Author name code: wheatland
ADS astronomy entries on 2022-09-14
author:"Wheatland, Michael S."
------------------------------------------------------------------------
Title: Editorial Appreciation
Authors: Arregui, Iñigo; Leibacher, John; Mandrini, Cristina H.;
van Driel-Gesztelyi, Lidia; Wheatland, Michael S.
Bibcode: 2022SoPh..297...11A
Altcode:
No abstract at ADS
Title: The ASKAP Variables and Slow Transients (VAST) Pilot Survey
Authors: Murphy, Tara; Kaplan, David L.; Stewart, Adam J.; O'Brien,
Andrew; Lenc, Emil; Pintaldi, Sergio; Pritchard, Joshua; Dobie, Dougal;
Fox, Archibald; Leung, James K.; An, Tao; Bell, Martin E.; Broderick,
Jess W.; Chatterjee, Shami; Dai, Shi; d'Antonio, Daniele; Doyle,
Gerry; Gaensler, B. M.; Heald, George; Horesh, Assaf; Jones, Megan L.;
McConnell, David; Moss, Vanessa A.; Raja, Wasim; Ramsay, Gavin; Ryder,
Stuart; Sadler, Elaine M.; Sivakoff, Gregory R.; Wang, Yuanming; Wang,
Ziteng; Wheatland, Michael S.; Whiting, Matthew; Allison, James R.;
Anderson, C. S.; Ball, Lewis; Bannister, K.; Bock, D. C. -J.; Bolton,
R.; Bunton, J. D.; Chekkala, R.; Chippendale, A. P.; Cooray, F. R.;
Gupta, N.; Hayman, D. B.; Jeganathan, K.; Koribalski, B.; Lee-Waddell,
K.; Mahony, Elizabeth K.; Marvil, J.; McClure-Griffiths, N. M.;
Mirtschin, P.; Ng, A.; Pearce, S.; Phillips, C.; Voronkov, M. A.
Bibcode: 2021PASA...38...54M
Altcode: 2021arXiv210806039M
The Variables and Slow Transients Survey (VAST) on the Australian
Square Kilometre Array Pathfinder (ASKAP) is designed to detect
highly variable and transient radio sources on timescales from 5
s to $∼ 5$ yr. In this paper, we present the survey description,
observation strategy and initial results from the VAST Phase I Pilot
Survey. This pilot survey consists of $∼ 162$ h of observations
conducted at a central frequency of 888 MHz between 2019 August and
2020 August, with a typical rms sensitivity of $0.24 mJy beam^{-1}$
and angular resolution of $12-20$ arcseconds. There are 113 fields,
each of which was observed for 12 min integration time, with between
5 and 13 repeats, with cadences between 1 day and 8 months. The total
area of the pilot survey footprint is 5 131 square degrees, covering
six distinct regions of the sky. An initial search of two of these
regions, totalling 1 646 square degrees, revealed 28 highly variable
and/or transient sources. Seven of these are known pulsars, including
the millisecond pulsar J2039-5617. Another seven are stars, four of
which have no previously reported radio detection (SCR J0533-4257, LEHPM
2-783, UCAC3 89-412162 and 2MASS J22414436-6119311). Of the remaining
14 sources, two are active galactic nuclei, six are associated with
galaxies and the other six have no multi-wavelength counterparts and
are yet to be identified.
Title: Modelling magnetic flux ropes in solar, stellar, and laboratory
contexts
Authors: Wheatland, Michael S.
Bibcode: 2021cosp...43E1754W
Altcode:
Magnetic flux ropes are generally accepted to be critical to the
processes of energy storage and release in solar activity, and by
extension stellar activity, and are fundamental to the description
of laboratory plasma devices. In this talk I will present a review
of the understanding of the physics of magnetic flux ropes in
solar, stellar, and laboratory contexts, with a focus on methods
for modelling flux ropes, and the insight they provide into the
mechanisms for solar/stellar activity, and magnetic energy release
more generally. I will highlight the similarities and differences in
the physical assumptions underlying the models, and identify possible
future directions for work.
Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
Lidia; Wheatland, Michael S.
Bibcode: 2021SoPh..296...14L
Altcode:
No abstract at ADS
Title: Failed Eruption Caused by Interacting Multi-current System
in the Solar Corona
Authors: Yang, Kai; Cao, Wenda; Wheatland, Michael S.
Bibcode: 2021cosp...43E1780Y
Altcode:
Solar flares are one of the most energetic activities of the Sun,
and are caused by current systems in the solar corona. Sometimes the
eruption of a current system is confined in the solar corona and fails
to trigger a coronal mass ejection or jet. A multi-current system
(multi-flux rope system) makes the confined/failed eruption process
more complex. To further investigate this phenomenon, we conduct a
data-driven zero-beta magnetohydrodynamics (MHD) simulation using the
Message Passing Interface Adaptive Mesh Refinement Versatile Advection
Code (MPI-AMRVAC). The initial condition is obtained by applying the
three-dimensional nonlinear force-free model to an observed vector
magnetogram from HMI. From the force-free magnetic field, three
flux ropes are identified in the active region, and the results are
compared with H$\alpha$ observation by the Goode Solar Telescope at
Big Bear Solar Observatory. The MHD simulation is driven by the time
series of the observed magnetogram and the inferred photospheric plasma
velocity. The simulation and observation confirm an interaction between
the three flux ropes, which leads to the initial eruption. With the
development of the interaction, magnetic reconnection mixes the flux
ropes and leads the system to a new stable state.
Title: The CME Initiation Mechanism
Authors: Wheatland, Michael S.
Bibcode: 2021cosp...43E.995W
Altcode:
The kink and torus instabilities in a magnetic flux rope are the
most popular mechanisms used to explain coronal mass ejections
(CMEs). However, these instabilities apply to idealised magnetic field
configurations, which may not match conditions on the Sun, and they
occur in ideal MHD, so they do not explain the dissipation in the
flare associated with the CME. In the standard (CHSKP) flare model
dissipation is attributed to secondary processes, but this presents
additional problems. Finally, even if these mechanisms operate, it
is necessary to explain how the system becomes unstable. This talk
presents a review of our current understanding of CME initiation,
based on recent observations, theory, simulation, and results from
laboratory plasma experiments.
Title: Reconstructing Highly-twisted Magnetic Fields
Authors: Demcsak, Victor; Yang, Kai; Wheatland, Michael S.; Mastrano,
Alpha
Bibcode: 2021cosp...43E1732D
Altcode:
We investigate the ability of a nonlinear force-free code to
calculate highly-twisted magnetic field configurations using the
Titov and D\'{e}moulin (1999) equilibrium field as a test case. The
code calculates a force-free field using boundary conditions on the
normal component of the field in the lower boundary, and the normal
component of the current density over one polarity of the field in
the lower boundary. The code can also use the current density over
both polarities of the field in the lower boundary as a boundary
condition. We investigate the accuracy of the reconstructions with
increasing flux-rope twist number $N_{\textrm{t}}$, achieved by
decreasing the buried line current in the model. We find that the code
can approximately reconstruct the Titov-D\'{e}moulin field for twist
numbers $N_{\textrm{t}} \approx 8.8$. This includes configurations
with bald patches, for which the magnetic skeleton is accurately
reproduced. We identify the limitations of our method for highly-twisted
fields. The results have implications for our ability to reconstruct
coronal magnetic fields from observational data.
Title: Self-consistent Grad-Rubin nonlinear force-free field
extrapolation from weighted boundary conditions
Authors: Mastrano, Alpha; Yang, Kai; Wheatland, Michael S.
