of stochastic magnetic fields in the early
Universe. For helical magnetic fields an inverse cascade effect is
observed in which magnetic helicity and energy is transfered from
smaller scales to larger scales, accompanied by power law growth in
the characteristic length scale of the magnetic field. The magnetic
field quickly reaches a scaling regime with self-similar evolution,
and power law behaviour at high wavenumbers. We also find power law
decay in the magnetic and kinematic energies.

---------------------------------------------------------
Title: How magnetic helicity ejection can speed up large scale dynamos
Authors: Brandenburg, A.; Blackman, E.
2002cosp...34E3053B Altcode: 2002cosp.meetE3053B
There is mounting evidence that the ejection of magnetic helicity
from the solar surface is of tremendous importance for the solar
dynamo. Observations suggest that in the northern hemisphere the
magnetic helicity flux is negative. We argue that this magnetic helicity
flux is mostly due to small scale magnetic fields -- in contrast to the
much more systematic large scale field of the 11 year cycle. We show,
using idealized simulations of MHD turbulence as well as a simple two
-scale model, that losses of small scale field can be responsible for
enhancing the strength of the large scale field to observed levels. The
losses of small scale field are also crucial for allowing the evolution
of the large scale field to proceed on time scales shorter than the
resistive time scale, that would otherwise be enforced by magnetic
helicity conservation.

---------------------------------------------------------
Title: Numerical simulations of turbulent dynamos
Authors: Brandenburg, Axel
2002HiA....12..742B Altcode:
Using a periodic box calculation it is shown that, owing to helicity
conservation, a large scale field can only develop on a resistive
timescale. This behaviour can be reproduced by a mean-field dynamo
with α and ηt quenchings that are equally strong and
"catastrophic".

---------------------------------------------------------
Title: Astrophysical significance of the anisotropic kinetic alpha
effect
Authors: Brandenburg, A.; Rekowski, B. V.
2001A&A...379.1153B Altcode: 2001astro.ph..6280B
The generation of large scale flows by the anisotropic kinetic
alpha (AKA) effect is investigated in simulations with a suitable
time-dependent space- and time-periodic anisotropic forcing lacking
parity invariance. The forcing pattern moves relative to the fluid,
which leads to a breaking of the Galilean invariance as required for the
AKA effect to exist. The AKA effect is found to produce a clear large
scale flow pattern when the Reynolds number, R, is small as only a few
modes are excited in linear theory. In this case the non-vanishing
components of the AKA tensor are dynamically independent of the
Reynolds number. For larger values of R, many more modes are excited
and the components of the AKA tensor are found to decrease rapidly
with increasing value of R. However, once there is a magnetic field
(imposed and of sufficient strength, or dynamo-generated and saturated)
the field begins to suppress the AKA effect, regardless of the value of
R. It is argued that the AKA effect is unlikely to be astrophysically
significant unless the magnetic field is weak and R is small.

---------------------------------------------------------
Title: Search for non-helical disc dynamos in simulations
Authors: Arlt, R.; Brandenburg, A.
2001A&A...380..359A Altcode: 2001astro.ph..6557A
The origin of large scale magnetic fields in accretion discs is
investigated. Using global three-dimensional simulations of accretion
disc turbulence, a recent suggestion of Vishniac &amp; Cho (2001,
ApJ 550, 752) is re-examined, according to which large scale fields
in accretion discs could be understood without explicitly invoking
the usual helicity effect. Particular emphasis is placed on a certain
correlation between vorticity and azimuthal velocity gradient which
has been predicted to drive large scale dynamo action, independent
of the presence or absence of kinetic helicity. In the global disc
simulations two types of behaviours are found: those which do show this
type of velocity correlation and those which do not. The former ones are
typically also the cases where the resistivity is larger. The latter
ones show signs typical of dynamo action based on the usual helicity
effect. In the idealized simulations without rotation and just shear
the above correlation is found to be particularly strong. In both cases
there is, as expected, a systematic flux of magnetic helicity through
the midplane. However, very little magnetic helicity leaves the domain
through the top and bottom boundaries. The idealized simulations reveal
that much of this systematic flux comes from the rotational component
of the helicity flux and does not contribute to its divergence.

---------------------------------------------------------
Title: Burgers Turbulence and the Problem of Star Formation
Authors: Brandenburg, A.; Boldyrev, S.
2001AAS...19914901B Altcode: 2001BAAS...33Q1528B
Star forming molecular clouds are thought to be governed by supersonic,
possibly super-Alfvenic turbulence. We introduce a one-dimensional
Burgers model with magnetic pressure that explains sustaining of the
turbulence on small scales, the turbulent shock fragmentation, and the
formation of the universal density statistics,-- features characteristic
of the three-dimensional supersonic turbulence. We present an analytical
solution for the model and confirm it by direct numerical simulations.

---------------------------------------------------------
Title: Inverse cascade in decaying three-dimensional
magnetohydrodynamic turbulence
Authors: Christensson, Mattias; Hindmarsh, Mark; Brandenburg, Axel
2001PhRvE..64e6405C Altcode: 2000astro.ph.11321C
We perform direct numerical simulations of three-dimensional freely
decaying magnetohydrodynamic turbulence. For helical magnetic fields,
an inverse cascade effect is observed in which power is transfered
from smaller scales to larger scales. The magnetic field reaches a
scaling regime with self-similar evolution, and power-law behavior at
high wave numbers. We also find power-law decay in the magnetic and
kinematic energies, and power-law growth in the characteristic length
scale of the magnetic field.

---------------------------------------------------------
Title: Magnetohydrodynamic turbulence in warped accretion discs
Authors: Torkelsson, Ulf; Ogilvie, Gordon I.; Brandenburg, Axel;
Pringle, James E.; Nordlund, Åke; Stein, Robert F.
2001AIPC..586..681T Altcode: 2001tsra.conf..681T; 2001astro.ph..3057T
Warped, precessing accretion discs appear in a range of astrophysical
systems, for instance the X-ray binary Her X-1 and in the active
nucleus of NGC4258. In a warped accretion disc there are horizontal
pressure gradients that drive an epicyclic motion. We have studied
the interaction of this epicyclic motion with the magneto-hydrodynamic
turbulence in numerical simulations. We find that the turbulent stress
acting on the epicyclic motion is comparable in size to the stress that
drives the accretion, however an important ingredient in the damping
of the epicyclic motion is its parametric decay into inertial waves. .

---------------------------------------------------------
Title: Magnetoconvection and dynamo coefficients:. Dependence of
the alpha effect on rotation and magnetic field
Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A.
2001A&A...376..713O Altcode: 2001astro.ph..8274O
We present numerical simulations of three-dimensional compressible
magnetoconvection in a rotating rectangular box that represents
a section of the solar convection zone. The box contains a
convectively unstable layer, surrounded by stably stratified layers
with overshooting convection. The magnetic Reynolds number, Rm, is
chosen subcritical, thus excluding spontaneous growth of the magnetic
field through dynamo action, and the magnetic energy is maintained by
introducing a constant magnetic field into the box, once convection
has attained a statistically stationary state. Under the influence
of the Coriolis force, the advection of the magnetic field results
in a non-vanishing contribution to the mean electric field, given by
&lt;vec{u}xvec{b}&gt;. From this electric field, we calculate the alpha
-effect, separately for the stably and the unstably stratified layers,
by averaging over time and over suitably defined volumes. From the
variation of alpha we derive an error estimate, and the dependence of
alpha on rotation and magnetic field strength is studied. Evidence is
found for rotational quenching of the vertical alpha effect, and for
a monotonic increase of the horizontal alpha effect with increasing
rotation. For Rm~ 30, our results for both vertical and horizontal
alpha effect are consistent with magnetic quenching by a factor [1+Rm
(B0/Beq)2]-1. The signs
of the small-scale current helicity and of the vertical component of
alpha are found to be opposite to those for isotropic turbulence.

---------------------------------------------------------
Title: The helicity constraint in turbulent dynamos with shear
Authors: Brandenburg, Axel; Bigazzi, Alberto; Subramanian, Kandaswamy
2001MNRAS.325..685B Altcode: 2000astro.ph.11081B
The evolution of magnetic fields is studied using simulations of
forced helical turbulence with strong imposed shear. After some initial
exponential growth, the magnetic field develops a large-scale travelling
wave pattern. The resulting field structure possesses magnetic helicity,
which is conserved in a periodic box by the ideal magnetohydrodynamics
equations and can hence only change on a resistive time-scale. This
strongly constrains the growth time of the large-scale magnetic field,
but less strongly constrains the length of the cycle period. Comparing
this with the case without shear, the time-scale for large-scale
field amplification is shortened by a factor Q, which depends on the
relative importance of shear and helical turbulence, and which also
controls the ratio of toroidal to poloidal field. The results of the
simulations can be reproduced qualitatively and quantitatively with a
mean-field αΩ-dynamo model with alpha-effect and turbulent magnetic
diffusivity coefficients that are less strongly quenched than in the
corresponding α2-dynamo.

---------------------------------------------------------
Title: Thermal production of gravitinos
Authors: Bolz, M.; Brandenburg, A.; Buchmüller, W.
2001NuPhB.606..518B Altcode: 2000hep.ph...12052B
We evaluate the gravitino production rate in supersymmetric QCD at high
temperature to leading order in the gauge coupling. The result, which is
obtained by using the resummed gluon propagator, depends logarithmically
on the gluon plasma mass. As a byproduct, a new result for the axion
production rate in a QED plasma is obtained. The implications for the
cosmological dark matter problem are briefly discussed, in particular
the intriguing possibility that gravitinos are the dominant part of
cold dark matter.

---------------------------------------------------------
Title: Magnetic Mysteries
Authors: Brandenburg, A.
2001Sci...292.2440B Altcode:
At present--some 14 billion years after the Big Bang--magnetic fields
of appreciable strength are found in virtually all galaxies and also in
galaxy clusters. Although weak compared with the fields at Earth's or
the Sun's surface, these fields are enormous considering the scales
involved and may influence the formation of stars and galaxies,
the dynamics of galaxy clusters, and energy transport within galaxy
clusters. Even 1 to 2 billion years after the Big Bang, such fields
must already have existed at about the same strength as today. How
did these fields arise? And did primordial magnetic fields exist in
the early universe? Answers to these questions remain speculative,
but upcoming space missions promise exciting insights.

---------------------------------------------------------
Title: The effects of vertical outflows on disk dynamos.
Authors: Bardou, A.; von Rekowski, B.; Dobler, W.; Brandenburg, A.;
Shukurov, A.
2001A&A...370..635B Altcode: 2000astro.ph.11545B
We consider the effect of vertical outflows on the mean-field dynamo
in a thin disk. These outflows could be due to winds or magnetic
buoyancy. We analyse both two-dimensional finite-difference numerical
solutions of the axisymmetric dynamo equations and a free-decay
mode expansion using the thin-disk approximation. Contrary to
expectations, a vertical velocity can enhance dynamo action, provided
the velocity is not too strong. In the nonlinear regime this can lead
to super-exponential growth of the magnetic field.

---------------------------------------------------------
Title: Evolution of highly buoyant thermals in a stratified layer
Authors: Brandenburg, A.; Hazlehurst, J.
2001A&A...370.1092B Altcode: 2000astro.ph..8099B
The buoyant rise of thermals (i.e. bubbles of enhanced entropy, but
initially in pressure equilibrium) is investigated numerically in three
dimensions for the case of an adiabatically stratified layer covering
6-9 pressure scale heights. It is found that these bubbles can travel
to large heights before being braked by the excess pressure that builds
up in order to drive the gas sideways in the head of the bubble. Until
this happens, the momentum of the bubble grows as described by the
time-integrated buoyancy force. This validates the simple theory of
bubble dynamics whereby the mass entrainment of the bubble provides an
effective braking force well before the bubble stops ascending. This
is quantified by an entrainment parameter alpha which is calculated
from the simulations and is found to be in good agreement with the
experimental measurements. This work is discussed in the context of
contact binaries whose secondaries could be subject to dissipative
heating in the outermost layers.

---------------------------------------------------------
Title: The Inverse Cascade and Nonlinear Alpha-Effect in Simulations
of Isotropic Helical Hydromagnetic Turbulence
Authors: Brandenburg, Axel
2001ApJ...550..824B Altcode: 2000astro.ph..6186B
A numerical model of isotropic homogeneous turbulence with helical
forcing is investigated. The resulting flow, which is essentially the
prototype of the α2 dynamo of mean field dynamo theory,
produces strong dynamo action with an additional large-scale field
on the scale of the box (at wavenumber k=1; forcing is at k=5). This
large-scale field is nearly force free and exceeds the equipartition
value. As the magnetic Reynolds number Rm increases,
the saturation field strength and the growth rate of the dynamo
increase. However, the time it takes to build up the large-scale
field from equipartition to its final superequipartition value
increases with magnetic Reynolds number. The large-scale field
generation can be identified as being due to nonlocal interactions
originating from the forcing scale, which is characteristic of the
α-effect. Both α and turbulent magnetic diffusivity ηt
are determined simultaneously using numerical experiments where the
mean field is modified artificially. Both quantities are quenched in
an Rm-dependent fashion. The evolution of the energy of the
mean field matches that predicted by an α2 dynamo model with
similar α and ηt quenchings. For this model an analytic
solution is given that matches the results of the simulations. The
simulations are numerically robust in that the shape of the spectrum
at large scales is unchanged when changing the resolution from
303 to 1203 mesh points, or when increasing the
magnetic Prandtl number (viscosity/magnetic diffusivity) from 1 to
100. Increasing the forcing wavenumber to 30 (i.e., increasing the
scale separation) makes the inverse cascade effect more pronounced,
although it remains otherwise qualitatively unchanged.

---------------------------------------------------------
Title: Large scale dynamos with helicity loss through boundaries
Authors: Brandenburg, A.; Dobler, W.
2001A&A...369..329B Altcode: 2000astro.ph.12472B
Dynamo action is investigated in simulations of locally isotropic
and homogeneous turbulence in a slab between open boundaries. It is
found that a “pseudo-vacuum” boundary condition (where the field is
vertical) leads to strong helicity fluxes which significantly reduce
the amplitude of the resulting large-scale field. On the other hand,
if there is a conducting halo outside the dynamo-active region, the
large scale field amplitude can reach larger values, but the time
scale after which this field is reached increases linearly with the
magnetic Reynolds number. In both cases, most of the helicity flux is
found to occur on large scales. From the variety of models considered
we conclude that open boundaries tend to lower the saturation field
strength compared to the case with periodic boundaries. The rate at
which this lower saturation field strength is attained is roughly
independent of the strength of the turbulence and of the boundary
conditions. For dynamos with less helicity, however, significant field
strengths could be reached in a shorter time.

---------------------------------------------------------
Title: Dynamical friction of bodies orbiting in a gaseous sphere
Authors: Sánchez-Salcedo, F. J.; Brandenburg, A.
2001MNRAS.322...67S Altcode: 2000astro.ph.10003S
The dynamical friction experienced by a body moving in a gaseous medium
is different from the friction in the case of a collisionless stellar
system. Here we consider the orbital evolution of a gravitational
perturber inside a gaseous sphere using three-dimensional simulations,
ignoring however self-gravity. The results are analysed in terms of a
`local' formula with the associated Coulomb logarithm taken as a free
parameter. For forced circular orbits, the asymptotic value of the
component of the drag force in the direction of the velocity is a
slowly varying function of the Mach number in the range 1.0-1.6. The
dynamical friction time-scale for free decay orbits is typically only
half as long as in the case of a collisionless background, which
is in agreement with E. C. Ostriker's recent analytic result. The
orbital decay rate is rather insensitive to the past history of the
perturber. It is shown that, similarly to the case of stellar systems,
orbits are not subject to any significant circularization. However,
the dynamical friction time-scales are found to increase with increasing
orbital eccentricity for the Plummer model, whilst no strong dependence
on the initial eccentricity is found for the isothermal sphere.

---------------------------------------------------------
Title: Further Analysis of Stellar Magnetic Cycle Periods
Authors: Saar, S.; Brandenburg, A.
2001ASPC..248..231S Altcode: 2001astro.ph..5070S; 2001mfah.conf..231S
We further investigate relationships between activity cycle periods in
cool stars and rotation to include new cycle data, and explore different
parameterizations of the problem. We find that relations between cycle
and rotational frequencies (omega_cyc vs. Omega) and between their
ratio and the inverse Rossby number (omega_cyc/Omega vs. Ro^{-1})
show many similarities, including three branches and similar rms
scatter. We briefly discuss some implications for dynamo models.

---------------------------------------------------------
Title: The Solar Dynamo: Old, Recent, and New Problems
Authors: Brandenburg, A.
2001IAUS..203..144B Altcode: 2000astro.ph.11579B
There are a number of fundamental uncertainties in our understanding
of the solar dynamo. What is the significance of the lower overshoot
layer, does the dynamo work in the entire convection zone, why is
the field oscillatory, migratory, and dipole-like? Although some
of those properties can be understood in the framework of α-Ω
dynamo theory, there are some basic questions whether this theory can
actually work. In my talk I will present a model of helically forced
turbulence that allows us to address the question what generates the
large scale field (e.g. α-effect and/or inverse cascade). Next,
a simulation of a convective dynamo with shear will be presented,
where a large scale magnetic field is found to develop near the lower
overshoot layer. Finally, comparisons will be made with dynamo action
in galaxies and accretion discs. In all cases the effects of noise are
rather strong, and it is the presence of large scale shear which is
crucial in producing a well-defined large scale field. The importance of
magnetic instabilities will be highlighted in connection with stellar
dynamos, where the observed cycle periods point toward the existence
of different branches of activity.

---------------------------------------------------------
Title: Helicity in Hydro and MHD Reconnection
Authors: Brandenburg, Axel; Kerr, Robert M.
2001LNP...571..358B Altcode: 2000astro.ph.12210B; 2001qvds.conf..358B
Helicity, a measure of the linkage of flux lines, has subtle and
largely unknown effects upon dynamics. Both magnetic and hydrodynamic
helicity are conserved for ideal systems and could suppress nonlinear
dynamics. What actually happens is not clear because in a fully
three-dimensional system there are additional channels whereby intense,
small-scale dynamics can occur. This contribution shows one magnetic
and one hydrodynamic case where for each the presence of helicity does
not suppr ess small-scale intense dynamics of the type that might lead
to reconnection.

---------------------------------------------------------
Title: Two-dimensional disk dynamos with vertical outflows into a halo
Authors: von Rekowski, B.; Dobler, W.; Shukurov, A.; Brandenburg, A.
2000astro.ph.12013V Altcode:
We study the effects of vertical outflows on mean-field dynamos
in disks. These outflows could be due to thermal winds or magnetic
buoyancy. We analyse numerical solutions of the nonlinear mean-field
dynamo equations using a two-dimensional finite-difference
model. Contrary to expectations, a modest vertical velocity can
enhance dynamo action. This can lead to super-exponential growth of
the magnetic field and to higher magnetic energies at saturation in
the nonlinear regime.

---------------------------------------------------------
Title: The inverse cascade in turbulent dynamos
Authors: Brandenburg, Axel
2000astro.ph.12112B Altcode:
The emergence of a large scale magnetic field from randomly forced
isotropic strongly helical flows is discussed in terms of the inverse
cascade of magnetic helicity and the alpha-effect. In simulations of
such flows the maximum field strength exceeds the equipartition field
strength for large scale separation. However, helicity conservation
controls the speed at which this final state is reached. In the
presence of open boundaries magnetic helicity fluxes out of the domain
are possible. This reduces the timescales of the field growth, but it
also tends to reduce the maximum attainable field strength.

---------------------------------------------------------
Title: Sheared helical turbulence and the helicity constraint in
large-scale dynamos
Authors: Bigazzi, A.; Brandenburg, A.; Subramanian, K.
2000astro.ph.12240B Altcode:
The effect of shear on the growth of large scale magnetic fields in
helical turbulence is investigated. The resulting large-scale magnetic
field is also helical and continues to evolve, after saturation of
the small scale field, on a slow resistive time scale. This is a
consequence of magnetic helicity conservation. Because of shear, the
time scale needed to reach an equipartition-strength large scale field
is shortened proportionally to the ratio of the resulting toroidal to
poloidal large scale fields.

---------------------------------------------------------
Title: Magnetohydrodynamics of Accretion Disks
Authors: Brandenburg, A.
2000eaa..bookE2226B Altcode:
An ACCRETION DISK is a flat formation of gas and dust rotating about
a central object and accreting matter inwards by transporting angular
momentum outwards, so that the centrifugal support is gradually removed
from the fluid parcels. There are three main classes of accretion disks:
(i) disks around accreting compact stars (white dwarfs, neutron stars
or black holes) in binary systems, (ii) disks...

---------------------------------------------------------
Title: The response of a turbulent accretion disc to an imposed
epicyclic shearing motion
Authors: Torkelsson, Ulf; Ogilvie, Gordon I.; Brandenburg, Axel;
Pringle, James E.; Nordlund, Åke; Stein, Robert F.
2000MNRAS.318...47T Altcode: 2000astro.ph..5199T
We excite an epicyclic motion, the amplitude of which depends on the
vertical position, z, in a simulation of a turbulent accretion disc. An
epicyclic motion of this kind may be caused by a warping of the disc. By
studying how the epicyclic motion decays, we can obtain information
about the interaction between the warp and the disc turbulence. A
high-amplitude epicyclic motion decays first by exciting inertial
waves through a parametric instability, but its subsequent exponential
damping may be reproduced by a turbulent viscosity. We estimate the
effective viscosity parameter, αv, pertaining to such a
vertical shear. We also gain new information on the properties of the
disc turbulence in general, and measure the usual viscosity parameter,
αh, pertaining to a horizontal (Keplerian) shear. We
find that, as is often assumed in theoretical studies, αv
is approximately equal to αh and both are much less than
unity, for the field strengths achieved in our local box calculations
of turbulence. In view of the smallness (~0.01) of αv and
αh we conclude that for βpgaspmag~10
the time-scale for diffusion or damping of a warp is much shorter than
the usual viscous time-scale. Finally, we review the astrophysical
implications.

---------------------------------------------------------
Title: Numerical simulations of turbulent dynamos
Authors: Brandenburg, Axel
2000astro.ph.10495B Altcode:
Using a periodic box calculation it is shown that, owing to helicity
conservation, a large scale field can only develop on a resistive
timescale. This behaviour can be reproduced by a mean-field dynamo with
alpha and eta_t quenchings that are equally strong and `catastrophic'.

---------------------------------------------------------
Title: Large scale dynamos with ambipolar diffusion nonlinearity
Authors: Brandenburg, A.; Subramanian, K.
2000A&A...361L..33B Altcode: 2000astro.ph..7450B
It is shown that ambipolar diffusion as a useful model for nonlinearity
leads to similar behaviour of large scale turbulent dynamos as
full MHD. This is demonstrated using both direct simulations in a
periodic box and a closure model for the magnetic correlation functions
applicable to infinite space. Large scale fields develop via a nonlocal
inverse cascade as described by the alpha -effect. However, magnetic
helicity can only change on a resistive timescale, so the time it
takes to organize the field into large scales increases with magnetic
Reynolds number.

---------------------------------------------------------
Title: Non-linear magnetic diffusivity in mean-field electrodynamics
Authors: Urpin, V.; Brandenburg, A.
2000MNRAS.316..684U Altcode:
We consider non-linear transport and drift processes caused by an
inhomogeneous magnetic field in a turbulent fluid. The coefficients of
magnetic diffusivity and drift velocity are calculated by making use of
the second-order correlation approximation. Transport processes in the
presence of a sufficiently strong magnetic field become anisotropic with
larger diffusion rate and turbulent electrical resistivity across the
field than along the field. Non-linear effects also lead to a drift of
the magnetic field away from the regions with a higher magnetic energy.

---------------------------------------------------------
Title: Astrophysical convection and dynamos
Authors: Brandenburg, A.; Nordlund, A.; Stein, R. F.
2000gac..conf...85B Altcode:
Convection can occur in various astrophysical settings. In this review
some aspects of solar convection are highlighted. In deeper layers
of the solar convection zone, rotation becomes important and can
lead to effects such as downward pumping of vorticity and magnetic
fields. Rotation has the tendency to partially evacuate vortex tubes
making them lighter. This effect can sometimes reverse the core of
a downdraft and make it buoyant. The problem of different thermal
and dynamic a time scales is addressed and finally the formation of
magnetic structures by convection is discussed.

---------------------------------------------------------
Title: Magnetohydrodynamic Turbulence in Accretion Discs
Authors: Torkelsson, U.; Brandenburg, A.; Nordlund, A.; Stein, R. F.
2000IAUS..195..241T Altcode:
We present results from numerical simulations of magnetohydrodynamic
turbulence in accretion discs. Our simulations show that the turbulent
stresses that drive the accretion are less stratified than the matter;
thus, the surface layers are more strongly heated than the interior
of the disc.

---------------------------------------------------------
Title: The inverse cascade and nonlinear alpha-effect in simulations
of isotropic helical hydromagnetic turbulence
Authors: Brandenburg, A.
2000astu.confE..25B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Discussion on Accretion Disk Turbulence
Authors: Brandenburg, Axel; Gammie, Charles; Stone, Jim
2000astu.confE...5B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Relationship Between Vortex and Magnetic Reconnection
Authors: Brandenburg, Axel; Kerr, Robert
2000astu.progE...3B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Dynamo-generated Turbulence and Outflows from Accretion Discs
Authors: Brandenburg, A.
2000RSPTA.358..759B Altcode: 2000RSLPT.358..759B
Local hydromagnetic simulations of accretion-disc turbulence currently
provide the most convincing evidence that the origin of turbulence in
discs could be the Balbus-Hawley magnetorotational instability. The main
results of such calculations are highlighted with particular emphasis
on the generation of large-scale magnetic fields. Comparison with
mean-field dynamo theory is made. This theory is then used to address
the question of the launching and collimation of winds emanating from
the disc surfaces.

---------------------------------------------------------
Title: Dynamo mechanisms
Authors: Brandenburg, A.; Saar, S. H.
2000ASPC..198..381B Altcode: 2000scac.conf..381B
No abstract at ADS

---------------------------------------------------------
Title: The dynamo effect in stars
Authors: Brandenburg, Axel
2000ASSL..254....1B Altcode: 2000stas.conf....1B
No abstract at ADS

---------------------------------------------------------
Title: Large scale dynamos: direct simulations
Authors: Brandenburg, A.
2000IAUJD..14E..14B Altcode:
Simulations of driven helical turbulence and of naturally driven
turbulence are presented. Signs of the inverse cascade are presented
and discussed in the framework of the alpha-effect. The large scale
fields represent the outermost scale of the turbulent spectrum into
which energy can be pumped gradually via the inverse cascade. Under
somewhat idealised conditions (fully helical turbulence, no shear),
these fields tend to be close to force-free and hence are not
drastically felt by the turbulence, yielding fields that can saturate in
superequipartition. Althought this is not realistic in real galaxies,
strong field amplification by differential rotation produces toroidal
flux tubes in which the field can still exceed equipartition locally.

---------------------------------------------------------
Title: Pressure-Driven Outflow and Magneto-Centrifugal Wind from a
Dynamo Active Disc
Authors: Dobler, Wolfgang; Brandenburg, Axel; Shukurov, Anvar
1999ptep.proc..347D Altcode:
We present a numerical model of an accretion disc with mean-field
dynamo action that develops pressure-driven collimated outflow near the
rotation axis and a centrifugally driven uncollimated wind in the outer
parts. The jet is collimated and confined by the azimuthal magnetic
field that is produced by the dynamo in the disc and advected to the
disc corona. The jet is hot and dense, but has low angular momentum. We
also briefly discuss the possible generation of magnetic fields in a
jet by the screw dynamo.

---------------------------------------------------------
Title: Evolution of a superbubble in a turbulent, multi-phased and
magnetized ISM
Authors: Korpi, M. J.; Brandenburg, A.; Shukurov, A.; Tuominen, I.
1999A&A...350..230K Altcode:
The evolution of a superbubble is simulated using a local
three-dimensional, non-ideal MHD model, which includes galactic
differential rotation, an external gravitational potential, heating via
supernova explosions and radiative cooling of the interstellar medium
(ISM). In our model a superbubble is formed due to the clustering of
supernova activity, mimicking an OB association. Supernovae are modelled
as instantaneous explosions that release 10(51) erg of thermal energy
and 3M_sun of gas in a small volume. We implement a superbubble with
the luminosity 3 x 10(37) erg {s(-1) into an initial ISM, which is
taken from our earlier calculations modelling the warm and hot phases
of the ISM. The simulated ISM has a multi-phase structure with hot,
dilute and warm, denser gas coexisting in pressure equilibrium; there
is also some cold, dense gas in the form of clouds and filaments
arising from supernova compression. The multicomponent gas is in a
state of developed turbulence, with r.m.s. velocity 10 and 40{km s(-1)
for the warm and hot gas, respectively. At the developed state of
the simulation there is a magnetic field of 1.3muG strength having
both uniform and random components. The evolution of a superbubble
is rather different from that indicated by models with quasi-uniform
ambient medium. The superbubble loses its spherical symmetry at very
early stages of expansion. Its break-through from the disc is strongly
facilitated by the nonuniformity of its environment. A superbubble
which would be confined in the disc according to criteria obtained
for a quasi-uniform ISM can break out to the halo.

---------------------------------------------------------
Title: Time Evolution of the Magnetic Activity Cycle
Period. II. Results for an Expanded Stellar Sample
Authors: Saar, Steven H.; Brandenburg, Axel
1999ApJ...524..295S Altcode:
We further explore nondimensional relationships between the
magnetic dynamo cycle period Pcyc, the rotational period
Prot, the activity level (as observed in Ca II HK), and
other stellar properties by expanding the stellar sample studied in
the first paper in this series. We do this by adding photometric
and other cycles seen in active stars and the secondaries of CV
systems and by selectively adding less certain cycles from the Mount
Wilson HK survey; evolved stars, long-term HK trends and secondary
Pcyc are also considered. We confirm that most stars with
age t&gt;~0.1 Gyr occupy two roughly parallel branches, separated
by a factor of ~6 in Pcyc, with the ratio of cycle and
rotational frequencies ωcyc/Ω~Ro-0.5, where
Ro is the Rossby number. Using the model of the first paper in this
series, this result implies that the α effect increases with mean
magnetic field (contrary to the traditional α-quenching concept)
and that α and ωcyc decrease with t. Stars are not
strictly segregated onto one or the other branch by activity level,
though the high-ωcyc/Ω branch is primarily composed of
inactive stars. The expanded data set suggests that for t&gt;~1 Gyr,
stars can have cycles on one or both branches, though among older
stars, those with higher (lower) mass tend to have their primary
Pcyc on the lower (upper) ωcyc/Ω branch. The
Sun's ~80 yr Gleissberg cycle agrees with this scenario, suggesting that
long-term activity “trends” in many stars may be segments of long
(Pcyc~50-100 yr) cycles not yet resolved by the data. Most
very active stars (Prot&lt;3 days) appear to occupy a new,
third branch with ωcyc/Ω~Ro0.4. Many RS CVn
variables lie in a transition region between the two most active
branches. We compare our results with various models, discuss their
implications for dynamo theory and evolution, and use them to predict
Pcyc for three groups: stars with long-term HK trends,
stars in young open clusters, and stars that may be in Maunder-like
magnetic minima.

---------------------------------------------------------
Title: Deceleration by Dynamical Friction in a Gaseous Medium
Authors: Sánchez-Salcedo, F. J.; Brandenburg, A.
1999ApJ...522L..35S Altcode:
The drag force experienced by a gravitational body moving in a
straight-line trajectory through a homogeneous isothermal gaseous
medium of given sound speed is investigated numerically. For perturbers
with constant velocity, linear theory describes successfully the
temporal evolution and magnitude of the force. The result obtained
recently by E. Ostriker--that for Mach numbers \Mscr=1-2 the force
is stronger in a gaseous medium than in a collisionless medium, as
described by the standard Chandrasekhar formula--is confirmed. The
corresponding minimum impact radius rmin for a body
described with a Plummer model with core radius Rsoft
is rmin/Rsoft~2.25. When \Mscr&lt;1, the drag
force is strongly suppressed, which is consistent with Ostriker's
results but in disagreement with the Chandrasekhar formula. However,
when the perturber is decelerated by its own wake to \Mscr&lt;1,
the effective drag force remains initially somewhat larger than the
value in the case of constant velocity because it takes some time to
get rid of the wake that was generated during its supersonic history.

---------------------------------------------------------
Title: Evidence for a Singularity in Ideal Magnetohydrodynamics:
Implications for Fast Reconnection
Authors: Kerr, Robert M.; Brandenburg, Axel
1999PhRvL..83.1155K Altcode: 1998physics..12017K
Numerical evidence for a finite-time singularity in ideal 3D
magnetohydrodynamics is presented. The simulations start from two
interlocking magnetic flux rings with no initial velocity. Curvature
shrinks the rings until they touch and current sheets form
between them. The evidence for a singularity in a finite time
tc is that the peak current density behaves like
||J||∞~1/$tc-t$ for a range of sound
speeds and initial conditions. For the incompressible calculations
||ω||∞/||J||∞--&gt;const. In resistive
reconnection the magnetic helicity is nearly conserved while energy
is dissipated.