Bibcode: 2021cosp...43E1801M
Altcode:
Vector magnetogram data are often used as photospheric boundary
condition in coronal force-free field extrapolations. One class of
field extrapolation method, Grad-Rubin extrapolation, is attractive
because it requires only the values of vertical field strength
and the force-free parameter $\alpha$ over one magnetic polarity
on the surface as boundary conditions. In general, however, vector
magnetogram data are not flux-balanced and not consistent with the
force-free assumption. This leads to an inconsistency between the
solution generated from the $\alpha$ values in the positive magnetic
polarity region and that generated from the values in the negative
polarity region. In this talk, we present a method to arrive at a
self-consistent field extrapolation from vector magnetogram data using
the Grad-Rubin method and we show its application to active regions
12017 and 12673. The method allows the use of a weighted average of
the boundary conditions of $\alpha$ on the two polarities. Different
choices of the weighting lead to different solutions, and this freedom
can be used to achieve better agreement between the model and magnetic
structures inferred from short wavelength observations of the corona.
Title: A Flare-type IV Burst Event from Proxima Centauri and
Implications for Space Weather
Authors: Zic, Andrew; Murphy, Tara; Lynch, Christene; Heald,
George; Lenc, Emil; Kaplan, David L.; Cairns, Iver H.; Coward, David;
Gendre, Bruce; Johnston, Helen; MacGregor, Meredith; Price, Danny C.;
Wheatland, Michael S.
Bibcode: 2020ApJ...905...23Z
Altcode: 2020arXiv201204642Z
Studies of solar radio bursts play an important role in understanding
the dynamics and acceleration processes behind solar space weather
events, and the influence of solar magnetic activity on solar system
planets. Similar low-frequency bursts detected from active M-dwarfs
are expected to probe their space weather environments and therefore
the habitability of their planetary companions. Active M-dwarfs
produce frequent, powerful flares which, along with radio emission,
reveal conditions within their atmospheres. However, to date, only
one candidate solar-like coherent radio burst has been identified from
these stars, preventing robust observational constraints on their space
weather environment. During simultaneous optical and radio monitoring
of the nearby dM5.5e star Proxima Centauri, we detected a bright,
long-duration optical flare, accompanied by a series of intense,
coherent radio bursts. These detections include the first example of an
interferometrically detected coherent stellar radio burst temporally
coincident with a flare, strongly indicating a causal relationship
between these transient events. The polarization and temporal structure
of the trailing long-duration burst enable us to identify it as a type
IV burst. This represents the most compelling detection of a solar-like
radio burst from another star to date. Solar type IV bursts are strongly
associated with space weather events such as coronal mass ejections
and solar energetic particle events, suggesting that stellar type IV
bursts may be used as a tracer of stellar coronal mass ejections. We
discuss the implications of this event for the occurrence of coronal
mass ejections from Proxima Cen and other active M-dwarfs.
Title: On Measuring Divergence for Magnetic Field Modeling
Authors: Gilchrist, S. A.; Leka, K. D.; Barnes, G.; Wheatland, M. S.;
DeRosa, M. L.
Bibcode: 2020ApJ...900..136G
Altcode: 2020arXiv200808863G
A physical magnetic field has a divergence of zero. Numerical error
in constructing a model field and computing the divergence, however,
introduces a finite divergence into these calculations. A popular metric
for measuring divergence is the average fractional flux $\left\langle
| {f}_{i}| \right\rangle $ . We show that $\left\langle | {f}_{i}|
\right\rangle $ scales with the size of the computational mesh, and
may be a poor measure of divergence because it becomes arbitrarily
small for increasing mesh resolution, without the divergence actually
decreasing. We define a modified version of this metric that does
not scale with mesh size. We apply the new metric to the results of
DeRosa et al., who measured $\left\langle | {f}_{i}| \right\rangle
$ for a series of nonlinear force-free field models of the coronal
magnetic field based on solar boundary data binned at different spatial
resolutions. We compute a number of divergence metrics for the DeRosa et
al. data and analyze the effect of spatial resolution on these metrics
using a nonparametric method. We find that some of the trends reported
by DeRosa et al. are due to the intrinsic scaling of $\left\langle |
{f}_{i}| \right\rangle $ . We also find that different metrics give
different results for the same data set and therefore there is value
in measuring divergence via several metrics.
Title: Reconstructing Highly-twisted Magnetic Fields
Authors: Demcsak, Victor M.; Wheatland, Michael S.; Mastrano, Alpha;
Yang, Kai E.
Bibcode: 2020SoPh..295..116D
Altcode: 2020arXiv200802985D
We investigate the ability of a nonlinear force-free code to calculate
highly-twisted magnetic field configurations using the Titov and
Démoulin (Astron. Astrophys. 351:707, 1999) equilibrium field as
a test case. The code calculates a force-free field using boundary
conditions on the normal component of the field in the lower boundary,
and the normal component of the current density over one polarity of the
field in the lower boundary. The code can also use the current density
over both polarities of the field in the lower boundary as a boundary
condition. We investigate the accuracy of the reconstructions with
increasing flux-rope surface twist number Nt, achieved by
decreasing the sub-surface line current in the model. We find that
the code can approximately reconstruct the Titov-Démoulin field
for surface twist numbers up to Nt≈8.8 . This includes
configurations with bald patches. We investigate the ability to recover
bald patches, and more generally identify the limitations of our
method for highly-twisted fields. The results have implications for our
ability to reconstruct coronal magnetic fields from observational data.
Title: Self-consistent Nonlinear Force-Free Field Reconstruction
from Weighted Boundary Conditions
Authors: Mastrano, A.; Yang, K. E.; Wheatland, M. S.
Bibcode: 2020SoPh..295...97M
Altcode: 2020arXiv200412510M
Photospheric vector magnetogram data are often used as boundary
conditions for force-free coronal magnetic field extrapolations. In
general, however, vector magnetogram data are not consistent with the
force-free assumption. In this article, we demonstrate a way to deal
with inconsistent boundary data, by generalizing the "self-consistency
procedure" of Wheatland and Régnier (Astrophys. J. Lett.700,
L88, 2009). In that procedure, the inconsistency is resolved by an
iterative process of constructing two solutions based on the values
of the force-free parameter α on the two polarities of the field in
the boundary (the P and N polarities), and taking uncertainty-weighted
averages of the boundary α values in the P and N solutions. When the α
values in the P and N regions are very different, the self-consistent
solution may lose high α values from the boundary conditions. We
show how, by altering the weighting of the uncertainties in the
P or N boundary conditions, we can preserve high α values in the
self-consistent solution. The weighted self-consistent extrapolation
method is demonstrated on an analytic bipole field and applied to vector
magnetogram data taken by the Helioseismic and Magnetic Imager (HMI)
instrument on board the Solar Dynamics Observatory (SDO) spacecraft
for NOAA active region AR 12017 on 2014 March 29.
Title: Relative Magnetic Helicity Based on a Periodic Potential Field
Authors: Yang, Kai E.; Wheatland, Michael S.; Gilchrist, Stuart A.
Bibcode: 2020ApJ...894..151Y
Altcode: 2020arXiv200408590Y
Magnetic helicity is conserved under ideal magnetohydrodynamics and
quasi-conserved even under a resistive process. The standard definition
for magnetic helicity cannot be applied directly to an open magnetic
field in a volume, because it is gauge-dependent. Instead, the relative
magnetic helicity is widely used. We find that the energy of a potential
magnetic field in a rectangular domain with periodic lateral boundary
conditions is less than that of the field with a fixed normal component
on all six boundaries. To make use of this lower energy potential
field in the analysis of relative magnetic helicity, we introduce a
new definition for magnetic helicity for the magnetic field, which
involves the periodic potential field. We apply this definition to
a sequence of analytic solutions and a numerical simulation. The
results show that our new gauge-invariant helicity is very close
to the current-carrying part of the relative magnetic helicity of
the original magnetic field. We find also that the ratio between the
current-carrying helicity and the relative magnetic helicity for the
original and our defined relative helicity show different behavior. It
seems that the new helicity is more sensitive to the component of the
field due to the electric current in the volume, which is the source
for instabilities and solar eruptive phenomena.
Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
Lidia; Wheatland, Michael S.
Bibcode: 2020SoPh..295....9L
Altcode:
No abstract at ADS
Title: Comparisons Between the Field Lines Using an Accelerating
and a Constant Solar Wind model
Authors: Tasnim, S.; Cairns, Iver H.; Wheatland, M. S.; Li, B.; Zank,
Gary P.
Bibcode: 2019JPhCS1332a2015T
Altcode:
Magnetic field line mapping between the Sun and the Earth is important
to trace the nonthermal particles. We generalize a recently developed
mapping approach (B stepping) where this approach allows us to
map the magnetic field lines by stepping along the local magnetic
field direction. We employ an advanced solar wind model which
includes acceleration, angular momentum conservation, and intrinsic
non-radial velocities and magnetic fields at the inner boundary /
source surface. We map the field lines using Wind spacecraft data
for two solar rotation periods: one near a solar minimum between
CR2118 and CR2119 and other CR1992 near a solar maximum. Maps using
the accelerating solar wind model are compared with the maps using a
constant solar wind model. On a broad scale, maps using two solar wind
models for the same solar rotation periods are very similar. However,
in a small scale, there are significant differences, e.g. differences
are evident in connectivities, paths, and winding angles. In addition,
field lines using the accelerating solar wind model are more azimuthally
oriented for during the solar maximum. These differences demonstrate
the significance of inclusion of the accelerating radial speed profile,
intrinsic azimuthal velocity and magnetic field components.
Title: Mapping Magnetic Field Lines for an Accelerating Solar Wind
Authors: Tasnim, S.; Cairns, Iver H.; Li, B.; Wheatland, M. S.
Bibcode: 2019SoPh..294..155T
Altcode: 2019arXiv190708683T
Mapping of magnetic field lines is important for studies of the
solar wind and the sources and propagation of energetic particles
between the Sun and observers. A recently developed mapping approach
is generalized to use a more advanced solar wind model that includes
the effects of solar wind acceleration, non-radial intrinsic magnetic
fields and flows at the source surface/inner boundary, and conservation
of angular momentum. The field lines are mapped by stepping along B
and via a Runge-Kutta algorithm, leading to essentially identical
maps. The new model's maps for Carrington rotation CR 1895 near
solar minimum (19 April to 15 May 1995) and a solar rotation between
CR 2145 and CR 2146 near solar maximum (14 January to 9 February
2014) are compared with the published maps for a constant solar wind
model. The two maps are very similar on a large scale near both solar
minimum and solar maximum, meaning that the field-line orientations,
winding angles, and connectivity generally agree very well. However,
close inspection shows that the field lines have notable small-scale
structural differences. An interpretation is that inclusion of the
acceleration and intrinsic azimuthal velocity has significant effects
on the local structure of the magnetic field lines. Interestingly,
the field lines are more azimuthal for the accelerating solar wind
model for both intervals. In addition, predictions for the pitch angle
distributions (PADs) for suprathermal electrons agree at the 90 - 95%
level with observations for both solar wind models for both intervals.
Title: Energy Balance in Avalanche Models for Solar Flares
Authors: Farhang, Nastaran; Wheatland, Michael S.; Safari, Hossein
Bibcode: 2019ApJ...883L..20F
Altcode: 2019arXiv190900195F
The distributions of solar flare energies and waiting times have not
been described simultaneously by a single physical model, yet. In this
research, we investigate whether recent avalanche models can describe
the distributions for both the released energies and waiting times
of flares in an active region. Flaring events are simulated using the
modified Lu and Hamilton model and also the optimized model. Applying
a probability balance equation approach, we study the statistics of
the simulated flaring events and investigate the origin of the observed
power law in the flare frequency-size distribution. The results indicate
that the power law originates in the distribution of transition rates
(the distribution of the probabilities of transitions between different
energies) rather than the distribution of the energy of the active
region. It is also observed that the waiting-time distribution of
simulated flaring events follows a q-exponential function, which
approximates a simple Poisson distribution.
Title: Flare Reconnection-driven Magnetic Field and Lorentz Force
Variations at the Sun’s Surface
Authors: Barczynski, Krzysztof; Aulanier, Guillaume; Masson, Sophie;
Wheatland, Michael S.
Bibcode: 2019ApJ...877...67B
Altcode: 2019arXiv190405447B
During eruptive flares, vector magnetograms show an increasing
horizontal magnetic field and downward Lorentz force in the Sun’s
photosphere around the polarity-inversion line (PIL). This behavior
has often been associated with the implosion conjecture and has
been interpreted as the result of either momentum conservation while
the eruption moves upward or of the contraction of flare loops. We
characterize the physical origin of these observed behaviors by
analyzing a generic 3D magnetohydrodynamics simulation of an eruptive
flare. Even though the simulation was not designed to recover the
magnetic field and Lorentz force properties, it is fully consistent
with them, and it provides key additional information for understanding
them. The area where the magnetic field increases gradually develops
between current ribbons, which spread away from each other and are
connected to the coronal region. This area is merely the footprint of
the coronal post-flare loops, whose contraction increases their shear
field component and the magnetic energy density, in line with the ideal
induction equation. For simulated data, we computed the Lorentz force
density map by applying the method used in observations. We obtained an
increase in the downward component of the Lorentz force density around
the PIL, consistent with observations. However, this significantly
differs from the Lorentz force density maps that are obtained directly
from the 3D magnetic field and current. These results altogether
question previous interpretations that were based on the implosion
conjecture and momentum conservation with the coronal mass ejection,
and rather imply that the observed increases in photospheric horizontal
magnetic fields result from the reconnection-driven contraction of
sheared flare loops.
Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
Lidia; Wheatland, Michael S.
Bibcode: 2019SoPh..294....3L
Altcode:
We are pleased to acknowledge, with sincere thanks, the following
colleagues who supported the community by reviewing articles for Solar
Physics during 2018.
Title: Very narrow coronal mass ejections producing solar energetic
particles
Authors: Bronarska, K.; Wheatland, M. S.; Gopalswamy, N.; Michalek, G.
Bibcode: 2018A&A...619A..34B
Altcode:
Aims: Our main aim is to study the relationship between
low-energy solar particles (energies below 1 MeV) and very narrow
coronal mass ejections ("jets" with angular width ≤ 20°).
Methods: For this purpose, we considered 125 very narrow coronal mass
ejections (CMEs) from 1999 to 2003 that are potentially associated
with low-energy solar particles (LESPs). These events were chosen on
the basis of their source location. We studied only very narrow CMEs at
the western limb, which are expected to have good magnetic connectivity
with Earth.
Results: We found 24 very narrow CMEs associated
with energetic particles such as ions (protons and 3He),
electrons, or both. We show that arrival times at Earth of energetic
particles are consistent with onset times of the respective CMEs, and
that in the same time intervals, there are no other potential sources
of energetic particles. We also demonstrate statistical differences
for the angular width distributions using the Kolmogorov-Smirnov
test for angular widths for these 24 events. We consider a coherent
sample of jets (mostly originating from boundaries of coronal holes)
to identify properties of events that produce solar energetic particles
(velocities, widths, and position angles). Our study presents a new
approach and result: very narrow CMEs can generate low-energy particles
in the vicinity of Earth without other activity on the Sun. The results
could be very useful for space weather forecasting.
Title: Flare reconnection driven magnetic field and Lorentz force
variations at the Sun's surface
Authors: Barczynski, Krzysztof; Aulanier, Guillaume; Masson, Sophie;
Wheatland, Michael S.
Bibcode: 2018csc..confE..27B
Altcode:
We show that the simulation is fully consistent with the observed
increase of the photospheric horizontal magnetic field and electric
currents around flaring PILs. The simulation also finds that the surface
integral coming from the volume integral of the Maxwell stress tensor,
as usually used in observational data analysis as the proxy of the
Lorentz force, shows an increased downard component in the photosphere,
as observed. But we also find that this proxy is significantly
different from the true Lorentz force, which does not reveal this
downward component. This result questions every previous interpretation
based on the implosion conjecture and momentum conservation. However
based on the analysis of the induction equation in the simulation,
we unveil that the increase of the horizontal magnetic filed around
active region PILs during eruptions is solely and exclusively result
of the flare reconnection-driven contraction of flare loops.