---------------------------------------------------------
Title: Comment on “The sunspot as a self-excited dynamo”
Authors: Moss, David; Brandenburg, Axel
1999A&A...346.1009M Altcode:
A recent paper claims that the well known Cowling `anti-dynamo' theorem
is a “misconception”, and that a simple axisymmetric sunspot model
constitutes a counter example. We do not believe these claims to have
been substantiated.

---------------------------------------------------------
Title: The influence of geometry and topology on axisymmetric
mean-field dynamos
Authors: Covas, Eurico; Tavakol, Reza; Tworkowski, Andrew; Brandenburg,
Axel; Brooke, John; Moss, David
1999A&A...345..669C Altcode: 1998astro.ph.11079C
We study the changes in the dynamical behaviour of axisymmetric
spherical mean-field dynamo models produced by changes in their
geometry and topology, by considering a two parameter family of models,
ranging from a full sphere to spherical shell, torus and disc-like
configurations, within a unified framework. We find that the two
parameter space of the family of models considered here separates into
at least three different regions with distinct characteristics for
the onset of dynamo action. In two of these regions, the most easily
excited fields are oscillatory, in one case with dipolar symmetry,
and in the other with quadrupolar, whereas in the third region the most
easily excited field is steady and quadrupolar. In the nonlinear regime,
we find that topological changes can alter significantly the dynamical
behaviour, whilst modest changes in geometry can produce qualitative
changes, particularly for thin disc-like configurations. This is of
potential importance, since the exact shapes of astrophysical bodies,
especially accretion discs and galaxies, are usually not precisely
known.

---------------------------------------------------------
Title: Magnetic drift processes in differentially rotating turbulence
Authors: Urpin, V.; Brandenburg, A.
1999A&A...345.1054U Altcode:
The mean electromotive force is considered in a differentially
rotating fluid taking into account stretching of the turbulent magnetic
field. Calculations are performed by making use of the second order
correlation approximation. Non-uniformity of the angular velocity
leads to specific drift processes in the azimuthal direction. Due to
this drift the magnetic field can rotate with a somewhat different
angular velocity than the fluid. Differential rotation can also lead
in a new instability of a non-axisymmetric mean field. Regardless of
the law of the differential rotation this instability can result in
an exponential amplification of the field.

---------------------------------------------------------
Title: A Supernova-regulated Interstellar Medium: Simulations of
the Turbulent Multiphase Medium
Authors: Korpi, M. J.; Brandenburg, A.; Shukurov, A.; Tuominen, I.;
Nordlund, Å.
1999ApJ...514L..99K Altcode:
The dynamic state of the interstellar medium, heated and stirred by
supernovae (SNe), is simulated using a three-dimensional, nonideal
MHD model in a domain extended 0.5×0.5 kpc horizontally and 2 kpc
vertically, with the gravitational field symmetric about the midplane
of the domain, z=0. We include both Type I and Type II SNe, allowing
the latter to cluster in regions with enhanced gas density. The
system segregates into two main phases: a warm, denser phase and a
hot, dilute gas in global pressure equilibrium; there is also dense,
cool gas compressed into filaments, shells, and clumps by expanding
SN remnants. The filling factor of the hot phase grows with height,
so it dominates at z&gt;~0.5 kpc. The multicomponent structure persists
throughout the simulation, and its statistical parameters show little
time variation. The warm gas is in hydrostatic equilibrium, which is
supported by thermal and turbulent pressures. The multiphase gas is in
a state of developed turbulence. The rms random velocity is different
in the warm and hot phases, 10 and 40 km s-1, respectively,
at z&lt;~1 kpc; the turbulent cell size (twice the velocity correlation
scale) is about 60 pc in the warm phase.

---------------------------------------------------------
Title: Simulations and Observations of Stellar Dynamos: Evidence
for a Magnetic Alpha-Effect
Authors: Brandenburg, A.
1999ASPC..178...13B Altcode: 1999sdnc.conf...13B
No abstract at ADS

---------------------------------------------------------
Title: Magneto-Convection
Authors: Stein, R. F.; Georgobiani, D.; Bercik, D. J.; Brandenburg,
A.; Nordlund, Å.
1999ASPC..173..193S Altcode: 1999sstt.conf..193S
No abstract at ADS

---------------------------------------------------------
Title: Vortex tube models for turbulent dynamo action
Authors: Bigazzi, Alberto; Brandenburg, Axel; Moss, David
1999PhPl....6...72B Altcode:
The possibility of dynamo action resulting from a pair of elongated
vortex structures immersed in an electrically conducting fluid is
investigated. For elongated vortex structures, the critical magnetic
Reynolds number for dynamo action is about half that for the spherical
rotors that have been studied previously. When applied to Kolmogorov
turbulence with vortex structures of scale comparable to the dissipation
length, this model can explain dynamo action only when the magnetic
Prandtl number (=kinematic viscosity/magnetic diffusivity) exceeds
a critical value that is larger than unity. It is argued that in
astrophysical bodies where this condition is not satisfied (in stellar
convection zones, for example), dynamo action must instead result from
motions on all scales up to the size of the region.

---------------------------------------------------------
Title: Vortical Motions Driven by Supernova Explosions
Authors: Korpi, Maarit; Brandenburg, Axel; Shukurov, Anvar; Tuominen,
Ilkka
1999intu.conf..127K Altcode:
We investigate supernova driven interstellar turbulence using local
three-dimensional MHD simulations and adopting conditions corresponding
to the Galaxy. Our model includes the effects of large-scale shear
due to galactic differential rotation, density stratification,
compressibility, magnetic fields, heating via supernova explosions and
parameterized radiative cooling of the interstellar medium. We allow
for multiple supernova explosions distributed randomly in the galactic
disc and exponentially in the vertical direction. We found that there
are two major stages governing the evolution of a supernova remnant
that is isolated, i.e. does not interact with other remnants. During
the first 2 Myr the explosion drives a strong shock. After the shock
stage there is a cool, dense shell with a hot interior left from
the remnant. During this dense shell stage large-scale shear and
Coriolis force act on the remnant, but the effect of these processes
was found to be rather weak. The result of an ensemble of isolated
supernova explosions was a relatively wide shock spectrum in the
kinetic energy. When supernova interactions, i.e. shock-shock and
shock-dense shell collisions, become abundant the situation changes. In
these collisions vorticity is effectively generated by the baroclinic
effect. After some vorticity has been generated, the vortex stretching
term can have an important role as redistributing the vorticity.

---------------------------------------------------------
Title: A Local Three-dimensional Model of the Supernova-regulated ISM
Authors: Korpi, M. J.; Tuominen, I.; Brandenburg, A.; Shukurov, A.
1999ASPC..168..445K Altcode: 1999npim.conf..445K
No abstract at ADS

---------------------------------------------------------
Title: The Dynamics of Turbulent Viscosity
Authors: Torkelsson, U.; Ogilvie, G. I.; Pringle, J. E.; Brandenburg,
A.; Nordlund, Å.; Stein, R. F.
1999ASPC..161..422T Altcode: 1999hepa.conf..422T
No abstract at ADS

---------------------------------------------------------
Title: A helicity proxy from horizontal solar flow patterns
Authors: Rüdiger, G.; Brandenburg, A.; Pipin, V. V.
1999AN....320..135R Altcode:
Motivated by new observations of solar surface flow patterns
of mesogranulation, theoretical computations of the horizontal
diver\-gence-vorticity correlation are presented. Because of its close
relation to the helicity in rotating turbulence such observations
and discussions are of particular importance for the conventional
dynamo theory. For the northern hemisphere we find a small, but always
negative, divergence-vorticity correlation. Both an analytical Second
Order Correlation Approximation for slow rotation as well as a numerical
simulation (originally done for accretion disks) for fast rotation
yield very similar results.

---------------------------------------------------------
Title: Time Evolution of the Magnetic Activity Cycle Period: Results
for an Expanded Stellar Sample
Authors: Saar, S. H.; Brandenburg, A.
1998AAS...193.4404S Altcode: 1998BAAS...30S1315S
We explore non-dimensional relationships between the magnetic dynamo
cycle period P_cyc, the rotational period P_rot, the activity level
(as observed in Ca ii HK), and other stellar properties using a
large stellar sample including Ca ii, photometric and other cycles
in dwarfs, evolved stars, active binaries, and the secondaries of
CV systems. We confirm that most stars with age t ga 0.3 Gyr occupy
two roughly parallel branches, separated by a factor of ~ 6 in P_cyc,
with P_rot/P_cyc ~ Ro(-0.5) , where Ro is the Rossby number. Using the
simple model of Brandenburg, Saar, &amp; Turpin (1998 ApJ 498, L51),
this result implies that the alpha effect increases with mean magnetic
field B, and that alpha and omega_cyc decrease with age along these
branches. Stars are not strictly segregated onto one or the other branch
by activity level, though the high P_rot/P_cyc branch is primarily
composed of inactive stars. The expanded dataset suggests that for t
ga 1 Gyr, stars can have P_cyc on one or both branches (double P_cyc
stars), though among older stars, those with higher mass (F) tend to
have their primary P_cyc on the low P_rot/P_cyc branch, while lower
mass (K) stars occupy the high P_rot/P_cyc branch. The sun's ~ 80 year
Gleissberg cycle agrees with this scenario, suggesting that long-term
“trends" in many stars may be segments of long (P_cyc ~ 50-100 yr)
cycles not yet resolved by the data. Most extremely active stars
(P_rot &lt; 3 days) appear to occupy a third branch with P_rot/P_cyc ~
Ro(0.4) , where some kind of alpha -quenching may be operating. Many RS
CVn variables lie in a transition region between the two most active
branches. We discuss implications for dynamo theory and evolution,
and compare our results with various other models. The results are also
used to predict P_cyc for stars with long-term HK trends, a sample of
young open cluster members, and a group which may be in the stellar
analog of the Maunder minimum.

---------------------------------------------------------
Title: Simulations of an alpha-effect due to magnetic buoyancy
Authors: Brandenburg, Axel; Schmitt, Dieter
1998A&A...338L..55B Altcode:
Three-dimensional simulations of a thermally stably stratified gas
with a localized layer of toroidal magnetic field are carried out. The
magnetic field gives rise to a magnetic buoyancy instability. Due to
the presence of rotation the resulting fluid motions are helical and
lead to an alpha -effect, i.e. to a component of the electromotive
force in the direction of the mean magnetic field. The value of
alpha is estimated during the exponential growth phase of the
instability. The mean vertical transport velocity of the magnetic
field is also calculated. It is found that alpha varies with latitude
and its value is positive in the northern hemisphere.

---------------------------------------------------------
Title: Mean Field Dynamos with Algebraic and Dynamic alpha-Quenchings
Authors: Tworkowski, A.; Covas, E.; Tavakol, R.; Brandenburg, A.
1998astro.ph..8214T Altcode:
Calculations for mean field dynamo models (in both full spheres and
spherical shells), with both algebraic and dynamic $\alpha$--quenchings,
show qualitative as well as quantitative differences and similarities
in the dynamical behaviour of these models. We summarise and enhance
recent results with extra examples. Overall, the effect of using a
dynamic $\alpha$ appears to be complicated and is affected by the
region of parameter space examined.

---------------------------------------------------------
Title: The radial disc structure around a magnetic neutron star:
analytic and semi-analytic solutions
Authors: Brandenburg, Axel; Campbell, Chris G.
1998MNRAS.298..223B Altcode:
The radial structure of a thin accretion disc is calculated in the
presence of a central dipole magnetic field aligned with the rotation
axis. The problem is treated using a modified expression for the
turbulent magnetic diffusion, which allows the angular momentum equation
to be integrated analytically. The governing algebraic equations
are solved iteratively between 1 and 10^4 stellar radii. An analytic
approximation is provided that is valid near the disruption radius
at about 100 stellar radii. At that point, which is approximately
60 per cent of the Alfven radius and typically about 30 per cent
of the corotation radius, the disc becomes viscously unstable. This
instability results from the fact that both radiation pressure and
opacity caused by electron scattering become important. This in turn
is a consequence of the magnetic field which leads to an enhanced
temperature in the inner parts. This is because the magnetic field
gives rise to a strongly enhanced vertically integrated viscosity,
so that the viscous torque can balance the magnetic torque.

---------------------------------------------------------
Title: Turbulence and Magnetic Fields in Clusters of Galaxies
Authors: Sánchez-Salcedo, F. J.; Brandenburg, A.; Shukurov, A.
1998Ap&SS.263...87S Altcode: 1999Ap&SS.263...87S
We consider turbulence generated by galaxies moving transonically
through the intracluster gas. We show that neither the gravitational
drag nor the gas stripping from the galaxies are able, by themselves,
to generate turbulence at a level required to feed the dynamo in
the intracluster gas. Some implications for cluster radio halos are
discussed.

---------------------------------------------------------
Title: New results for the Herzenberg dynamo: steady and oscillatory
solutions
Authors: Brandenburg, A.; Moss, D.; Soward, A. M.
1998RSPSA.454.1283B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Time Evolution of the Magnetic Activity Cycle Period
Authors: Brandenburg, Axel; Saar, Steven H.; Turpin, Christen R.
1998ApJ...498L..51B Altcode:
We propose a new interpretation of the relationships between the
dynamo cycle period (Pcyc) as observed in Ca II H and K,
the rotational period (Prot), the activity level, and other
stellar properties. Viewed within this framework, the data suggest
that the dynamo α-parameter increases with magnetic field strength,
contrary to the conventional idea of α-quenching. The data also
suggest a possibly discontinuous dependence of the ratio of cycle
to rotation frequency, ωcyc/Ω, as a function of Rossby
number, Ro (or equivalently, activity or age). Stars evolve with
ωcyc/Ω~t-0.35 (or Ro-0.7), until
age t~2-3 Gyr (roughly at the Vaughan-Preston gap), where a sharp
transition occurs, in which ωcyc/Ω increases by a factor
of ~6. Thereafter, evolution with ωcyc/Ω~t-0.35
continues. The age at which transition occurs may be mass dependent,
with K stars making the transition first.

---------------------------------------------------------
Title: Intermittent Behaviour in Axisymmetric Mean-Field Dynamo
Models in Spherical Shells
Authors: Tworkowski, Andrew; Tavakol, Reza; Brandenburg, Axel; Brooke,
John M.; Moss, David; Tuominen, Ilkka
1998MNRAS.296..287T Altcode:
Axisymmetric mean-field dynamo models in spherical shells are shown
to be capable of producing temporally intermittent behaviour. This is
of potential importance since (i) it is, as far as we are aware, the
first time such behaviour has been produced internally by a mean-field
dynamo model in a spherical shell, without requiring any additional
assumptions or truncations, and (ii) it may be characteristic of the
type of behaviour observed in the long-term record of solar activity,
such as Maunder minima. We also show that these types of behaviour
persist when the functional form of the alpha quenching is altered and
also occur over intervals of the shell thickness and the dynamo number.

---------------------------------------------------------
Title: Magnetic fields in young galaxies due to the cross-helicity
effect
Authors: Brandenburg, Axel; Urpin, Vadim
1998A&A...332L..41B Altcode:
It is shown that the cross-helicity effect facilitates rapid growth
of the large scale magnetic field in young galaxies. This field then
acts as a seed for the standard alpha Omega -type dynamo at later
stages. This mechanism may be responsible for the relatively strong
magnetic fields observed in young high redshift galaxies.

---------------------------------------------------------
Title: Exploring magnetohydrodynamic turbulence on the computer
Authors: Torkelsson, Ulf; Ogilvie, Gordon I.; Brandenburg, Axel;
Nordlund, A. ˚Ke; Stein, Robert F.
1998AIPC..431...69T Altcode: 1998apas.conf...69T
Although numerical simulations have established magnetohydrodynamic
turbulence as a possible candidate for the angular momentum transport
mechanism in accretion discs there is still a need for a deeper
understanding of the physics of the shear-induced turbulence. There
are two complementary pathways to this goal, to analyze the results of
a simulation at depth or to start from a simple state, whose evolution
can be understood by semi-analytical methods and `extrapolate' to the
turbulent state that we want to understand. We will show examples of
these two approaches.