Title: Nonlinear Force-free Modeling of Flare-related Magnetic Field
Changes at the Photosphere and Chromosphere
Authors: Kleint, Lucia; Wheatland, Michael S.; Mastrano, Alpha;
McCauley, Patrick I.
Bibcode: 2018ApJ...865..146K
Altcode: 2018arXiv180807079K
Rapid and stepwise changes of the magnetic field are often observed
during flares but cannot be explained by models yet. Using a 45 minute
sequence of Solar Dynamics Observatory/Helioseismic and Magnetic
Imager 135 s fast-cadence vector magnetograms of the X1 flare on 2014
March 29 we construct, at each timestep, nonlinear force-free models
for the coronal magnetic field. Observed flare-related changes in the
line-of-sight magnetic field B LOS at the photosphere and
chromosphere are compared with changes in the magnetic fields in the
models. We find a moderate agreement at the photospheric layer (the
basis for the models), but no agreement at chromospheric layers. The
observed changes at the photosphere and chromosphere are surprisingly
different, and are unlikely to be reproduced by a force-free model. The
observed changes are likely to require a change in the magnitude of
the field, not just in its direction.
Title: A Check on the Validity of Magnetic Field Reconstructions
Authors: Mastrano, A.; Wheatland, M. S.; Gilchrist, S. A.
Bibcode: 2018SoPh..293..130M
Altcode:
We investigate a method to test whether a numerically computed model
coronal magnetic field B departs from the divergence-free condition
(also known as the solenoidality condition). The test requires a
potential field B0 to be calculated, subject to Neumann
boundary conditions, given by the normal components of the model
field B at the boundaries. The free energy of the model field may
be calculated using 1/2 μ0 ∫(B−B0)
2d V , where the integral is over the computational volume of
the model field. A second estimate of the free energy is provided
by calculating 1/2 μ0 ∫B2d V −1/2
μ0 ∫B02d V . If B is divergence
free, the two estimates of the free energy should be the same. A
difference between the two estimates indicates a departure from ∇
⋅B =0 in the volume. The test is an implementation of a procedure
proposed by Moraitis et al. (Solar Phys.289, 4453, 2014) and is a
simpler version of the Helmholtz decomposition procedure presented
by Valori et al. (Astron. Astrophys.553, A38, 2013). We demonstrate
the test in application to previously published nonlinear force-free
model fields, and also investigate the influence on the results of
the test of a departure from flux balance over the boundaries of the
model field. Our results underline the fact that, to make meaningful
statements about magnetic free energy in the corona, it is necessary to
have model magnetic fields that satisfy the divergence-free condition
to a good approximation.
Title: Photospheric Response to a Flare
Authors: Wheatland, Michael S.; Melrose, Donald B.; Mastrano, Alpha
Bibcode: 2018ApJ...864..159W
Altcode: 2018arXiv180803097W
Flares produce sudden and permanent changes in the horizontal
photospheric magnetic field. In particular, flares generally produce
increased magnetic shear in the photospheric field along the neutral
line. Recent observations also show that flares can produce sudden
photospheric motion. We present a model for the observed changes as
the response of the photosphere to a large-amplitude shear Alfvén
wave propagating down from the corona on either side of the neutral
line. The Alfvénic front is assumed to impact the photosphere close to
the neutral line first and then successively further away with time,
such that the line of impact coincides with the flare ribbon. The
wave introduces magnetic shear and velocity shear. The magnetic shear
introduced at the photosphere has the same sign on either side of
the neutral line, while the velocity shear has the opposite sign. We
discuss the possibility that this process is responsible for particle
acceleration in flares.
Title: Mapping Magnetic Field Lines for an Accelerating Solar Wind
Authors: Tasnim, Samira; Wheatland, . M. S.; Cairns, Iver; Li, Bo
Bibcode: 2018cosp...42E3339T
Altcode:
A new accelerating solar wind [Tasnim et al., 2018] is developed that
includes conservation of angular momentum, deviations from corotation,
and non-radial intrinsic velocity and magnetic field components from
an inner boundary to beyond 1 AU. We fit the model to near-Earth
observations of the Wind spacecraft for the solar rotation period
between 19 April to 15 May 1995 (CR 1895). Later, we employ this
accelerating solar wind to predict the magnetic field vectors and map
the magnetic field lines. Note that magnetic field line mapping is
important to trace the paths of solar energetic particles and electron
beams in type III radio burst since superthermal beams move along the
field lines from the Sun towards the Earth and even beyond. We map
the magnetic field lines from the source surface towards 1 AU using
the field line mapping algorithm developed by Li et al. [JGR,2016]. We
compare these magnetic field lines with the field lines predicted by
Li et al. [JGR,2016] using Schulte in den Baumen et al. [JGR,2012]'s
model. The maps for accelerating and constant speed models are very
similar. However, close comparisons show that the magnetic field lines
for the radial speed model move further out than theaccelerating wind
model. The obvious interpretation is that the accelerating solar wind
is slower at small heliocentric distance (r) and so travels less far
outward than the constant speed solar wind.
Title: Principle of Minimum Energy in Magnetic Reconnection in a
Self-organized Critical Model for Solar Flares
Authors: Farhang, Nastaran; Safari, Hossein; Wheatland, Michael S.
Bibcode: 2018ApJ...859...41F
Altcode: 2018arXiv180410356F
Solar flares are an abrupt release of magnetic energy in the Sun’s
atmosphere due to reconnection of the coronal magnetic field. This
occurs in response to turbulent flows at the photosphere that twist
the coronal field. Similar to earthquakes, solar flares represent the
behavior of a complex system, and expectedly their energy distribution
follows a power law. We present a statistical model based on the
principle of minimum energy in a coronal loop undergoing magnetic
reconnection, which is described as an avalanche process. We show that
the distribution of peaks for the flaring events in this self-organized
critical system is scale-free. The obtained power-law index of 1.84 ±
0.02 for the peaks is in good agreement with satellite observations
of soft X-ray flares. The principle of minimum energy can be applied
for general avalanche models to describe many other phenomena.
Title: Electric Currents in Geospace and Beyond.
Authors: Keiling, Andreas; Marghitu, Octav; Wheatland, Michael
Bibcode: 2018GMS...235.....K
Altcode:
No abstract at ADS
Title: A Generalized Equatorial Model for the Accelerating Solar Wind
Authors: Tasnim, S.; Cairns, Iver H.; Wheatland, M. S.
Bibcode: 2018JGRA..123.1061T
Altcode:
A new theoretical model for the solar wind is developed that includes
the wind's acceleration, conservation of angular momentum, deviations
from corotation, and nonradial velocity and magnetic field components
from an inner boundary (corresponding to the onset of the solar
wind) to beyond 1 AU. The model uses a solution of the time-steady
isothermal equation of motion to describe the acceleration and
analytically predicts the Alfvénic critical radius. We fit the
model to near-Earth observations of the Wind spacecraft during the
solar rotation period of 1-27 August 2010. The resulting data-driven
model demonstrates the existence of noncorotating, nonradial flows
and fields from the inner boundary (r = rs) outward and
predicts the magnetic field B = (Br,Bϕ),
velocity v = (vr,vϕ), and density n(r,ϕ,t),
which vary with heliocentric distance r, heliolatitude ϕ, and
time t in a Sun-centered standard inertial plane. The description
applies formally only in the equatorial plane. In a frame corotating
with the Sun, the transformed velocity v' and a field B' are not
parallel, resulting in an electric field with a component Ez'
along the z axis. The resulting E'×B'=E'×B drift lies in the
equatorial plane, while the ∇B and curvature drifts are out of
the plane. Together these may lead to enhanced scattering/heating of
sufficiently energetic particles. The model predicts that deviations
δvϕ from corotation at the inner boundary are common,
with δvϕ(rs,ϕs,ts)
comparable to the transverse velocities due to
granulation and supergranulation motions. Abrupt changes in
δvϕ(rs,ϕs,ts) are
interpreted in terms of converging and diverging flows at the cell
boundaries and centers, respectively. Large-scale variations in the
predicted angular momentum demonstrate that the solar wind can drive
vorticity and turbulence from near the Sun to 1 AU and beyond.
Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
Lidia; Wheatland, Michael S.
Bibcode: 2018SoPh..293...14L
Altcode:
No abstract at ADS
Title: A Study of External Magnetic Reconnection that Triggers a
Solar Eruption
Authors: Zhou, G. P.; Zhang, J.; Wang, J. X.; Wheatland, M. S.
Bibcode: 2017ApJ...851L...1Z
Altcode:
External magnetic reconnection (EMR) is suggested to play an
essential role in triggering a solar eruption, but is rarely directly
observed. Here, we report on a filament eruption on 2014 October 3
that apparently involves the process of an early EMR. A total of 1.7 ×
1020 Mx flux was first canceled along the filament-related
polarity inversion line over 12 hr, and then the filament axis started
to brighten in extreme ultraviolet (EUV). An impulsive EUV brightening
began 30 minutes later, and we attribute this to EMR, as it is located
at the center of a bidirectional outflow with a velocity of 60-75 km
s-1 along large-scale magnetic loops from active regions
NOAA 12178 and 12179, respectively, and over the filament mentioned
above. Following the EMR, the filament was activated; then, partial
eruption occurred 6 minutes later in the west, in which the decay
index above the magnetic flux rope (MFR) reached the critical value of
1.5. The observations are interpreted in terms of underlying magnetic
flux cancelation leading to the buildup and eventual formation of the
MFR with a filament embedded in it, and the MFR is elevated later. The
activated MFR rises and pushes the overlying sheared field and forms a
current sheet causing the EMR. The EMR in turn weakens the constraining
effect of the overlying field, leading to the arising of the MFR,
and subsequently erupting due to torus instability.
Title: Editorial: Last Print Issue of Solar Physics
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
Lidia; Wheatland, Michael S.
Bibcode: 2017SoPh..292..196L
Altcode:
No abstract at ADS
Title: Predicting the Where and the How Big of Solar Flares
Authors: Leka, K. D.; Barnes, G.; Gilchrist, S.; Wheatland, M.
Bibcode: 2017shin.confE..87L
Altcode:
The approach to predicting solar flares generally characterizes global
properties of a solar active region, for example the total magnetic flux
or the total length of a sheared magnetic neutral line, and compares new
data (from which to make a prediction) to similar observations of active
regions and their associated propensity for flare production. We take
here a different tack, examining solar active regions in the context
of their energy storage capacity. Specifically, we characterize not
the region as a whole, but summarize the energy-release prospects
of different sub-regions within, using a sub-area analysis of the
photospheric boundary, the CFIT non-linear force-free extrapolation
code, and the Minimum Current Corona model. We present here early
results from this approach whose objective is to understand the
different pathways available for regions to release stored energy, thus
eventually providing better estimates of the 'where' (what sub-areas
are storing how much energy) and the 'how big' (how much energy is
stored, and how much is available for release) of solar flares.
Title: Sunspot and Starspot Lifetimes in a Turbulent Erosion Model
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2017ApJ...834..108L
Altcode: 2016arXiv161103920L
Quantitative models of sunspot and starspot decay predict the timescale
of magnetic diffusion and may yield important constraints in stellar
dynamo models. Motivated by recent measurements of starspot lifetimes,
we investigate the disintegration of a magnetic flux tube by nonlinear
diffusion. Previous theoretical studies are extended by considering
two physically motivated functional forms for the nonlinear diffusion
coefficient D: an inverse power-law dependence D ∝ B-ν
and a step-function dependence of D on the magnetic field magnitude
B. Analytical self-similar solutions are presented for the power-law
case, including solutions exhibiting “superfast” diffusion. For the
step-function case, the heat-balance integral method yields approximate
solutions, valid for moderately suppressed diffusion in the spot. The
accuracy of the resulting solutions is confirmed numerically, using a
method which provides an accurate description of long-time evolution by
imposing boundary conditions at infinite distance from the spot. The
new models may allow insight into the differences and similarities
between sunspots and starspots.
Title: Prediction of Solar Flares Using Unique Signatures of Magnetic
Field Images
Authors: Raboonik, Abbas; Safari, Hossein; Alipour, Nasibe; Wheatland,
Michael S.
Bibcode: 2017ApJ...834...11R
Altcode: 2016arXiv161003222R
Prediction of solar flares is an important task in solar physics. The
occurrence of solar flares is highly dependent on the structure and
topology of solar magnetic fields. A new method for predicting large (M-
and X-class) flares is presented, which uses machine learning methods
applied to the Zernike moments (ZM) of magnetograms observed by the
Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory
for a period of six years from 2010 June 2 to 2016 August 1. Magnetic
field images consisting of the radial component of the magnetic field
are converted to finite sets of ZMs and fed to the support vector
machine classifier. ZMs have the capability to elicit unique features
from any 2D image, which may allow more accurate classification. The
results indicate whether an arbitrary active region has the potential
to produce at least one large flare. We show that the majority of large
flares can be predicted within 48 hr before their occurrence, with only
10 false negatives out of 385 flaring active region magnetograms and 21
false positives out of 179 non-flaring active region magnetograms. Our
method may provide a useful tool for the prediction of solar flares,
which can be employed alongside other forecasting methods.
Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
Lidia; Wheatland, Michael S.
Bibcode: 2017SoPh..292...19L
Altcode:
We are pleased to acknowledge, with sincere thanks, the following
referees who supported the community by refereeing articles for Solar
Physics during 2016.
Title: Is Cyclotron Maser Emission in Solar Flares Driven by a
Horseshoe Distribution?
Authors: Melrose, D. B.; Wheatland, M. S.
Bibcode: 2016SoPh..291.3637M
Altcode: 2016SoPh..tmp..171M; 2016arXiv161004299M
Since the early 1980s, decimetric spike bursts have been attributed
to electron cyclotron maser emission (ECME) by the electrons that
produce hard X-ray bursts as they precipitate into the chromosphere
in the impulsive phase of a solar flare. Spike bursts are regarded
as analogous to the auroral kilometric radiation (AKR), which is
associated with the precipitation of auroral electrons in a geomagnetic
substorm. Originally, a loss-cone-driven version of ECME, developed
for AKR, was applied to spike bursts, but it is now widely accepted
that the measured distribution function is horseshoe-like (an isotropic
distribution with a one-sided loss cone), and that a horseshoe-driven
version of ECME applies to AKR. We explore the implications of the
assumption that horseshoe-driven ECME also applies to spike bursts. We
develop a 1D model for the acceleration of the electrons by a parallel
electric field, and show that under plausible assumptions it leads
to a horseshoe distribution of electrons in a solar flare. A second
requirement for horseshoe-driven ECME is an extremely low plasma
density, referred to as a density cavity. We argue that a coronal
density cavity should develop in association with a hard X-ray burst,
and that such a density cavity can overcome a long-standing problem with
the escape of ECME through the second-harmonic absorption layer. Both
the horseshoe distribution and the associated coronal density cavity
are highly localized, and could not be resolved in the statistically
large number of local precipitation regions needed to explain a hard
X-ray burst. The model highlights the "number problem" in the supply
of the electrons needed to explain a hard X-ray burst.
Title: Editorial: 50 Years of Solar Physics
Authors: Charbonneau, Paul; Leibacher, John; Mandrini, Cristina;
van Driel-Gesztelyi, Lidia; Wheatland, Michael S.