---------------------------------------------------------
Title: Magnetic and vertical shear instabilities in accretion discs
Authors: Urpin, V.; Brandenburg, A.
1998MNRAS.294..399U Altcode:
The stability properties of magnetized discs rotating with angular
velocity Omega=Omega(s,z), dependent on both the radial and the vertical
coordinates s and z, are considered. Such a rotation law is adequate
for many astrophysical discs (e.g., galactic and protoplanetary discs,
as well as accretion discs in binaries). In general, the angular
velocity depends on height, even in thin accretion discs. A linear
stability analysis is performed in the Boussinesq approximation,
and the dispersion relation is obtained for short-wavelength
perturbations. Any dependence of Omega on z can destabilize the
flow. This concerns primarily small-scale perturbations for which
the stabilizing effect of buoyancy is strongly suppressed due to the
energy exchange with the surrounding plasma. For a weak magnetic field,
instability of discs is mainly associated with vertical shear, whilst
for an intermediate magnetic field the magnetic shear instability,
first considered by Chandrasekhar and Velikhov, is more efficient. This
instability is caused by the radial shear which is typically much
stronger than the vertical shear. Therefore the growth time for the
magnetic shear instability is much shorter than for the vertical shear
instability. A relatively strong magnetic field can suppress both these
instabilities. The vertical shear instability could be the source of
turbulence in protoplanetary discs, where the conductivity is low.

---------------------------------------------------------
Title: Turbulence effects in planetesimal formation
Authors: Hodgson, Lindsay S.; Brandenburg, Axel
1998A&A...330.1169H Altcode:
The formation of planetesimals is investigated by studying the transport
of dust particles in a local three-dimensional simulation of accretion
disc turbulence. Heavy particles fall rapidly towards the midplane,
whereas lighter particles are strongly advected by the flow. For light
particles the turbulence leads to a rapid redistribution of particles
such that their density per unit mass is approximately constant with
height. There is no pronounced concentration of particles in vortices
or anticyclones, as was suggested previously. This is partly because
of the adverse effect of keplerian shear and also because in our
simulation vortices are only short lived. However, if we assume the
gas velocity to be frozen in time, there is a concentration of dust
in ring-like structures after a few orbits. This is caused mainly
by a convergence of the gas flow in those locations, rather than the
presence of vortices or anticyclones.

---------------------------------------------------------
Title: Theoretical Basis of Stellar Activity Cycles
Authors: Brandenburg, Axel
1998ASPC..154..173B Altcode: 1998csss...10..173B
Numerical simulations of hydromagnetic turbulence in the presence of
shear and/or convection have given us new clues as to how the solar
dynamo might work. Simulations suggest that there is significant
large-scale magnetic field generation at the bottom of the convection
zone, where the radial shear is largest. The nature of the dynamo
in the simulations seems to be qualitatively similar to an alpha
Omega-dynamo. However, the origin of the effective alpha in the
simulations is not thermal convection, but magnetobuoyancy and magnetic
shear instabilities. This results in a negative alpha-effect. The
efficiency of the alpha-effect on the one hand, and losses on the other,
should increase as the field strength increases. It is argued that this
could lead to an increasing ratio between cycle and rotation frequency
with increasing field strength, as is indicated by the stellar cycle
data of Baliunas and collaborators. Furthermore, to explain the cycle
data for active stars one has to invoke another, as yet unknown,
type of magnetic instability for which both alpha and the flux loss
are abruptly reduced above a certain field strength. However, details
of this speculation are still unclear.

---------------------------------------------------------
Title: Solar Magneto-Convection
Authors: Stein, R. F.; Bercik, D. J.; Brandenburg, A.; Georgobiani,
D.; Nordlund, A.
1998AAS...191.7417S Altcode: 1998BAAS...30..758S
We present results of realistic simulations of magneto-convection near
the solar surface. The simulations were performed with two magnetic
field topologies - (1) a unipolar, initially vertical field, and (2)
a bipolar field, where fluid entering at the base of the computational
domain advects in horizontal field. As the unipolar flux is increased,
the magnetic field concentrates in the intergranule lanes and develops
large, dark, cool regions. These regions surround smaller areas where
convection has not been suppressed. In contrast, for the bipolar case,
the strongest fields appear as bright points in the intergranule lanes.

---------------------------------------------------------
Title: Axisymmetric mean field dynamos with dynamic and algebraic
alpha -quenchings
Authors: Covas, Eurico; Tavakol, Reza; Tworkowski, Andrew; Brandenburg,
Axel
1998A&A...329..350C Altcode: 1997astro.ph..9062C
We study axisymmetric mean field spherical and spherical shell dynamo
models, with both dynamic and algebraic alpha -quenchings. Our results
show that there are qualitative as well as quantitative differences
and similarities between these models. Regarding similarities, both
groups of models exhibit symmetric, antisymmetric and mixed modes of
behaviour. As regards differences, the important feature in the full
sphere models is the occurrence of chaotic behaviour in the algebraic
alpha -quenching models. For the spherical shell models with dynamic
alpha the main features include the possibility of multi-attractor
regimes with final state sensitivity with respect to small changes in
the magnitude of alpha and the initial parity. We find the effect of
introducing a dynamic alpha is likely to be complicated and depend on
the region of the parameter space considered, rather than a uniform
change towards simplicity or complexity.

---------------------------------------------------------
Title: Disc turbulence and viscosity.
Authors: Brandenburg, A.
1998tbha.conf...61B Altcode: 1998npad.conf...61B
Three-dimensionsional simulations of hydromagnetic flows in accretion
disc provide strong evidence that the turbulence in discs is driven
by a magnetic instability. Some basic results of those simulations
are reviewed, current shortcomings discussed, and open questions and
important issues are highlighted. The main motivation behind thise
simulations was imply to show tht turbulence is self-sustained. However,
an important quantitative outcome has been the determination of the
magnitude of the Shakura-Sunyaev viscosity parameter αSS. It
is emphasized that αSS cannot be considered a constant,
as it does in fact depend on a number of factors: the magnetic field
strength, the height above the midplane, and the magnitude of the
velocity shear - to mention just a few. Given the availability of
detailed simulations, it is now possible to address specific questions,
for example what are the rates of Joule and viscous heating, where is
the energy deposited, what are the values of turbulent Prandtl numbers,
and how efficiently does the flow disperse and mix particles? Finally,
the disc simulations have significantly affected and enhanced research
in dynamo theory in different fields of astrophysics, because some
of the ideas (dynamo-generated turbulence) may also apply to stars
and galaxies.

---------------------------------------------------------
Title: Current Sheet Formation in the Interstellar Medium: Erratum
Authors: Zweibel, Ellen G.; Brandenburg, Axel
1997ApJ...485..920Z Altcode:
In the paper "Current Sheet Formation in the Interstellar Medium"
by Ellen G. Zweibel and Axel Brandenburg (ApJ, 478, 563 [1997]), the
address given for Dr. Brandenburg is incorrect. It should be Department
of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU,
England, UK. His e-mail address is Axel.Brandenburg@newcastle.ac.uk.

---------------------------------------------------------
Title: The dependence of the dynamo alpha on vorticity
Authors: Brandenburg, Axel; Donner, Karl Johan
1997MNRAS.288L..29B Altcode:
We use data from numerical simulations of dynamo-generated turbulence in
the shearing box approximation to determine the dynamo alpha-effect and
its dependence on the rotation law Omega(r). The data suggest that the
dynamo alpha is not simply proportional to the local angular velocity
Omega(r), as is usually assumed, but rather is proportional to the
local vorticity omega(r)=r^-1d/dr(Omegar^2). We also find tentative
evidence to support the proposition that the backreaction of the
magnetic field on alpha sets in when the field reaches equipartition
with the energy in the turbulent motions. Furthermore, we propose an
explanation as to why the sign of alpha is found to be opposite to
that in the standard picture.

---------------------------------------------------------
Title: Robustness of truncated α Ω dynamos with a dynamic α
Authors: Covas, Eurico; Tworkowski, Andrew; Tavakol, Reza; Brandenburg,
Axel
1997SoPh..172....3C Altcode: 1997astro.ph..8094C; 1997ESPM....8....3C
In a recent work (Covas et al., 1996), the behaviour and the robustness
of truncated α Ω dynamos with a dynamic α were studied with respect
to a number of changes in the driving term of the dynamic α equation,
which was considered previously by Schmalz and Stix (1991) to be
of the form ∼ AΦBΦ. Here we review and extend our previous work
and consider the effect of adding a quadratic quenching term of the
form α|B|2. We find that, as before, such a change can
have significant effects on the dynamics of the related truncated
systems. We also find intervals of (negative) dynamo numbers, in
the system considered by Schmalz and Stix (1991), for which there is
sensitivity with respect to small changes in the dynamo number and
the initial conditions, similar to what was found in our previous
work. This latter behaviour may be of importance in producing the
intermittent type of behaviour observed in the Sun.

---------------------------------------------------------
Title: Current Sheet Formation in the Interstellar Medium
Authors: Zweibel, Ellen G.; Brandenburg, Axel
1997ApJ...478..563Z Altcode:
There is phenomenological evidence that magnetic reconnection
operates in the interstellar medium, and magnetic reconnection is
also necessary for the operation of a galactic dynamo. The extremely
long ohmic diffusion times of magnetic fields in typical interstellar
structures suggest that reconnection occurs in two stages, with thin
current layers that have relatively short resistive decay times forming
by magnetohydrodynamical processes first, followed by reconnection of
the fields in the layers. We propose that ambipolar drift can lead to
the formation of these thin sheets in weakly ionized interstellar gas
and can delineate the parameter regime in which this occurs by means
of a numerical model: we find that the magnetic field cannot be too
large and the medium cannot be too diffusive. Both limits are imposed
by the requirement that the field be wound up about 1 time by the eddy.

---------------------------------------------------------
Title: The effect of Silk damping on primordial magnetic fields
Authors: Brandenburg, Axel; Enqvist, Kari; Olesen, Poul
1997PhLB..392..395B Altcode: 1996hep.ph....8422B
We study the effects of plasma viscosity on the dynamics of primordial
magnetic fields by simulating magnetohydrodynamics in the early universe
by appropriate non-linear cascade models. We find numerically that
even in the presence of large kinetic viscosity, magnetic energy is
transferred to large length scales. There are indications, however,
that the inverse cascade stops at a given time which depends on the
magnitude of viscosity. For realistic viscosities we do not find
equipartition between magnetic and kinetic energies.

---------------------------------------------------------
Title: Dynamos with different formulations of a dynamic α-effect.
Authors: Covas, E.; Tworkowski, A.; Brandenburg, A.; Tavakol, R.
1997A&A...317..610C Altcode: 1997astro.ph..8093C
We investigate the behaviour of α{OMEGA} dynamos with a dynamic
α, whose evolution is governed by the imbalance between a driving
and a damping term. We focus on truncated versions of such dynamo
models which are often studied in connection with solar and stellar
variability. Given the approximate nature of such models, it is
important to study how robust they are with respect to reasonable
changes in the formulation of the driving and damping terms. For each
case, we also study the effects of changes of the dynamo number and its
sign, the truncation order and initial conditions. Our results show
that changes in the formulation of the driving term have important
consequences for the dynamical behaviour of such systems, with the
detailed nature of these effects depending crucially on the form of the
driving term assumed, the value and the sign of the dynamo number and
the initial conditions. On the other hand, the change in the damping
term considered here seems to produce little qualitative effect.

---------------------------------------------------------
Title: An Incoherent α-Ω Dynamo in Accretion Disks
Authors: Vishniac, Ethan T.; Brandenburg, Axel
1997ApJ...475..263V Altcode: 1995astro.ph.10038V
We use the mean-field dynamo equations to show that spatially
and temporally incoherent fluctuations in the helicity in
mirror-symmetric turbulence in a shearing flow can generate
a large-scale, coherent magnetic field. We illustrate this
effect with simulations of a few simple systems. For statistically
homogeneous turbulence, we find that the dynamo growth rate is roughly
τ-1/3eddyτ-2/3shearN-1/3eddy(λeddy/LB)2/3,
where τeddy is the eddy turnover time,
τ-1shear is the local shearing rate,
Neddy is the number of eddies per magnetic domain,
λeddy is the size of an eddy, and LB is
the extent of a magnetic domain perpendicular to the mean flow
direction. Even in the presence of turbulence and shear the dynamo
can be stopped by turbulent dissipation if (for example) the eddy
scale is close to the magnetic domain scale and τshear
&gt; τeddy. We also identify a related incoherent
dynamo in a system with a stationary distribution of helicity with
a high-spatial frequency and an average value of zero. In accretion
disks, the incoherent dynamo can lead to axisymmetric magnetic domains
the radial and vertical dimensions of which will be comparable to
the disk height. This process may be responsible for dynamo activity
seen in simulations of dynamo-generated turbulence involving, for
example, the Balbus-Hawley instability. However, although it explains
the generation of a magnetic field in numerical simulations without
significant large-scale average helicity and the occasional field
reversals, it also predicts that the dimensionless viscosity will scale
as ~(h/r)2, which is not seen in the simulations. On the
other hand, this result is consistent with phenomenological models of
accretion disks, although these suggest a slightly shallower dependence
on h/r. We discuss some possible resolutions to these contradictions.

---------------------------------------------------------
Title: Modelling magnetised accretion discs
Authors: Brandenburg, A.; Campbell, C.
1997LNP...487..109B Altcode: 1997adna.conf..109B
Some recent results are reviewed that lead us now to believe that
accretion discs are basically always magnetised. The main components
are Balbus-Hawley and Parker instabilities on the one hand and a
dynamo process on the other. A mechanical model for the Balbus-Hawley
instability is presented and analysed quantitatively. Three-dimensional
simulations are discussed, especially the resulting magnetic field
structure. Possibilities of reproducing the field by an αΩ dynamo
are investigated, especially its symmetry with respect to the midplane.

---------------------------------------------------------
Title: Magnetohydrodynamic Turbulence in Accretion Discs: Towards
More Realistic Models
Authors: Torkelsson, U.; Brandenburg, A.; Nordlund, A.; Stein, R. F.
1997ASPC..121..210T Altcode: 1997apro.conf..210T; 1997IAUCo.163..210T
No abstract at ADS

---------------------------------------------------------
Title: Recent developments in the theory of large-scale dynamos
Authors: Brandenburg, A.
1997ppvs.conf..359B Altcode:
Large-scale magnetic fields in the Sun Traditional αΩ dynamos The
effective α in accretion disc simulations Strengths of fluctuations
Quenching of α and ηt Convection with shear Forced
turbulence with shear Variety of solar dynamo models

---------------------------------------------------------
Title: The dependence of the viscosity in accretion discs on the
shear/vorticity ratio
Authors: Abramowicz, Marek; Brandenburg, Axel; Lasota, Jean-Pierre
1996MNRAS.281L..21A Altcode:
We estimate the Shakura-Sunyaev viscosity parameter cc for different
values of the shear/vorticity ratio, w, using local simulations of
dynamo-generated turbulence. We find that the time average of cc is
approximately proportional to co (at least for &lt;10). We point out
that this result may have important implications for the properties
of thick accretion discs, because there w is small and cc would then
tend to be large. Our result may also be important for accretion
discs around black holes, because o becomes large in the inner 10
Schwarzschild radii as a result of relativistic effects.

---------------------------------------------------------
Title: Large-scale magnetic fields from hydromagnetic turbulence in
the very early universe
Authors: Brandenburg, Axel; Enqvist, Kari; Olesen, Poul
1996PhRvD..54.1291B Altcode: 1996astro.ph..2031B
We investigate hydromagnetic turbulence of primordial magnetic fields
using magnetohydrodynamics (MHD) in an expanding universe. We present
the basic, covariant MHD equations, find solutions for MHD waves
in the early universe, and investigate the equations numerically
for random magnetic fields in two spatial dimensions. We find the
formation of magnetic structures at larger and larger scales as time
goes on. In three dimensions we use a cascade (shell) model that has
been rather successful in the study of certain aspects of hydrodynamic
turbulence. Using such a model we find that after ~109
times the initial time the scale of the magnetic field fluctuation
(in the comoving frame) has increased by 4-5 orders of magnitude as a
consequence of an inverse cascade effect (i.e., transfer of energy from
smaller to larger scales). Thus at large scales primordial magnetic
fields are considerably stronger than expected from considerations
which do not take into account the effects of MHD turbulence.

---------------------------------------------------------
Title: Testing Cowling's Antidynamo Theorem near a Rotating Black Hole
Authors: Brandenburg, Axel
1996ApJ...465L.115B Altcode:
The kinematic evolution of axisymmetric magnetic and electric fields
is investigated numerically in Kerr geometry for a simplified Keplerian
disk near a rotating black hole. In the cases investigated it is found
that a magnetic field cannot be sustained against ohmic diffusion. In
flat space this result is known as Cowling's antidynamo theorem. No
support is found for the possibility that the gravitomagnetic dynamo
effect of Khanna &amp; Camenzind could lead to self-excited axisymmetric
solutions. In practice, therefore, Cowling's antidynamo theorem may
still hold in Kerr geometry, although here the original proof can no
longer be applied.

---------------------------------------------------------
Title: Supercomputer windows into the solar convection zone
Authors: Nordlund, Å.; Stein, R. F.; Brandenburg, A.
1996BASI...24..261N Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Disk Accretion Rate for Dynamo-generated Turbulence
Authors: Brandenburg, Axel; Nordlund, Ake; Stein, Robert F.;
Torkelsson, Ulf
1996ApJ...458L..45B Altcode:
Dynamo-generated turbulence is simulated in a modified shearing
box approximation that removes scale invariance and allows finite
accretion rates for a given distance from the central object. The
effective Shakura-Sunyaev viscosity parameter, alpha SS, is estimated
in three different ways using the resulting mass accretion rate, the
heating rate, and the horizontal components of the Maxwell and Reynolds
stress tensors. The results are still resolution dependent: doubling
the resolution leads to 1.4--1.6 times larger values for the viscosity
parameter. For 63 x 127 x 64 meshpoints we find that alpha SS = 0.007.

---------------------------------------------------------
Title: Magnetic structures in a dynamo simulation
Authors: Brandenburg, A.; Jennings, R. L.; Nordlund, Å.; Rieutord,
M.; Stein, R. F.; Tuominen, I.
1996JFM...306..325B Altcode:
We use three-dimensional simulations to study compressible convection
in a rotating frame with magnetic fields and overshoot into surrounding
stable layers. The, initially weak, magnetic field is amplified and
maintained by dynamo action and becomes organized into flux tubes
that are wrapped around vortex tubes. We also observe vortex buoyancy
which causes upward flows in the cores of extended downdraughts. An
analysis of the angles between various vector fields shows that there
is a tendency for the magnetic field to be parallel or antiparallel
to the vorticity vector, especially when the magnetic field is
strong. The magnetic energy spectrum has a short inertial range with
a slope compatible with k(+1/3) during the early growth phase of the
dynamo. During the saturated state the slope is compatible with k(-1). A
simple analysis based on various characteristic timescales and energy
transfer rates highlights important qualitative ideas regarding the
energy budget of hydromagnetic dynamos.

---------------------------------------------------------
Title: The Turbulent Viscosity in Accretion Discs
Authors: Torkelsson, U.; Brandenburg, A.; Nordlund, Å.; Stein, R. F.
1996ApL&C..34..383T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Dynamo-generated turbulence in disks: value and variability
of alpha.
Authors: Brandenburg, A.; Nordlund, Å.; Stein, R. F.; Torkelsson, U.
1996bpad.conf..285B Altcode: 1996pada.conf..285B
Dynamo-generated turbulence seems to be a universal mechanism for
angular momentum transport in accretion disks. The authors discuss the
resulting value of the viscosity parameter alpha and emphasize that this
value is in general not constant. Alpha varies with the magnetic field
strength which, in turn, can vary in an approximately cyclic manner. The
authors also show that the stress does not vary significantly with
depth, even though the density drops by a factor of about 30.

---------------------------------------------------------
Title: Galactic Magnetism: Recent Developments and Perspectives
Authors: Beck, Rainer; Brandenburg, Axel; Moss, David; Shukurov,
Anvar; Sokoloff, Dmitry
1996ARA&A..34..155B Altcode:
We discuss current observational and theoretical knowledge of magnetic
fields, especially the large-scale structure in the disks and halos
of spiral galaxies. Among other topics, we consider the enhancement of
global magnetic fields in the interarm regions, magnetic spiral arms,
and representations as superpositions of azimuthal modes, emphasizing
a number of unresolved questions. It is argued that a turbulent
hydromagnetic dynamo of some kind and an inverse cascade of magnetic
energy gives the most plausible explanation for the regular galactic
magnetic fields. Primordial theory is found to be unsatisfactory, and
fields of cosmological origin may not even be able to provide a seed
field for a dynamo. Although dynamo theory has its own problems, the
general form of the dynamo equations appears quite robust. Finally,
detailed models of magnetic field generation in galaxies, allowing
for factors such as spiral structure, starburts, galactic winds,
and fountains, are discussed and confronted with observations.

---------------------------------------------------------
Title: An Incoherent alpha -Omega Dynamo Mechanism for Accretion Disks
Authors: Vishniac, E. T.; Brandenburg, A.
1995AAS...18710409V Altcode: 1995BAAS...27.1435V
We use the mean-field dynamo equations to show that an incoherent
alpha effect in mirror-symmetric turbulence in a shearing flow can
generate a large scale, coherent magnetic field. In other words,
a shearing environment can create an organized magnetic field even
if the time averaged helicity is zero. We illustrate this effect
with simulations of a few simple systems. In accretion disks, this
process can lead to axisymmetric magnetic domains whose radial and
vertical dimensions will be comparable to the disk height. This
process may be responsible for observations of dynamo activity
seen in simulations of dynamo-generated turbulence involving, for
example, the Balbus-Hawley instability. In this case the magnetic
field strength will saturate at ~ (h/r)(2) times the ambient pressure
in real accretion disks. The resultant dimensionless viscosity will
be of the same order. In numerical simulations the azimuthal extent
of the simulated annulus should be substituted for r. We compare
the predictions of this model to numerical simulations previously
reported by Brandenburg et al. (1995). In a radiation pressure dominated
environment this estimate for viscosity should be reduced by a factor of
(Pgas/Pradiation)(6) due to magnetic buoyancy.

---------------------------------------------------------
Title: Generalized entropies in a turbulent dynamo simulation
Authors: Brandenburg, Axel; Klapper, Isaac; Kurths, Jürgen
1995PhRvE..52.4602B Altcode:
A simulation of hydromagnetic turbulence exhibiting dynamo action is
employed to estimate the generalized entropies, Hq, from
the distribution of moments of local expansion factors of material
line elements. These generalized entropies can be used to characterize
the dynamics of turbulence and of nonlinear dynamo action. The value
of the metric entropy, H1, is comparable to the largest
Lyapunov exponent describing the divergence of trajectories in phase
space, which in turn is somewhat larger than the growth rate of the
magnetic energy. The value of the topological entropy, H0,
is similar to the conversion rate of kinetic to magnetic energy,
but larger than the growth rate of the dynamo. This is in agreement
with results stating that the growth rate of the kinematic dynamo is
limited by the topological entropy. The dependence of Hq
on q leads to a criterion from which we infer that the degree of
intermittency in our particular system is weak.

---------------------------------------------------------
Title: Chaos in accretion disk dynamos?
Authors: Torkelsson, U.; Brandenburg, A.
1995CSF.....5.1975T Altcode:
Accretion disks appear to be favourable places for dynamo action,
because of their strong differential rotation. A simple estimate of
the strength of an accretion disk dynamo indicates that it will be
highly nonlinear. In spite of this, most studies hitherto have assumed
a linear model for the dynamo. The authors investigate nonlinear,
axisymmetric mean-field dynamos in accretion disks in order to study
the route to chaotic solutions in certain parameter regimes. The authors
find a sequence of bifurcations that lead eventually to chaos. Finally,
the physical significance of these results is discussed.

---------------------------------------------------------
Title: Flux tubes and scaling in MHD dynamo simulations.
Authors: Brandenburg, A.
1995CSF.....5.2023B Altcode:
MHD simulations of compressible convection in a layer heated from below
are discussed and the results analysed in various ways. The ultimate aim
of these simulations is to understand the generation and evolution of
the magnetic field in the Sun. The formation of flux tubes is addressed,
and it is concluded that random field line stretching plays the
dominant rôle, which is in contrast to vortex tubes where both shear
instabilities and vortex stretching contribute almost equally to the
generation of vorticity. Magnetic flux tubes occur preferentially near
stagnation points, but there remains a significant flow component along
the tube. Various scaling properties of the magnetic field generated in
such simulations are investigated. Multifractal dimensions, cancellation
exponents, and generalized power spectra are computed. While the spectra
show a tendency for power law scaling, no such behavior is found for
the cancellation exponent. Finally, implications for the generation
of large-scale fields in the solar dynamo are discussed.

---------------------------------------------------------
Title: Galactic Fountains as Magnetic Pumps
Authors: Brandenburg, A.; Moss, D.; Shukurov, A.
1995MNRAS.276..651B Altcode:
We study a simple, kinematical model of a galactic fountain flow and
show that a horizontal field in the galactic plane can be pumped
into the halo to a height of several kiloparsecs. This pumping
effect results from the topological structure of the flow in which
the updraughts (represented by hot gas) form a connected network,
whereas the downdraughts (associated with isolated cool clouds)
are disconnected from each other. Such a flow traps the large-scale
magnetic field in the disc and deposits it at the top of the fountain
flow. Unlike previously studied models of topological pumping, in
our case the flow is not constrained to a closed box and horizontal
magnetic flux can leak out at the top. We find significant pumping
of mean magnetic field into the halo, which can be parametrized by
an advection velocity of order 1-10 km s^-1^. The resulting magnetic
field strength at a height of several kiloparsecs above the galactic
plane is comparable with that at the base of the flow.

---------------------------------------------------------
Title: Effects of Pressure and Resistivity on the Ambipolar Diffusion
Singularity: Too Little, Too Late
Authors: Brandenburg, Axel; Zweibel, Ellen G.
1995ApJ...448..734B Altcode:
Ambipolar diffusion, or ion-neutral drift, can lead to steepening of the
magnetic field profile and even to the formation of a singularity in the
current density. These results are based on an approximate treatment
of ambipolar drift in which the ion pressure is assumed vanishingly
small and the frictional coupling is assumed to be very strong, so
that the medium can be treated as a single fluid. This steepening, if
it really occurs, must act to facilitate magnetic reconnection in the
interstellar medium, and so could have important consequences for the
structure and evolution of the galactic magnetic field on both global
and local scales. In actuality, the formation of a singularity
must be prevented by physical effects omitted by the strong coupling
approximation. In this paper we solve the coupled equations for charged
and neutral fluids in a simple slab geometry, which was previously shown
to evolve to a singularity in the strong coupling approximation. We
show that both ion pressure and resistivity play a role in removing the
singularity, but that, for parameters characteristic of the interstellar
medium, the peak current density is nearly independent of ion pressure
and scales inversely with resistivity. The current gradient length
scale, however, does depend on ion pressure. In the end, effects
outside the fluid approximation, such as the finite ion gyroradius,
impose the strictest limit on the evolution of the magnetic profile.

---------------------------------------------------------
Title: Non-Local Transport in Turbulent MHD Convection
Authors: Miesch, M.; Brandenburg, A.; Zweibel, E.; Toomre, J.
1995ESASP.376b.253M Altcode: 1995help.confP.253M; 1995soho....2..253M
No abstract at ADS

---------------------------------------------------------
Title: Dynamo-generated Turbulence and Large-Scale Magnetic Fields
in a Keplerian Shear Flow
Authors: Brandenburg, Axel; Nordlund, Ake; Stein, Robert F.;
Torkelsson, Ulf
1995ApJ...446..741B Altcode:
The nonlinear evolution of magnetized Keplerian shear flows is
simulated in a local, three-dimensional model, including the effects
of compressibility and stratification. Supersonic flows are initially
generated by the Balbus-Hawley magnetic shear instability. The
resulting flows regenerate a turbulent magnetic field which, in
turn, reinforces the turbulence. Thus, the system acts like a dynamo
that generates its own turbulence. However, unlike usual dynamos,
the magnetic energy exceeds the kinetic energy of the turbulence by
a factor of 3-10. By assuming the field to be vertical on the outer
(upper and lower) surfaces we do not constrain the horizontal magnetic
flux. Indeed, a large-scale toroidal magnetic field is generated,
mostly in the form of toroidal flux tubes with lengths comparable
to the toroidal extent of the box. This large-scale field is mainly
of even (i.e., quadrupolar) parity with respect to the midplane and
changes direction on a timescale of ∼30 orbits, in a possibly cyclic
manner. The effective Shakura-Sunyaev alpha viscosity parameter is
between 0.001 and 0.005, and the contribution from the Maxwell stress
is ∼3-7 times larger than the contribution from the Reynolds stress.

---------------------------------------------------------
Title: A solar dynamo in the overshoot layer: cycle period and
butterfly diagram.
Authors: Ruediger, G.; Brandenburg, A.
1995A&A...296..557R Altcode:
We construct a solar dynamo model for the overshoot layer where a
strong gradient in the turbulence velocity is assumed to produce
the α-effect. A recent rotation law from helioseismology is adopted
and meridional flows are ignored. Since in the overshoot layer the
convective turnover time is long compared with the rotation period,
the full structure of the alpha and turbulent diffusion tensors
appearing in the expressions for the turbulent electromotive force
(EMF) must be retained in the computations. The important toroidal
component of α is negative in the overshoot layer. In this layer
the turbulence is considered as rarefied with a "dilution factor"
ɛ&lt;1 to account for the reduced EMF due to the intermittent nature
of the magnetism. The cycle period increases with decreasing ɛ, and
for ɛ=~0.2-0.5 the 22yr solar cycle period is reproduced, depending
on details of the model. The effect of magnetic buoyancy can increase
the cycle period further. If this layer is thinner than =~30Mm, the
number of toroidal field belts is too large compared to the sun. Due
to the strong rotational influence on the turbulence in the presence
of a sharp change of the turbulence intensity at the bottom of the
convection zone, the α-effect is more concentrated to the equatorial
region. This leads to more realistic butterfly diagrams. Observations
indicate, however, that radial and azimuthal field components are out
of phase, which is not reproduced by our model.

---------------------------------------------------------
Title: Structural stability of axisymmetric dynamo models.
Authors: Tavakol, R.; Tworkowski, A. S.; Brandenburg, A.; Moss, D.;
Tuominen, I.
1995A&A...296..269T Altcode:
We examine the stability of the dynamical behaviour of axisymmetric
α^2^ ω dynamo models in rotating spherical shells as well as in
spheres. Overall, our results show that the spherical dynamo models
are more stable in the following senses: spherical models (i) do not
seem to allow chaotic behaviour and (ii) are robust with respect to
changes in the functional form of α. On the other hand, spherical
shell models (i) are capable of producing chaotic behaviour for certain
ranges of parameter values and (ii) possess, in the combined "space" of
parameters and boundary conditions, regions of complicated behaviours,
in the sense that there are regimes in which small changes in either
the dynamo parameters or the boundary conditions can drastically change
the qualitative behaviour of the model. Finally, we discuss briefly
the physical relevance of our results.

---------------------------------------------------------
Title: Multiple far-supercritical solutions for an α{LAMBDA}-dynamo.
Authors: Muhli, P.; Brandenburg, A.; Moss, D.; Tuominen, I.
1995A&A...296..700M Altcode:
We compute numerical solutions for axisymmetric, dynamically consistent
mean-field dynamos in a spherical shell of conducting incompressible
fluid. In the process of investigating the stability properties of
solutions in the far-supercritical regime we found an unusual behaviour,
with the magnetic energy decreasing discontinuously as the dynamo number
is increased. A new stable solution with a more complicated field
geometry emerges. In addition, a stable mixed parity state occurs at
the discontinuity of the magnetic energy, between the two branches of
stable pure parity solutions. For a given dynamo number there may be
as many as four metastable solutions.

---------------------------------------------------------
Title: The size and dynamics of magnetic flux structures in
magnetohydrodynamic turbulence
Authors: Brandenburg, Axel; Procaccia, Itamar; Segel, Daniel
1995PhPl....2.1148B Altcode:
The structures in magnetohydrodynamic (MHD) flow, flux tubes in
particular, are investigated with respect to coherence in the direction
of the magnetic field. A length scale, which is interpreted as the
diameter of the tubes, is derived from the MHD equations. This scale
implies that the tendency towards alignment of flux lines in tubes
is a diffusion driven phenomenon. The dynamics of the tubes is also
investigated; the major conclusion is that stronger tubes are expected
to be straighter. These ideas are tested out on data from numerical
simulations of turbulent MHD convection. It is also seen that alignment
of flux lines increases with the strength of the tube. Possible reasons
for this effect are discussed.

---------------------------------------------------------
Title: Nonaxisymmetric dynamo solutions and extended starspots on
late-type stars.
Authors: Moss, D.; Barker, D. M.; Brandenburg, A.; Tuominen, I.
1995A&A...294..155M Altcode:
We have computed mean field dynamo models in a deep spherical shell,
without restriction on spatial symmetries, in which the growth of the
magnetic field is limited solely by the back reaction of the large
scale Lorentz force on the large scale motions. A parameterization
of the Reynolds stress tensor is included to describe the generation
of differential rotation. We find for moderate values of the Taylor
number, when the differential rotation is also small, that the stable
magnetic fields are nonaxisymmetric, with the same basic topology
as a "perpendicular dipole". For larger Taylor numbers, and stronger
absolute differential rotation, we expect axisymmetric fields to be
stable. We briefly discuss the relevance of our results to the large
scale nonaxisymmetric structures and extended starspots observed on
late type "active giant" and other stars.