Bibcode: 2016SoPh..291.3461C
Altcode: 2016SoPh..tmp..189C
No abstract at ADS
Title: A Comparison of Flare Forecasting Methods. I. Results from
the “All-Clear” Workshop
Authors: Barnes, G.; Leka, K. D.; Schrijver, C. J.; Colak, T.;
Qahwaji, R.; Ashamari, O. W.; Yuan, Y.; Zhang, J.; McAteer, R. T. J.;
Bloomfield, D. S.; Higgins, P. A.; Gallagher, P. T.; Falconer, D. A.;
Georgoulis, M. K.; Wheatland, M. S.; Balch, C.; Dunn, T.; Wagner, E. L.
Bibcode: 2016ApJ...829...89B
Altcode: 2016arXiv160806319B
Solar flares produce radiation that can have an almost immediate effect
on the near-Earth environment, making it crucial to forecast flares
in order to mitigate their negative effects. The number of published
approaches to flare forecasting using photospheric magnetic field
observations has proliferated, with varying claims about how well
each works. Because of the different analysis techniques and data
sets used, it is essentially impossible to compare the results from
the literature. This problem is exacerbated by the low event rates of
large solar flares. The challenges of forecasting rare events have long
been recognized in the meteorology community, but have yet to be fully
acknowledged by the space weather community. During the interagency
workshop on “all clear” forecasts held in Boulder, CO in 2009,
the performance of a number of existing algorithms was compared
on common data sets, specifically line-of-sight magnetic field and
continuum intensity images from the Michelson Doppler Imager, with
consistent definitions of what constitutes an event. We demonstrate
the importance of making such systematic comparisons, and of using
standard verification statistics to determine what constitutes a good
prediction scheme. When a comparison was made in this fashion, no one
method clearly outperformed all others, which may in part be due to the
strong correlations among the parameters used by different methods to
characterize an active region. For M-class flares and above, the set
of methods tends toward a weakly positive skill score (as measured
with several distinct metrics), with no participating method proving
substantially better than climatological forecasts.
Title: Nonlinear force-free modeling of magnetic fields in
flare-productive active regions
Authors: Wheatland, M. S.; Gilchrist, S. A.
Bibcode: 2016IAUS..320..167W
Altcode:
We review nonlinear force-free field (NLFFF) modeling of magnetic
fields in active regions. The NLFFF model (in which the electric
current density is parallel to the magnetic field) is often adopted
to describe the coronal magnetic field, and numerical solutions to
the model are constructed based on photospheric vector magnetogram
boundary data. Comparative tests of NLFFF codes on sets of boundary
data have revealed significant problems, in particular associated
with the inconsistency of the model and the data. Nevertheless NLFFF
modeling is often applied, in particular to flare-productive active
regions. We examine the results, and discuss their reliability.
Title: The Influence of Spatial resolution on Nonlinear Force-free
Modeling
Authors: DeRosa, M. L.; Wheatland, M. S.; Leka, K. D.; Barnes, G.;
Amari, T.; Canou, A.; Gilchrist, S. A.; Thalmann, J. K.; Valori,
G.; Wiegelmann, T.; Schrijver, C. J.; Malanushenko, A.; Sun, X.;
Régnier, S.
Bibcode: 2015ApJ...811..107D
Altcode: 2015arXiv150805455D
The nonlinear force-free field (NLFFF) model is often used to
describe the solar coronal magnetic field, however a series of
earlier studies revealed difficulties in the numerical solution of the
model in application to photospheric boundary data. We investigate
the sensitivity of the modeling to the spatial resolution of the
boundary data, by applying multiple codes that numerically solve the
NLFFF model to a sequence of vector magnetogram data at different
resolutions, prepared from a single Hinode/Solar Optical Telescope
Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December
13. We analyze the resulting energies and relative magnetic helicities,
employ a Helmholtz decomposition to characterize divergence errors, and
quantify changes made by the codes to the vector magnetogram boundary
data in order to be compatible with the force-free model. This study
shows that NLFFF modeling results depend quantitatively on the spatial
resolution of the input boundary data, and that using more highly
resolved boundary data yields more self-consistent results. The
free energies of the resulting solutions generally trend higher
with increasing resolution, while relative magnetic helicity values
vary significantly between resolutions for all methods. All methods
require changing the horizontal components, and for some methods also
the vertical components, of the vector magnetogram boundary field in
excess of nominal uncertainties in the data. The solutions produced
by the various methods are significantly different at each resolution
level. We continue to recommend verifying agreement between the modeled
field lines and corresponding coronal loop images before any NLFFF
model is used in a scientific setting.
Title: Nonlinear Force-Free Modelling of Magnetic Fields in Flare
Productive Active Regions
Authors: Wheatland, M. S.
Bibcode: 2015IAUGA..2286135W
Altcode:
This talk reviews nonlinear force-free field (NLFFF) modelling of
magnetic fields in flare-productive active regions. The NLFFF model
(in which the electric current density is parallel to the magnetic
field) is often adopted to describe the coronal magnetic field, and
numerical solutions to the model are constructed based on photospheric
vector magnetogram boundary data. Comparative tests of NLFFF codes
on sets of boundary data have revealed significant problems, in
particular associated with the inconsistency of the model and the
data. Nevertheless NLFFF modelling is often applied, in particular
for flaring active regions, and is used to infer details of the flare
process. We examine the results, and discuss their reliability.
Title: Estimating Electric Current Densities in Solar Active Regions
Authors: Wheatland, M. S.
Bibcode: 2015SoPh..290.1147W
Altcode: 2015arXiv150302741W; 2015SoPh..tmp...39W
Electric currents in solar active regions are thought to provide the
energy released via magnetic reconnection in solar flares. Vertical
electric current densities Jz at the photosphere may
be estimated from vector magnetogram data, subject to substantial
uncertainties. The values provide boundary conditions for nonlinear
force-free modelling of active region magnetic fields. A method is
presented for estimating values of Jz taking into account
uncertainties in vector magnetogram field values, and minimising
Jz2 across the active region. The method is
demonstrated using the boundary values of the field for a force-free
twisted bipole, with the addition of noise at randomly chosen locations.
Title: Modeling Sunspot and Starspot Decay by Turbulent Erosion
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2015ApJ...800..130L
Altcode: 2015arXiv150101699L
Disintegration of sunspots (and starspots) by fluxtube erosion,
originally proposed by Simon and Leighton, is considered. A moving
boundary problem is formulated for a nonlinear diffusion equation that
describes the sunspot magnetic field profile. Explicit expressions
for the sunspot decay rate and lifetime by turbulent erosion are
derived analytically and verified numerically. A parabolic decay law
for the sunspot area is obtained. For moderate sunspot magnetic field
strengths, the predicted decay rate agrees with the results obtained
by Petrovay and Moreno-Insertis. The new analytical and numerical
solutions significantly improve the quantitative description of sunspot
and starspot decay by turbulent erosion.
Title: Active Region Magnetic Field Modeling Guided by Coronal Loops
and Surface Fields
Authors: DeRosa, Marc L.; Malanushenko, Anna; Schrijver, Carolus J.;
Wheatland, Michael S
Bibcode: 2014AAS...22432319D
Altcode:
Dynamic events such as solar flares, filament eruptions, and mass
ejections are powered by the evolving coronal magnetic field. However,
the ways in which energy is stored in, and released from, the coronal
magnetic field are poorly understood, in large part because the field
configuration cannot be determined directly from observations and has
eluded the successful application of routine modeling based on surface
magnetograms. Recently, we have demonstrated that the Quasi-Grad-Rubin
(QGR) method for modeling the current-carrying field associated with
active regions shows promise. In Malanushenko et al. (2014, ApJ 783:102)
we have used the QGR method to construct the magnetic field at several
times during the evolution of AR11158 during February 2011. The QGR
method does not require vector magnetograms, and instead uses the
trajectories of observed coronal loops to constrain the locations
of electric currents within the modeling domain. In this study,
we continue to assess the utility of QGR by applying this method to
additional active regions from the current activity cycle, making use
of SDO/HMI line-of-sight magnetograms and imagery from the extreme
ultraviolet channels of SDO/AIA.