---------------------------------------------------------
Title: Dynamo Generated Turbulence in Discs
Authors: Brandenburg, A.; Nordlund, Å.; Stein, R. F.; Torkelsson, U.
1995LNP...462..385B Altcode: 1995ssst.conf..385B
The magnetic shear instability appears to be a workable mechanism
for generating turbulence in accretion discs. The magnetic field,
in turn, is generated by a dynamo process that taps energy from the
Keplerian shear flow. Large scale magnetic fields are generated, whose
strength is comparable with, or in excess of, the turbulent kinetic
energy. Such models enable us to investigate the detailed nature
of turbulence in discs. We discuss in particular the possibility of
generating convection, where the heat source is viscous and magnetic
heating in the bulk of the disc.

---------------------------------------------------------
Title: The generation of nonaxisymmetric magnetic fields in the
giant planets
Authors: Moss, D.; Brandenburg, A.
1995GApFD..80..229M Altcode:
We consider mean-field dynamo models in uniformly rotating spheres
and spherical shells, with anisotropic alpha and magnetic diffusivity
tensors which are functions of the inverse Rossby number, *. When we
include an a-quenching nonlinearity we show that, for all values of *
considered, nonaxisymmetric magnetic fields are stable to axisymmetric
perturbations. However the stability of nonaxisymmetric magnetic fields
is weakened for large values of *, which would make the generation of
axisymmetric magnetic fields more probable. When a small amount of
differential rotation is introduced, only axisymmetric dipole-like
solutions are stable. We draw attention to the possibility that the
nonaxisymmetric magnetic fields of Uranus and Neptune could be the
result of anisotropic alpha and magnetic diffusi vity tensors. The
more nearly axisymmetric magnetic fields of Jupiter and Saturn could
result from their more rapid rotation, or possibly because of internal
differential rotation.

---------------------------------------------------------
Title: The many incarnations of accretion disk dynamos: mixed parities
and chaos for large dynamo numbers.
Authors: Torkelsson, Ulf; Brandenburg, Axel
1994A&A...292..341T Altcode:
We study nonlinear accretion disk dynamos, and demonstrate
that different types of magnetic field configurations will arise
depending on the dynamo number. Dynamo action is parametrised by the
α-effect, whose strength is determined by a dimensionless number
Calpha_. Using α-quenching as the only nonlinearity,
we find for Calpha_&gt;0 that a steady quadrupolar field
is first excited. However this solution disappears before any other
field configuration is excited. Thus there is a gap without any
magnetic field. This is a feature of the particular nonlinearity used,
and has not been observed previously in other systems. At higher
dynamo numbers oscillatory dipolar and quadrupolar fields emerge,
and later the quadrupolar solution bifurcates to a chaotically varying
mixed parity solution. Finally, at extremely high dynamo numbers the
chaotic field transforms into a steady mixed parity solution, which is
dominated by an even parity component. For Calpha_&lt;0 we
first find an oscillatory dipolar field, which bifurcates to a doubly
periodic mixed parity field, and later also to a chaotically varying
field. Using magnetic buoyancy as the nonlinearity the gap no longer
occurs. However we are not able to go to as high dynamo numbers as
before. Nevertheless for the entire interval investigated, we only
find a steady quadrupolar field for Calpha_&gt;0, and an
oscillatory quadrupolar or dipolar field for Calpha_&lt;0.

---------------------------------------------------------
Title: The Formation of Sharp Structures by Ambipolar Diffusion
Authors: Brandenburg, Axel; Zweibel, Ellen G.
1994ApJ...427L..91B Altcode:
The effect of ambipolar diffusion is investigated using simple
numerical models. Examples are shown where sharp structures develop
around magnetic nulls. In contrast to the case of ordinary diffusion,
the magnetic field topology is conserved by ambipolar diffusion. This
is demonstrated in an example where differential rotation winds up an
initially uniform magnetic field and brings oppositely oriented field
lines close together. It is argued that ambipolar diffusion produces
structures of scales small enough for reconnection to occur.

---------------------------------------------------------
Title: Reynolds stresses and differential rotation in Boussinesq
convection in a rotating spherical shell.
Authors: Rieutord, Michel; Brandenburg, Axel; Mangeney, Andre;
Drossart, Pierre
1994A&A...286..471R Altcode:
We consider the problem of how numerical simulations of convection
in a spherical shell can be used to estimate turbulent transport
coefficients that may be used in mean field theory. For this purpose
we analyse data from simulations of three dimensional Boussinesq
convection. The rotational influence on convection is described in
terms of the {LAMBDA}-effect and anisotropic eddy conductivity. When
the resulting transport coefficients are used in a mean field model,
the original rotation law is recovered approximately. We thus conclude
that the flow can be described in terms of a {LAMBDA}-effect. Our
results are also compared with analytical theories and observations.

---------------------------------------------------------
Title: Does solar differential rotation ARISE from a large scale
instability?.
Authors: Tuominen, Ilkka; Brandenburg, Axel; Moss, David; Rieutord,
Michel
1994A&A...284..259T Altcode:
The suggestion by several authors that the solar differential rotation
is caused by a large scale instability of the basic convective state
is examined. We find that the proposed mean-field models are unstable
to a Rayleigh-Benard type instability, but argue that this cannot
explain the differential rotation of the Sun, because such a flow would
become nonaxisymmetric. We discuss the applicability of the mean-field
equations to the problem. hydrodynamics - Sun: rotation

---------------------------------------------------------
Title: Turbulent accretion disk dynamos ?
Authors: Torkelsson, Ulf; Brandenburg, Axel
1994A&A...283..677T Altcode:
We present numerical results for mean-field α^2OMEGA-
dynamos in an accretion disk. We first study the linear case in both
disks with constant thickness and disks with radially increasing
thickness. The preferred mode is dipolar for a thick disk, but
quadrupolar for a thin one. The quadrupolar mode generates a magnetic
torque that transports angular momentum outwards. The role of the
geometrical distribution of both the α-effect and the magnetic
diffusivity in the disk is considered for thin disks. It is found that
the parity of the most easily excited mode is unaffected, albeit the
distribution of the magnetic field and torque change in such a way
that a larger fraction of the field and the torque appears in regions
with small diffusivity. For some interesting cases we study nonlinear
effects like α-quenching and magnetic buoyancy. These effects can
affect significantly the magnetic field distribution, compared to the
linear case. A transition to chaotic behaviour is found for α-quenching
when α is negative in the upper part of the disk.

---------------------------------------------------------
Title: Stellar Dynamo Models: From F to K
Authors: Brandenburg, A.; Saar, S. H.; Moss, D.; Tuominen, I.
1994ASPC...64..357B Altcode: 1994csss....8..357B
We extend the two-dimensional solar dynamo models to stars of different
spectral types. Dynamo action is restricted to the overshoot layer.

---------------------------------------------------------
Title: The Evolution of Stellar Dynamo Variations.
Authors: Saar, S. H.; Brandenburg, A.; Donahue, R. A.; Baliunas, S. L.
1994ASPC...64..468S Altcode: 1994csss....8..468S
No abstract at ADS

---------------------------------------------------------
Title: Angular Momentum Loss from the Young Sun: Improved Wind and
Dynamo Models
Authors: Keppens, R.; Charbonneau, P.; MacGregor, K. B.; Brandenburg,
A.
1994ASPC...64..193K Altcode: 1994csss....8..193K
No abstract at ADS

---------------------------------------------------------
Title: Stellar Dynamos: The Rossby Number Dependence
Authors: Brandenburg, A.; Charbonneau, P.; Kitchatinov, L. L.;
Rudiger, G.
1994ASPC...64..354B Altcode: 1994csss....8..354B
No abstract at ADS

---------------------------------------------------------
Title: Hydrodynamical simulations of the solar dynamo
Authors: Brandenburg, Axel
1994LNP...432...73B Altcode: 1994LNPM...11...73B
Hydrodynamic simulations of the solar convection zone can be used to
model the generation of differential rotation and magnetic fields,
and to determine mean-field transport coefficients that are needed
in mean-field models. The importance of the overshoot layer beneath
the solar convection zone is discussed: it is the place where the
magnetic field accumulates, although most of the field regeneration
can still occur in the convection zone proper. We also discuss how
systematically oriented bipolar regions can emerge from the convection
zone where the magnetic field is highly intermittent.

---------------------------------------------------------
Title: Solar Dynamos; Computational Background
Authors: Brandenburg, A.
1994lspd.conf..117B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Models for the Magnetic Field of M81
Authors: Moss, David; Brandenburg, Axel; Donner, Karl J.; Thomasson,
Magnus
1993ApJ...409..179M Altcode:
We study several mean field dynamo models in disk geometry in an
attempt to understand the origin of the nonaxisymmetric magnetic field
present in M81. There appear to be three (at least) relevant mechanisms,
which are not mutually exclusive. Because field growth times are not
very short compared to galactic ages, a predominantly nonaxisymmetric
seed field may still give a significantly nonaxisymmetric field after
times of order 10^10^ yr, even if the stable field configuration is
axisymmetric. The spiral structure may give a non-axisymmetric structure
to the disk turbulence, and thus to the turbulent coefficients appearing
in mean field dynamo theory. Third M81 may have undergone a close
encounter with a companion galaxy. A dynamical model of the interaction
predicts strong, nonaxisymmetric, large-scale gas velocities in the disk
plane, and these can produce nonaxisymmetric fields. In the absence of
the second of these effects, our models predict that nonaxisymmetric
fields will be present in the outer parts of the galaxy, together with
significant axisymmetric contributions in the inner part. However, we
do not find that any of these effects, taken individually, can produce
dominant nonaxisymmetric field structure. If they are simultaneously
present, they can reinforce one another. Further, our calculations are
for a relatively thick disk (thickness to radius ratio of order 0.2),
and a reduction to smaller, and plausibly more realistic, values will
also favor nonaxisymmetric field generation.

---------------------------------------------------------
Title: Vertical magnetic fields above the discs of spiral galaxies.
Authors: Brandenburg, A.; Donner, K. J.; Moss, D.; Shukurov, A.;
Sokoloff, D. D.; Tuominen, I.
1993A&A...271...36B Altcode:
We investigate the magnetic fields above the discs of spiral galaxies
in the framework of axisymmetric nonlinear mean-field dynamo models
for a disc surrounded by a spherical halo, using realistic rotation
curves. We consider, in particular, NGC 4631 and NGC 891, and include
turbulent diamagnetism, an anisotropy of the α effect and a galactic
wind. In these model magnetic field is generated in a disc of scale
height 1.5 kpc and distorted by the wind in the halo. For typical
wind velocities of 50.. .200 km/s in the halo we find good qualitative
agreement between the observed polarisation maps and those synthesised
from the magnetic fields of our models: Poloidal synthesised fields
dominate in the halo of NGC 4631, and horizontal fields in that of
NGC 891. In some cases, a galactic wind can enhance dynamo action,
contrary to previous expectations. Our results indicate that turbulent
diamagnetism plays an important role in galactic dynamos.

---------------------------------------------------------
Title: The excitation of nonaxisymmetric magnetic fields in galaxies.
Authors: Moss, D.; Brandenburg, A.
1993spd..conf..219M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Reynolds Stresses Derived from Simulations
Authors: Pulkkinen, P.; Tuominen, I.; Brandenburg, A.; Nordlund, A.
1993IAUS..157..123P Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Multifractality, near-singularities and the role of stretching
in turbulence.
Authors: Brandenburg, A.; Procaccia, I.; Segel, D.; Vincent, A.;
Manzini, M.
1993spd..conf...35B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Rotational effects on convection simulated at different
latitudes
Authors: Pulkkinen, Pentti; Tuominen, Ilkka; Brandenburg, Axel;
Nordlund, Ake; Stein, Robert F.
1993A&A...267..265P Altcode:
We simulate numerically convection inside the solar convection
zone under the influence of rotation at different latitudes. The
computational domain is a small rectangular box with stress-free upper
and lower boundaries, and with periodicity assumed in the lateral
directions. We study the transport of angular momentum, which is
important for the generation of differential rotation. The sign and
the latitudinal dependence of the horizontal Reynolds stress component
turn out to be in good agreement with correlation measurements of
sunspot proper motions and with predictions from the theory of the
Lambda effect. We also investigate the other components of the Reynolds
stress as well as the eddy heat flux tensor, both of which are needed
in mean field models of differential rotation.

---------------------------------------------------------
Title: Simulating the Solar Dynamo
Authors: Brandenburg, A.
1993IAUS..157..111B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Chaos in Nonlinear Dynamo Models
Authors: Kurths, J.; Brandenburg, A.; Feudel, U.; Jansen, W.
1993IAUS..157...83K Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Towards the Magnetic Field of M 81
Authors: Moss, D.; Brandenburg, A.; Donner, K. J.; Thomasson, M.
1993IAUS..157..339M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Galactic Dynamos and Dynamics
Authors: Donner, K. J.; Brandenburg, A.; Thomasson, M.
1993IAUS..157..333D Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Evolution of a magnetic flux tube in two-dimensional
penetrative convection
Authors: Jennings, R. L.; Brandenburg, A.; Nordlund, A.; Stein, R. F.
1992MNRAS.259..465J Altcode:
Highly supercritical compressible convection is simulated in a
two-dimensional domain in which the upper half is unstable to convection
while the lower half is stably stratified. This configuration is
an idealization of the layers near the base of the solar convection
zone. Once the turbulent flow is well developed, a toroidal magnetic
field Btor is introduced to the stable layer. The field's
evolution is governed by an advection-diffusion-type equation, and
the Lorentz force does not significantly affect the flow. After many
turnover times the field is stratified such that the absolute value
of Btor/rho is approximately constant in the convective
layer, where rho is density, while in the stable layer this ratio
decreases linearly with depth. Consequently most of the magnetic flux
is stored in the overshoot layer. The inclusion of rotation leads
to travelling waves which transport magnetic flux latitudinally in a
manner reminiscent of the migrations seen during the solar cycle.

---------------------------------------------------------
Title: Stratification and thermodynamics in mean-field dynamos
Authors: Brandenburg, Axel; Moss, David; Tuominen, Ilkka
1992A&A...265..328B Altcode:
Previous investigations of axisymmetric incompressible mean-field
dynamos are extended to the compressible case with strong
stratification. It is shown that the effects of stratification,
compressibility, and thermodynamics on the rotation law are small when
the present results are compared with those previously obtained for
incompressible models. For solar values of the Taylor number cylindrical
contours of the angular velocity typically occur, even for strong
stratification. The stagnation line of the meridional circulation is
close to the bottom of the convection zone. In the presence of magnetic
fields the meridional flow is amplified, in particular, close to the
surface where the density is small and the Lorentz force per unit mass
is large. The depth dependence of the magnetic energy density is not
much altered by the inclusion of a density stratification. For cyclical
dynamo magnetic fields thermal and magnetic energies are approximately
in antiphase. The cyclic variation in luminosity is small and lags
behind the variation in magnetic energy by about 1/8 of the period.

---------------------------------------------------------
Title: Stochastic effects in mean-field dynamos
Authors: Moss, David; Brandenburg, Axel; Tavakol, Reza; Tuominen, Ilkka
1992A&A...265..843M Altcode:
We investigate the effects of various forms of noise on previously
studied nonlinear (alpha-squared)(omega) dynamos in a sphere or
a spherical shell. We investigate the consequences of perturbing
solutions of both pure and mixed parity. In the former case we find
that there can be quite pronounced deviations from the pure parity,
and that these seem larger nearer to the relevant bifurcation. Effects
are also stronger in a shell dynamo than in the full sphere. However,
the magnetic period is relatively little changed in these examples. When
a 2-torus solution (of mixed parity) is perturbed, the effects on the
long period variations are much greater than on the short period,
but even for quite strong perturbations the solutions do not leave
the neighborhood of the underlying attractor.

---------------------------------------------------------
Title: Fractal level sets and multifractal fields in direct
simulations of turbulence
Authors: Brandenburg, Axel; Procaccia, Itamar; Segel, Daniel;
Vincent, Alain
1992PhRvA..46.4819B Altcode:
The fractal nature of level sets and the multifractal nature of
various scalar and vector fields in hydromagnetic and hydrodynamic
turbulence are investigated using data of direct simulations. It
turns out that fields whose evolution is governed by stretching
terms (vortex stretching, magnetic-field line stretching) exhibit
“near singularities” that result in a multifractal scaling. Such
stretching terms can lead to a rapid increase in the local value of
the field. Fields without rapid local increase have no multifractal
scaling. Furthermore, the simulations support recent theoretical
suggestions that the fractal properties of the level sets of various
fields are quite insensitive to the existence of stretching. Indeed, all
the fields under study (temperature, vorticity magnitude, magnetic-field
magnitude) show rather universal behavior in the geometry of their level
sets, consistent with a two-dimensional geometry at small scales, with a
crossover to a universal fractal geometry at large scales. The dimension
at large scales is compatible with the theoretical prediction of about
2.7. The most surprising result of the simulations is that it appears
that the “near singularities” are not efficiently eliminated by
viscous dissipation, but rather seem to be strongest at the Kolmogorov
cutoff. The effects of the singularities do not quite penetrate into the
inertial range. We offer a simple analytic model to account for this
behavior. We conclude that our findings may be due to the relatively
small Reynolds numbers, but may also be indicative of generic behavior
at larger Reynolds numbers. We offer some thoughts about the expected
scaling behavior in the inertial range in light of our findings.

---------------------------------------------------------
Title: Energy spectra in a model for convective turbulence
Authors: Brandenburg, Axel
1992PhRvL..69..605B Altcode:
The energy cascade in both hydrodynamic and hydromagnetic Boussinesq
convection is investigated at large Rayleigh numbers using a scalar
model for turbulence. Depending on the relative importance of direct and
inverse transfer, either classical Kolmogorov k exp -5/3 spectra are
derived or, if there is a strong inverse transfer of kinetic energy,
a K exp -7/5 spectrum is found for the temperature fluctuation and
a K exp -11/5 spectrum for the kinetic energy (Bolgiano-Obukhov
scaling). Dissipative cutoff wave numbers that are consistent with
these spectra are derived.

---------------------------------------------------------
Title: Dynamos in discs and halos of galaxies.
Authors: Brandenburg, A.; Donner, K. J.; Moss, D.; Shukurov, A.;
Sokolov, D. D.; Tuominen, I.
1992A&A...259..453B Altcode:
The authors investigate linear and nonlinear dynamo models for a
galactic disc embedded in a halo, assuming a relatively strong magnetic
diffusivity and a non-vanishing α effect in the halo. They take the
halo to be spherical and embedded in a vacuum. The field is assumed
to be axisymmetric, but they do not impose symmetry conditions at the
equatorial plane. In one parameter regime mixed parity solutions are
found. However, it is argued that the regular magnetic field in the
galactic halo can hardly reach a steady-state configuration during the
galactic lifetime. In the regime that is observably relevant the field
can have an even parity within and near the disc and an odd one in the
halo. This may have implications for explaining the occurrence of a
neutral sheet above the galactic plane. During certain time intervals
the rotation measure of these models shows a doubly peaked azimuthal
variation, which could be falsely interpreted as an indication of a
bisymmetric field structure.

---------------------------------------------------------
Title: Dynamo Action in Stratified Convection with Overshoot
Authors: Nordlund, Ake; Brandenburg, Axel; Jennings, Richard L.;
Rieutord, Michel; Ruokolainen, Juha; Stein, Robert F.; Tuominen, Ilkka
1992ApJ...392..647N Altcode:
Results are presented from direct simulations of turbulent compressible
hydromagnetic convection above a stable overshoot layer. Spontaneous
dynamo action occurs followed by saturation, with most of the generated
magnetic field appearing as coherent flux tubes in the vicinity
of strong downdrafts, where both the generation and destruction of
magnetic field is most vigorous. Whether or not this field is amplified
depends on the sizes of the magnetic Reynolds and magnetic Prandtl
numbers. Joule dissipation is balanced mainly by the work done against
the magnetic curvature force. It is this curvature force which is also
responsible for the saturation of the dynamo.

---------------------------------------------------------
Title: The influence of boundary conditions on the excitation of
disk dynamo modes
Authors: Moss, David; Brandenburg, Axel
1992A&A...256..371M Altcode:
Calculations of mean field dynamos for galaxies have largely been for
two rather disparate models. The thin disk model treats the ratio of
disk height to radius explicitly as a small parameter, and applies zero
tangential field boundary conditions at the disk surface. In contrast,
the embedded disk model calculates the magnetic field in a spherical
volume, whose radius is the disk radius and with the magnetic field
fitting smoothly on to a curl-free exterior field at the surface of
the sphere. The disk geometry is imposed by a flat distribution of the
α-effect (and maybe also of the diffusivity η. For computational
reasons this model has not been applied to very thin disks, so the
regions of validity of the two models are almost disjoint. Comparison
between their predictions is therefore difficult. In this paper we
calculate, in linear theory, galactic dynamo modes according to both
thin and embedded (or "thick") disk models for a simple underlying
distribution of α-effect and differential rotation, using a common
numerical scheme. For the smallest attainable ratio of disk height
to radius, we find the critical dynamo numbers are similar, but that
there are some significant differences in field topology.

---------------------------------------------------------
Title: Magnet Convection (Invited Review)
Authors: Stein, R. F.; Brandenburg, A.; Nordlund, A.
1992ASPC...26..148S Altcode: 1992csss....7..148S
No abstract at ADS

---------------------------------------------------------
Title: Turbulent Pumping in the Solar Dynamo
Authors: Brandenburg, Axel; Moss, David; Tuominen, Ilkka
1992ASPC...27..536B Altcode: 1992socy.work..536B
No abstract at ADS

---------------------------------------------------------
Title: Lyapunov exponents for hydromagnetic convection
Authors: Kurths, J.; Brandenburg, A.
1991PhRvA..44.3427K Altcode:
We estimate the two largest Lyapunov exponents in a three-dimensional
simulation of hydromagnetic convection in which there is dynamo
action. It turns out that these first two exponents (from a total
of 8×633) are positive and of similar magnitude. Thus we
conclude that the dynamo is chaotic. Furthermore, the consideration
of local exponents helps in our understanding of the relevant
dynamics. We find that the downdraft flows are more chaotic than the
upward motions. Likewise, the velocity and magnetic fields have more
chaotic dynamics than the temperature and density fields.

---------------------------------------------------------
Title: Properties of mean field dynamos with non-axisymmetric
alpha-effect
Authors: Moss, D.; Brandenburg, A.; Tuominen, I.
1991A&A...247..576M Altcode:
The influence of an azimuthally dependent alpha-effect on the
properties of alpha(2) and alpha(2)Omega-dynamos in spherical geometry
is investigated. Consideration is given solely to odd parity solutions
in linear theory. For all the present linear models an exponentially
growing mode, consisting of locked axisymmetric and nonaxisymmetric
parts is found. A strong nonaxisymmetry in alpha substantially increases
the linear growth rates at given dynamo number and can result in a
marginal dynamo number. Some exploratory nonlinear calculations are
also reported and the relevance of the present results to galactic
dyanmos and to stars is briefly discussed.

---------------------------------------------------------
Title: Nonlinear nonaxisymmetric dynamo models for cool stars
Authors: Moss, D.; Tuominen, I.; Brandenburg, A.
1991A&A...245..129M Altcode:
Observational evidence for long-lived nonaxisymmetric features on the
surfaces of rapidly rotating late-type giant stars (e.g., FK Comae and
RS CVn stars) is beginning to be found. By analogy with sunspots, these
features may be associated with large scale nonaxisymmetric magnetic
field structures, generated by a dynamo operating in the convective
envelopes. A nonlinear nonaxisymmetric dynamo model is described, and
it is shown that for a simple 'alpha-quenching' nonlinearity together
with suitable choices of underlying radial profiles of differential
rotation and the alpha-effect, stable nonaxisymmetric solution can be
found by numerical integration.

---------------------------------------------------------
Title: Challenges for solar dynamo theory: α-effect, differential
rotation and stability.
Authors: Brandenburg, A.; Tuominen, I.
1991NAWG.1991...26B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Can the Lorentz force accelerate magnetic field expansion?
Authors: Brandenburg, A.; Krause, F.; Moss, D.; Tuominen, I.
1991AGAb....6...32B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Hydromagnetic -type dynamos with feedback from large scale
motions
Authors: Brandenburg, A.; Moss, D.; Rüdiger, G.; Tuominen, I.
1991GApFD..61..179B Altcode:
Nonlinear axisymmetric mean-field -type dynamos in spherical shells of
conducting incompressible fluid are computed, with differential rotation
being generated by the Reynolds stress of anisotropic turbulence
(A-effect). The correlation time of the turbulence is assumed to be
short compared with the rotation period. In this case the angular
velocity tends to be constant on cylindrical surfaces as the Taylor
number, Ta, is increased (cf. the Taylor-Proudman theorem). The only
magnetic feedback mechanism considered is the Lorentz force of the
mean magnetic field acting on the macroscale motions (Malkus-Proctor
mechanism). The Elsasser number is in this case close to unity, but
grows slowly as Ta1'2. Restricting ourselves to strictly dipole-type
magnetic fields we find for Ta = 108, magnetic cycles with migrating
field belts close to the equator. For smaller Taylor numbers and only
slightly supercritical a-effect the magnetic field is steady and the
-effect becomes unimportant for the generation of toroidal field from
a poloidal one. However, magnetic cycles are still possible if the
-effect is sufficiently strong. In this case the field is concentrated
at high latitudes. Poloidal and toroidal fields can be in antiphase with
equatorward field migration only when the angular velocity increases
inwards and towards the poles. The energy of the mean magnetic field
generated is usually less than the energy of the turbulent convective
motions. The ratio between cycle period and rotational period can
reach values of around fifty.

---------------------------------------------------------
Title: The Solar Dynamo
Authors: Brandenburg, Axel; Tuominen, Ilkka
1991LNP...380..223B Altcode: 1991IAUCo.130..223B; 1991sacs.coll..223B
The traditional -dynamo as a model for the solar cycle has been
successful in explaining the butterfly diagram, phase relations
between poloidal and toroidal field, and polar branch migration
features. Observational and theoretical achievements in recent years
have however shaken this picture. The current trend is towards dynamos
operating in the overshoot region of the convection zone. Nevertheless,
there are many open questions and a consistent picture has not been
established. In this paper we compare recent approaches and discuss
remaining problems.

---------------------------------------------------------
Title: αΛ-dynamos
Authors: Brandenburg, A.; Moss, D.; Rieutord, M.; Rüdiger, G.;
Tuominen, I.
1991LNP...380..147B Altcode: 1991sacs.coll..147B; 1991IAUCo.130..147B
In contrast to -dynamos, where the angular velocity is arbitrarily
prescribed, we consider here -dynamos, for which the differential
rotation and meridional circulation are solutions of the momentum
equation. The non-diffusive parts of the Reynolds stress tensor are
parameterized by the -effect. In earlier investigations we have shown
that the turbulent magnetic diffusivity has to be much smaller than
the eddy viscosity, otherwise the dynamo is not oscillatory or else
the contours of constant angular velocity are cylindrical, contrary
to observations. In the present paper we investigate the effects of
compressibility.

---------------------------------------------------------
Title: The Role of Overshoot in Solar Activity - a Direct Simulation
of the Dynamo
Authors: Brandenburg, A.; Jennings, R. L.; Nordlund, Å.; Stein,
R. F.; Tuominen, I.
1991LNP...380...86B Altcode: 1991IAUCo.130...86B; 1991sacs.coll...86B
We investigate convective overshoot in a layer of electrically
conducting fluid. The radiative conductivity is assumed to be larger
in the lower part of the layer which makes it stable to convective
motions, yet penetrative convection from the upper layer can occur. The
numerical resolution is 633 gridpoints. We observe a dynamo effect for
magnetic Reynolds numbers around one thousand when a magnetic seed
field is rapidly concentrated to form flux tubes. Later the average
magnetic field is expelled from the convectively unstable regions,
but it accumulates in the interface between the convection zone and
the radiative interior.

---------------------------------------------------------
Title: Magnetic Tubes in Overshooting Compressible Convection
Authors: Jennings, R. L.; Brandenburg, A.; Nordlund, Å.; Stein,
R. F.; Tuominen, I.
1991LNP...380...92J Altcode: 1991sacs.coll...92J; 1991IAUCo.130...92J
A magnetic tube is introduced into turbulent compressible penetrative
convection. After being strongly advected, most of the magnetic flux
is stored in the overshoot region. With rotation there are meridional
travelling waves.

---------------------------------------------------------
Title: Rotational Effects on Reynolds Stresses in the Solar
Convection Zone
Authors: Pulkkinen, P.; Tuominen, I.; Brandenburg, A.; Nordlund, Å.;
Stein, R. F.
1991LNP...380...98P Altcode: 1991IAUCo.130...98P; 1991sacs.coll...98P
Three-dimensional hydrodynamic simulations are carried out in a
rectangular box. The angle between gravity and rotation axis is kept
as an external parameter in order to study the latitude-dependence
of convection. Special attention is given to the horizontal Reynolds
stress and the -effect (Rüdiger, 1989). The results of the simulations
are compared with observations and theory and a good agreement is found.

---------------------------------------------------------
Title: Buoyancy-limited thin shell dynamos
Authors: Moss, D.; Tuominen, I.; Brandenburg, A.
1990A&A...240..142M Altcode:
Axisymmetric nonlinear mean-field dynamos in spherical shells are
investigated that attempt to model the gross effects of a dynamo
operating in a thin layer at the base of a convective envelope. A
form of magnetic buoyancy restricts the fields to finite amplitude. As
the shell thickness decreases, the excitation conditions and spatial
structure of even and odd parity modes become almost identical. For very
thin shells the field forms a number of almost disjoint cells. Mixed
parity solutions are found which typically evolve very slowly toward
pure odd or even parity solutions. The time scale of these slow
variations is of the order of a hundred global diffusion times.

---------------------------------------------------------
Title: Generation and interpretation of galactic magnetic fields
Authors: Donner, K. J.; Brandenburg, A.
1990A&A...240..289D Altcode:
We present kinematic mean-field dynamo models for galaxies consisting of
a turbulent gas disc embedded in a low-conductivity spherical halo. In
the cases investigated an axisymmetric mode is the dominant one. This
mode can be of either even or odd parity (SO or A0, respectively). The
preference of S0 or A0 modes is governed mainly by the radial profiles
of the α effect and the turbulent magnetic diffusivity. If the gas disc
extends into the galactic centre, the dominant mode is of A0 type and it
is concentrated within the central region. If the model is changed so
that induction effects are absent in the centre, the dominant mode is
an axisymmetric spiral of even parity. We point out that a finite disc
thickness and a low- conductivity halo will both lead to appreciable
vertical magnetic fields outside the disc plane, and this may affect the
interpretation of polarisation observations. We integrate the transfer
equations for the three Stokes parameters I, Q, and U and produce in
this way synthetic maps for the observed polarisation and rotation
measures. Assuming a disc-like distribution of relativistic electrons,
our models suggest that for moderate disc thickness modifications of the
observed polarised emission due to fields above the plane are minor. For
more extended electron distributions quite complicated polarisation
patterns are obtained. Still, qualitatively the criteria distinguishing
axisymmetric and bisymmetric spiral patterns remain valid.

---------------------------------------------------------
Title: Nonlinear mean-field dynamo models - Stability and evolution
of three-dimensional magnetic field configurations.
Authors: Raedler, K. -H.; Wiedemann, E.; Brandenburg, A.; Meinel,
R.; Tuominen, I.
1990A&A...239..413R Altcode:
The stability and evolution of three-dimensional magnetic field
configurations of nonlinear mean-field dynamo models are investigated. A
single stable solution showing the same symmetry is found for two
models with isotropic alpha effect. A model with anisotropic alpha
effect is investigated for which the marginal solution is known to
be nonaxisymmetric, and a nonaxisymmetric solution is found to be
the only stable one for slightly supercritical dynamo numbers. A
stable axisymmetric solution is found for dynamo numbers exceeding
a certain value. For even higher dynamo numbers, the nonaxisymmetric
solution loses stability to the axisymmetric solution. Mixed parity
solutions with periodic time dependence are found for a model with
differential rotation in a parameter regime where four different modes
are approximately equally excitable.

---------------------------------------------------------
Title: Behaviour of highly supercritical alpha-effect dynamos
Authors: Meinel, R.; Brandenburg, A.
1990A&A...238..369M Altcode:
The behavior of alpha-squared-dynamos is discussed for highly
supercritical dynamo numbers, with alpha-quenching assumed to be the
dominant nonlinearity. Particular attention is paid to a one-dimensional
reduction of the dynamo equations. For sufficiently high dynamo
numbers both steady and time-dependent solutions (limit cycles) are
possible. The basins of attraction of these solutions depend on the
dynamo number as well as on the degree of the nonlinearity assumed. For
extreme nonlinearities the limit-cycle solutions, at particular time
instants (turning points), closely approach the steady solutions. In
this case some noise of small but finite amplitude may cause transitions
between the limit-cycle and the steady solutions. This leads to an
irregular time-behavior including nearly steady stages as well as
reversals of the magnetic polarity.