Title: Nonlinear Force-Free Modeling of the Corona in Spherical
Coordinates
Authors: Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2014SoPh..289.1153G
Altcode: 2013arXiv1308.5742G
We present a code for solving the nonlinear force-free equations
in spherical polar geometry, with the motivation of modeling the
magnetic field in the corona. The code is an implementation of the
Grad-Rubin method. Our method is applicable to a spherical domain of
arbitrary angular size. The implementation is based on a global spectral
representation for the magnetic field that makes no explicit assumptions
about the form of the magnetic field at the transverse boundaries of
the domain. We apply the code to a bipolar test case with analytic
boundary conditions, and demonstrate the convergence of the Grad-Rubin
method and the self-consistency of the resulting numerical solution.
Title: Bulk Energization of Electrons in Solar Flares by Alfvén Waves
Authors: Melrose, D. B.; Wheatland, M. S.
Bibcode: 2014SoPh..289..881M
Altcode: 2013arXiv1307.7772M
Bulk energization of electrons to 10 - 20 keV in solar flares is
attributed to dissipation of Alfvén waves that transport energy and
potential downward to an acceleration region near the chromosphere. The
acceleration involves the parallel electric field that develops in the
limit of inertial Alfvén waves (IAWs). A two-potential model for IAWs
is used to relate the parallel potential to the cross-field potential
transported by the waves. We identify a maximum parallel potential in
terms of a maximum current density that corresponds to the threshold
for the onset of anomalous resistivity. This maximum is of order 10
kV when the threshold is that for the Buneman instability. We argue
that this restricts the cross-field potential in an Alfvén wave to
about 10 kV. Effective dissipation requires a large number of up- and
down-current paths associated with multiple Alfvén waves. The electron
acceleration occurs in localized, transient, anomalously conducting
regions (LTACRs) and is associated with the parallel electric field
determined by Ohm's law with an anomalous resistivity. We introduce an
idealized model in which the LTACRs are (upward-)current sheets, a few
skin depths in thickness, separated by much larger regions of weaker
return current. We show that this model can account semi-quantitatively
for bulk energization.
Title: Using Coronal Loops to Reconstruct the Magnetic Field of an
Active Region before and after a Major Flare
Authors: Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland,
M. S.
Bibcode: 2014ApJ...783..102M
Altcode: 2013arXiv1312.5389M
The shapes of solar coronal loops are sensitive to the presence
of electrical currents that are the carriers of the non-potential
energy available for impulsive activity. We use this information in
a new method for modeling the coronal magnetic field of active region
(AR) 11158 as a nonlinear force-free field (NLFFF). The observations
used are coronal images around the time of major flare activity on
2011 February 15, together with the surface line-of-sight magnetic
field measurements. The data are from the Helioseismic and Magnetic
Imager and Atmospheric Imaging Assembly on board the Solar Dynamics
Observatory. The model fields are constrained to approximate the coronal
loop configurations as closely as possible, while also being subject
to the force-free constraints. The method does not use transverse
photospheric magnetic field components as input and is thereby
distinct from methods for modeling NLFFFs based on photospheric vector
magnetograms. We validate the method using observations of AR 11158
at a time well before major flaring and subsequently review the field
evolution just prior to and following an X2.2 flare and associated
eruption. The models indicate that the energy released during the
instability is about 1 × 1032 erg, consistent with what
is needed to power such a large eruptive flare. Immediately prior to
the eruption, the model field contains a compact sigmoid bundle of
twisted flux that is not present in the post-eruption models, which
is consistent with the observations. The core of that model structure
is twisted by ≈0.9 full turns about its axis.
Title: Using coronal loops to model the coronal magnetic field before
and after major eruptive events
Authors: Malanushenko, Anna; Schrijver, Carolus; Wheatland, M. S.;
DeRosa, Marc
Bibcode: 2014cosp...40E1960M
Altcode:
Solar flares are believed to be a manifestation of major release of
magnetic energy stored in active region field. Modeling the coronal
magnetic field may enable us to evaluate the energy available for
release, as well as possible sites of the reconnection and other
relevant properties of the field. We use a new method to aid this
problem by including the observed structure of the field (manifested
in coronal loops) as additional constraints. We verify that the method
(previously shown to work on synthetic data in Malanushenko et. al.,
ApJ, 756, 153, 2012) is generally acceptable for the solar data, as
it gives self-consistent, slowly changing results for slowly evolving
structures. We further develop the potential of this method to access
changes in the coronal magnetic field triggered by major eruptive
events, and compare the results with observations.
Title: Transfer of Energy, Potential, and Current by Alfvén Waves
in Solar Flares
Authors: Melrose, D. B.; Wheatland, M. S.
Bibcode: 2013SoPh..288..223M
Altcode: 2013arXiv1304.1938M
Alfvén waves play three related roles in the impulsive phase of
a solar flare: they transport energy from a generator region to an
acceleration region; they map the cross-field potential (associated
with the driven energy release) from the generator region onto the
acceleration region; and within the acceleration region they damp
by setting up a parallel electric field that accelerates electrons
and transfers the wave energy to them. The Alfvén waves may also be
regarded as setting up new closed-current loops, with field-aligned
currents that close across field lines at boundaries. A model is
developed for large-amplitude Alfvén waves that shows how Alfvén
waves play these roles in solar flares. A picket-fence structure for
the current flow is incorporated into the model to account for the
"number problem" and the energy of the accelerated electrons.
Title: The state of nonlinear force-free magnetic field extrapolation
Authors: Wheatland, M. S.; Gilchrist, S. A.
Bibcode: 2013JPhCS.440a2037W
Altcode:
Magnetic field extrapolation is the construction of a model solution for
the coronal magnetic field in active regions from magnetic boundary data
originating close to the Sun's surface. The nonlinear force-free model
(in which the electric current density is parallel to the magnetic
field) is often adopted to describe the coronal field. The solution
of the nonlinear force-free equations is a challenging computational
task, and the application of codes to available boundary data has
revealed a number of significant problems with nonlinear force-free
extrapolation. This paper summarises the present status of coronal
field extrapolation, and describes some recent developments.
Title: Origin and Use of the Laplace Distribution in Daily Sunspot
Numbers
Authors: Noble, P. L.; Wheatland, M. S.
Bibcode: 2013SoPh..282..565N
Altcode: 2012arXiv1210.3119N
Recently Pop (Solar Phys.276, 351, 2012) identified a Laplace (or double
exponential) distribution in the number of days with a given absolute
value in the change over a day, in sunspot number, for days on which
the sunspot number does change. We show this phenomenological rule has a
physical origin attributable to sunspot formation, evolution, and decay,
rather than being due to the changes in sunspot number caused by groups
rotating onto and off the visible disc. We also demonstrate a simple
method to simulate daily sunspot numbers over a solar cycle using the
Pop (Solar Phys.276, 351, 2012) result, together with a model for the
cycle variation in the mean sunspot number. The procedure is applied to
three recent solar cycles. We check that the simulated sunspot numbers
reproduce the observed distribution of daily changes over those cycles.
Title: A Magnetostatic Grad-Rubin Code for Coronal Magnetic Field
Extrapolations
Authors: Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2013SoPh..282..283G
Altcode: 2012SoPh..tmp..246G; 2012arXiv1209.5843G
The coronal magnetic field cannot be directly observed, but, in
principle, it can be reconstructed from the comparatively well
observed photospheric magnetic field. A popular approach uses a
nonlinear force-free model. Non-magnetic forces at the photosphere
are significant, meaning the photospheric data are inconsistent with
the force-free model, and this causes problems with the modeling (De
Rosa et al., Astrophys. J.696, 1780, 2009). In this paper we present a
numerical implementation of the Grad-Rubin method for reconstructing the
coronal magnetic field using a magnetostatic model. This model includes
a pressure force and a non-zero magnetic Lorentz force. We demonstrate
our implementation on a simple analytic test case and obtain the speed
and numerical error scaling as a function of the grid size.