---------------------------------------------------------
Title: The Nonlinear Solar Dynamo and Differential Rotation -
a Taylor Number Puzzle
Authors: Brandenburg, A.; Tuominen, I.; Moss, D.; Ruediger, G.
1990SoPh..128..243B Altcode: 1990IAUCo.121P.243B
We consider dynamically consistent mean-field dynamos in a spherical
shell of incompressible fluid. The generation of magnetic field and
differential rotation is parameterized by the α- and Λ-effects,
respectively. Extending previous investigations, we include now
the cases of moderate and rapid rotation in the sense that the
inverse Rossby number can approach or exceed unity: This can lead to
disk-shapedΩ-contours, which are in better accordance with recent
results of helioseismology than cylindricalΩ-contours. On the other
hand, in order to obtain αω-dynamo cycles the Taylor number has to be
so large, that eventually cylindrical Ω-contours become unavoidable
(cf. Taylor-Proudman theorem). We discuss the different possibilities
in a state diagram, where the inverse Rossby number and the relative
correlation length are taken as the elementary parameters for mean-field
dynamos.

---------------------------------------------------------
Title: 3-D simulation of turbulent cyclonic magneto-convection.
Authors: Brandenburg, A.; Tuominen, I.; Nordlund, A.; Pulkkinen, P.;
Stein, R. F.
1990A&A...232..277B Altcode:
Results are presented of a simulation of turbulent three-dimensional
magnetic convection under the influence of rotation in a fluid layer
whose depth is about 1 pressure-scale hight. The approach is similar
to that of Meneguzzi and Pouquet (1989), except for the assumptions
that the fluid is a compressible conducting gas and there is a
vanishing horizontal magnetic field at the boundaries. The results
demonstrate that topological effects may be of great importance for
MHD convection. It is shown that, as a consequence of topological
effects, anisotropies of the alpha-effect can play a dominant role. In
particular, the sign of alpha(V) can be opposite to that expected from
a first-order smoothing approach.

---------------------------------------------------------
Title: Can stellar dynamos be modelled in less than three dimensions?
Authors: Jennings, R.; Brandenburg, A.; Tuominen, I.; Moss, D.
1990A&A...230..463J Altcode:
Nonlinear alpha-omega dynamos in different geometries are compared. The
importance of radial structure is investigated via comparison of
axisymmetric one-dimensional models with their two-dimensional
counterparts. For the two-dimensional nonaxisymmetric extension of
the one-dimensional model, a finite-amplitude mixed solution with
nonaxisymmetric contributions is found.

---------------------------------------------------------
Title: Nonlinear dynamos with magnetic buoyancy in spherical geometry
Authors: Moss, D.; Tuominen, I.; Brandenburg, A.
1990A&A...228..284M Altcode:
Numerical solutions are computed for axisymmetric mean field dynamos of
alpha-sq and alpha-sq omega type in spherical geometry. In particular,
the effects of including a term in the magnetohydrodynamic equations
which represents the upward advection of fields by magnetic buoyancy
is studied. For the buoyancy-limited alpha-sq dynamo, it is found that,
for certain parameter values, this model may have two stable solutions,
of opposite parity properties with respect to the equator. In the dynamo
models for smaller values of a dynamo number, odd parity solutions
are stable, but, for larger values, it is the even parity solutions
that are stable. These results concerning the stability of pure parity
solutions are similar to those found in an earlier study in which the
nonlinearity was a simple alpha-quenching. Some models are presented
with both buoyancy and alpha-quenching included. The most noticeable
effect of adding a buoyancy term to the alpha-quenched solutions is
that the amplitude of the finite amplitude parity oscillations (tori
and limit cycles) previously found is reduced.

---------------------------------------------------------
Title: Magnetic field structure in differentially rotating discs
Authors: Donner, K. J.; Brandenburg, A.
1990GApFD..50..121D Altcode:
In order to gain a better understanding of the processes that may
give rise to non-axisymmetric magnetic fields in galaxies, we have
calculated field decay rates for models with a realistic galactic
rotation curve and including the effects of a locally enhanced turbulent
magnetic diffusivity within the disc. In all cases we have studied,
the differential rotation increases the decay rate of non-axisymmetric
modes, whereas axisymmetric ones are unaffected. A stronger magnetic
diffusivity inside the disc does not lead to a significant preference
for non-axisymmetric modes. Although Elsasser's antidynamo theorem
has not yet been proved for the present case of a non-spherical
distribution of the magnetic diffusivity, we do not find any evidence
for the theorem not to be valid in general.

---------------------------------------------------------
Title: Turbulent diffusivities derived from simulations.
Authors: Brandenburg, A.; Nordlund, Å.; Pulkkinen, P.; Stein, R. F.;
Tuominen, I.
1990fas..conf....1B Altcode:
By employing direct simulations of turbulent magneto-convection the
authors determine the turbulent diffusivities, such as the turbulent
magnetic diffusivity, the eddy viscosity and the turbulent heat
conductivity.

---------------------------------------------------------
Title: Challenges for the solar dynamo theory: α-effect, differential
rotation and stability
Authors: Brandenburg, Axel
1990PhDT.......290B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Challenges for solar dynamo theory: Alpha-effect, differential
rotation and stability
Authors: Brandenburg, Axel
1990csdt.book.....B Altcode: 1990QB539.M23B73...
No abstract at ADS

---------------------------------------------------------
Title: Surface Imaging of Giant Stars and Nonlinear Dynamos
Authors: Tuominen, I.; Piskunov, N. E.; Moss, D.; Brandenburg, A.
1990ASPC....9...73T Altcode: 1990csss....6...73T
Recent results of photometric cycles and surface images of active
giants are discussed in terms of nonlinear 3D mean-field dynamos. The
existence of mixed parity solutions with periodic and quasi-periodic
time dependence is suggestive for explaining the nonaxisymmetric
surface patterns observed on active giant stars.

---------------------------------------------------------
Title: Dynamos with a flat -effect distribution
Authors: Brandenburg, A.; Tuominen, I.; Krause, F.
1990GApFD..50...95B Altcode:
In order to obtain a better insight into the excitation conditions of
magnetic fields in flat objects, such as galaxies, we have calculated
critical dynamo numbers of different magnetic field modes for spherical
dynamos with a flat -effect distribution. A simple but realistic
approximation formula for the rotation curve is employed. In most cases
investigated a stationary quadrupole-type solution is preferred. This is
a consequence of the flat distribution of the -effect. Non-axisymmetric
fields are in all cases harder to excite than axisymmetric ones. This
seems to be the case particularly for flat objects in combination
with a realistic rotation curve for galaxies. The question of whether
non-axisymmetric (bisymmetric) fields, which are observed in some
galaxies, can be explained as dynamos generated by an axisymmetric
-effect is therefore still open.

---------------------------------------------------------
Title: Torsional Oscillations and the Solar Dynamo Regime
Authors: Tuominen, I.; Rüdiger, G.; Brandenburg, A.
1990IAUS..138..387T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Effect of a conducting halo on the structure of galactic
magnetic fields.
Authors: Donner, K. J.; Brandenburg, A.
1990nba..meet...85D Altcode: 1990taco.conf...85D
The authors give examples of the magnetic fields generated by dynamo
processes in galaxy models consisting of a turbulent disc embedded in
a conducting halo. As the halo conductivity increases, the dominant
marginally stable mode becomes more spatially extended and more nearly
azimuthal. This is because the critical strengths of the α effect is
smaller for higher halo conductivity.

---------------------------------------------------------
Title: Variation of Even and Odd Parity in the Solar Dynamo
Authors: Brandenburg, A.; Meinel, R.; Moss, D.; Tuominen, I.
1990IAUS..138..379B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Structure of dynamo generated galactic magnetic fields.
Authors: Donner, K. J.; Brandenburg, A.
1990apsu.conf...16D Altcode:
No abstract at ADS

---------------------------------------------------------
Title: IUE observations of the M dwarfs CM Draconis and Rossiter
137B : magnetic activity at saturated levels.
Authors: Vilhu, O.; Ambruster, C. W.; Neff, J. E.; Linsky, J. L.;
Brandenburg, A.; Ilyin, I. V.; Shakhovskaya, N. I.
1989A&A...222..179V Altcode:
IUE observations of two active M dwarfs with known rotation rate or age
and presumed to be almost totally convective are presented. The first
of these stars, CM Draconis (Gl 630.1), is an old Population II binary
with its components in tidally induced rapid rotation (P = 1.27 d, dM
4 + dM 4). The other one, Rossiter 137 B, forms with HD 36705 (AB Dor)
a visual pair of young active stars. The activity of CM Dra is due to
the forced rotation in a close binary, while Rst 137 B is assumed to
rotate fast enough to generate its magnetica activity. These results
are compared with those for M dwarfs, particularly AU Mic and YZ CMi,
that have known rotational periods and measured ultraviolet emission
line fluxes. The chromospheric-coronal saturation levels of cool dwarfs
between 0.3 less than B-V less than 1.6 is determined. It is found
that saturated F stars have stronger chromospheres than saturated
M stars, but the opposite is true for the corona. Results of these
observations seem to favor a rotation-dependent distributed dynamo
generating magnetic flux in totally convective stars.

---------------------------------------------------------
Title: The stability of nonlinear dynamos and the limited role of
kinematic growth rates
Authors: Brandenburg, A.; Krause, F.; Meinel, R.; Moss, D.; Tuominen,
I.
1989A&A...213..411B Altcode:
The growth rate behavior of several kinematic dynamo models was
investigated in the context of the observation that, as a rule, a
magnetic field of a single symmetry dominates in the sun and other
cosmic objects. For all dynamo models considered, it is shown that,
as the dynamo numbers increase, the kinematic growth rates of fields
of different parities are asymptotically equal, indicating that growth
rates do not dominate the final state of the field. The possibility that
the stability of different solutions of nonlinear dynamos determines the
final state was then investigated. Dynamo models in spherical geometry
were found in which both symmetric and antisymmetric solutions are
stable. The kind of symmetry finally established depends in these cases
on the initial conditions, i.e., on the history of the object. It is
noted that the basic mechanism stabilizing or destabilizing different
solutions is not well understood.

---------------------------------------------------------
Title: On the nonlinear stability of dynamo models
Authors: Brandenburg, A.; Tuominen, I.; Moss, D.
1989GApFD..49..129B Altcode:
The stability of nonlinear mean-field dynamo models in spherical
geometry has been investigated numerically. Assuming axisymmetry
and incompressibility we find stable stationary solutions of both
even and odd parity over a range of four decades in the Taylor
number. Furthermore, we extend studies on solutions with "mixed parity",
which have been found previously for an -dynamo model, neglecting
here, however, the explicit feedback on the mean motions. Plots of
trajectories in phase space and Poincaré maps, showing intersections
of the trajectories with certain hyperplanes in phase space, reveal
that the solution lies on a torus for some of these models.

---------------------------------------------------------
Title: On the generation of non-axisymmetric magnetic fields in
mean-field dynamos
Authors: Brandenburg, A.; Tuominen, I.; Rädler, K. -H.
1989GApFD..49...45B Altcode:
The magnetic fields of the Earth and other planets deviate in varying
degrees from symmetry about the rotational axis. While, for example,
the field of Saturn is highly symmetric, that of Uranus shows a
striking asymmetry. With these observations in mind we investigate
excitation conditions of axisymmetric and non-axisymmetric field modes
in spherical mean-field dynamo models. In models of 2-type the marginal
dynamo numbers for modes with different azimuthal dependences are close
together if the -effect is concentrated in a thin layer. Preference
of non-axisymmetric modes over axisymmetric ones occurs if we include
weak differential rotation, anisotropies of the -effect or the -effect,
the last one corresponding to a radial transport of magnetic flux. We
discuss consequences of these results for planetary dynamos.

---------------------------------------------------------
Title: Solar magnetic fields and dynamo process.
Authors: Brandenburg, A.; Tuominen, I.
1989sasf.confP.369B Altcode: 1989IAUCo.104P.369B; 1988sasf.conf..369B
The authors have computed kinematic dynamo models for the Sun making
realistic assumptions about the different induction effects. Recent
results of helioseismology are used to infer the differential
rotation. By changing the value of the angular velocity at the bottom
of the convection zone in the models the authors find more or less
agreement with the observations.

---------------------------------------------------------
Title: Parity selection in nonlinear dynamics.
Authors: Brandenburg, A.; Tuominen, I.; Krause, F.
1989tndm.conf...35B Altcode:
The stability of different nonlinear α-effect dynamos in spherical
geometry is studied. A critical value of the dynamo number is found,
above which steady hydromagnetic solutions of even and odd parity are
both stable. In αω-dynamos long-term variations between even and
odd parity are possible. Comparison with similar variations of the
sunspot number is made.

---------------------------------------------------------
Title: Non-axisymmetric magnetic fields in turbulent gas discs.
Authors: Donner, K. J.; Brandenburg, A.
1989dad..conf..151D Altcode:
Large-scale magnetic fields could play an important role in the dynamics
of astrophysical discs. Here the authors report some results showing
how the structure of non-axisymmetric magnetic fields is affected by
differential rotation. A turbulent disc is likely to be surrounded
by a gaseous corona. The authors study in particular how the field
structure in the disc is affected by surrounding gas. The results are
used to discuss the origin of galactic magnetic fields.

---------------------------------------------------------
Title: Hydrodynamic Green's functions for atmospheric oscillations
Authors: Brandenburg, A.
1988A&A...203..154B Altcode:
A Green's function tensor is derived giving the response of an
isothermal atmosphere to small disturbances representing deviations from
a state of static stratification. A Hermitian differential operator
is first derived that describes an adiabatic flow in a plane-parallel
isothermal atmosphere. This operator is inverted using a Fourier
transformation to give the Green's function tensor. The inverse
Fourier transformation is then carried out for an axisymmetric initial
condition. Different properties of g-modes and the range of validity
of the anelastic approximation are discussed. An approximate, explicit
solution for small bubbles is given.

---------------------------------------------------------
Title: Gravity Wave Generation by Largescale Bubbles
Authors: Brandenburg, A.
1988IAUS..123..383B Altcode:
The response of an isothermal atmosphere to small disturbances in
entropy is studied taking compressible effects fully into account. The
method of Green's functions is applied to solve the linearized
hydrodynamic equations by Fourier transformation. A bubble may be
created by perturbing the entropy within a finite volume. At first
Lamb waves will be then emitted radially and the bubble undergoes a
series of Brunt-Väisälä oscillations.

---------------------------------------------------------
Title: Observational Constraints for Solar-Type Dynamos
Authors: Tuominen, I.; Rüdiger, G.; Brandenburg, A.
1988ASSL..143...13T Altcode: 1988acse.conf...13T
The different phenomena of solar and stellar activity are generally
considered to have its origin in the turbulent convective envelopes
of these stars. The authors discuss how the problem can be treated in
the framework of the mean-field concept.

---------------------------------------------------------
Title: Solar oscillations in the two year range.
Authors: Brandenburg, A.
1988sfam.conf...34B Altcode:
Oscillations of the solar magnetic field pattern are considered as
global resonances. It is argued that they can be standing Alfvén
waves trapped in a cavity below the convection zone. Such a cavity can
be formed by a strong toroidal field in the Sun. Eigenfrequencies are
estimated to be in rough agreement with the observed diagnostic power
spectrum of Stenflo and Vogel (1986).

---------------------------------------------------------
Title: Variation of magnetic fields and flows during the solar cycle
Authors: Brandenburg, A.; Tuominen, I.
1988AdSpR...8g.185B Altcode: 1988AdSpR...8..185B
We have studied dynamo models with realistic assumptions for the
induction effects and compare the resulting magnetic fields with
observations. We make use of recent results of helioseismology to
infer the differential rotation and adopt mixing length approach to
get the form of the α-effect, which is in general anisotropic. Dynamo
models are computed numerically using an eigenvalue method. Finally, we
discuss the resulting Lorentz force, which is relevant for explaining
observed flows such as the torsional waves, as a back reaction of
the dynamo magnetic fields. Comparison is made in particular with
Mt. Wilson/Kitt Peak magnetograms and synoptic charts showing the
magnetic flux, torsional oscillation pattern, and the distribution of
ephemeral regions, coronal activity, and polar faculae.