Title: Guiding Nonlinear Force-free Modeling Using Coronal
Observations: First Results Using a Quasi-Grad-Rubin Scheme
Authors: Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland,
M. S.; Gilchrist, S. A.
Bibcode: 2012ApJ...756..153M
Altcode: 2012arXiv1202.5420M
At present, many models of the coronal magnetic field rely on
photospheric vector magnetograms, but these data have been shown
to be problematic as the sole boundary information for nonlinear
force-free field extrapolations. Magnetic fields in the corona
manifest themselves in high-energy images (X-rays and EUV) in the
shapes of coronal loops, providing an additional constraint that
is not at present used as constraints in the computational domain,
directly influencing the evolution of the model. This is in part due
to the mathematical complications of incorporating such input into
numerical models. Projection effects, confusion due to overlapping
loops (the coronal plasma is optically thin), and the limited number
of usable loops further complicate the use of information from
coronal images. We develop and test a new algorithm to use images of
coronal loops in the modeling of the solar coronal magnetic field. We
first fit projected field lines with those of constant-α force-free
fields to approximate the three-dimensional distribution of currents
in the corona along a sparse set of trajectories. We then apply a
Grad-Rubin-like iterative technique, which uses these trajectories as
volume constraints on the values of α, to obtain a volume-filling
nonlinear force-free model of the magnetic field, modifying a code
and method presented by Wheatland. We thoroughly test the technique
on known analytical and solar-like model magnetic fields previously
used for comparing different extrapolation techniques and compare the
results with those obtained by currently available methods relying
only on the photospheric data. We conclude that we have developed a
functioning method of modeling the coronal magnetic field by combining
the line-of-sight component of the photospheric magnetic field with
information from coronal images. Whereas we focus on the use of coronal
loop information in combination with line-of-sight magnetograms, the
method is readily extended to incorporate vector-magnetic data over
any part of the photospheric boundary.
Title: A current sheet traced from the Sun to interplanetary space
Authors: Zhou, Guiping; Xiao, C. J.; Wang, Jingxu; Wheatland, . M. S.;
Zhao, . Hui
Bibcode: 2012cosp...39.2273Z
Altcode: 2012cosp.meet.2273Z
Magnetic reconnection is a central concept for understanding solar
activity, including filament eruptions, flares, and coronal mass
ejections (CMEs). The existence of transverse and vertical current
sheets, sites where reconnection takes place in the solar atmosphere,
is frequently proposed as a precondition for flare/CME models, but is
rarely identified in observations. We aim at identifying a transverse
current sheet that existed in the pre-CME structure and persisted from
the CME solar source to interplanetary space. STEREO A/B provide us
a unique opportunity to calculate the interplanetary current sheets
for the magnetic cloud. We analyze such a structure related to the
fast halo CME of 2006 December 13 with assembled observations. A
current sheet at the front of the magnetic cloud is analyzed to its
origin in a transverse current sheet in the CME solar source, which
can be revealed in the magnetic field extrapolations, XRT, and LASCO
observations. Results. An interplanetary current sheet is identified
as coming from the CME solar source by carefully mapping and examining
multiple observations from the Sun to interplanetary space, along with
nonlinear force-free magnetic field extrapolations of the active region
NOAA 10930. The structure identified in the pre-flare state is a global
transverse current sheet, which plays a role in the CME initiation,
and propagates from the corona to interplanetary space.
Title: Non-Linear Force-Free Modeling of Solar Corona With The Aid
of Coronal Loops
Authors: Malanushenko, A.; DeRosa, M.; Schrijver, C.; Wheatland,
M. S.; Gilchrist, S.
Bibcode: 2012decs.confE.113M
Altcode:
Accurate models of the coronal magnetic field are vital for
understanding and predicting solar activity and are therefore of the
greatest interest for solar physics. As no reliable measurements of the
coronal magnetic field exists at present, the problem of constructing
field models is typically viewed as a boundary value problem. The
construction of realistic field models requires knowledge of the full
vector of magnetic field at the boundaries of the model domain; vector
magnetograms are, however, measured in the non force-free photosphere
and their horizontal components are subject to large uncertainties. Even
if an uncertainty-free vector magnetogram at the top layer of the
chromosphere was known, the problem remains an extremely challenging
non-linear problem. There are various methods for pre-processing
vector magnetograms and using them to construct models of the coronal
field. The success of these models is often judged based on how close
its field lines correspond to the observed coronal loops, which are
believed to follow lines of the coronal magnetic field. At present,
the correspondence between coronal loops and magnetic field lines
of many models based on the vector magnetograms is far from perfect
(DeRosa et. al., 2009). The estimates of free energy in the field as
well as distribution of the magnetic currents through the volume could
be dramatically different for different models used (Schrijver et. al.,
2008). This testifies to the need of a completely new approach to this
problem. We present such an approach and demonstrate its results based
on AIA and HMI data. We have developed a way to use coronal loops as a
constraint for magnetic modelling; the field is therefore constructed to
match coronal loops. We found that when tested on known magnetic fields
the new method is able to reproduce overall shape of the field lines,
large-scale spatial distribution of the electric currents and measure
up to 60% of the free energy stored in the field. This was achieved
with as little as line-of-sight magnetogram and less than hundred of
synthetic "loops", that is, lines of magnetic fields projected onto
a plane of the sky. We found that line-of-sight HMI magnetograms and
spatial resolution of the AIA instrument combined with the amount of
filters available are more than sufficient for obtaining such data. We
briefly describe this new method and demonstrate reconstructions of the
coronal magnetic field obtained using AIA and HMI data. We evaluate how
well it reproduces coronal features and how much energy and helicity
estimates fluctuate with time for a stable non-flaring active region,
thus establishing the reliability of the new method.
Title: The Free Energy of NOAA Solar Active Region AR 11029
Authors: Gilchrist, S. A.; Wheatland, M. S.; Leka, K. D.
Bibcode: 2012SoPh..276..133G
Altcode: 2011arXiv1110.4418G
The NOAA active region (AR) 11029 was a small but highly active
sunspot region which produced 73 GOES soft X-ray flares during
its transit of the disk in late October 2009. The flares appear
to show a departure from the well-known power law frequency-size
distribution. Specifically, too few GOES C-class and no M-class flares
were observed by comparison with a power law distribution (Wheatland,
Astrophys. J.710, 1324, 2010). This was conjectured to be due to
the region having insufficient magnetic energy to power the missing
large events. We construct nonlinear force-free extrapolations of the
coronal magnetic field of AR 11029 using data taken on 24 October by
the SOLIS Vector SpectroMagnetograph (SOLIS/VSM) and data taken on
27 October by the Hinode Solar Optical Telescope SpectroPolarimeter
(Hinode/SP). Force-free modeling with photospheric magnetogram data
encounters problems, because the magnetogram data are inconsistent with
a force-free model. We employ a recently developed "self-consistency"
procedure which addresses this problem and accommodates uncertainties
in the boundary data (Wheatland and Régnier, Astrophys. J.700,
L88, 2009). We calculate the total energy and free energy of
the self-consistent solution, which provides a model for the
coronal magnetic field of the active region. The free energy of
the region was found to be ≈ 4×1029 erg on 24 October
and ≈ 7×1031 erg on 27 October. An order of magnitude
scaling between RHESSI non-thermal energy and GOES peak X-ray flux is
established from a sample of flares from the literature and is used to
estimate flare energies from the observed GOES peak X-ray flux. Based
on the scaling, we conclude that the estimated free energy of AR
11029 on 27 October when the flaring rate peaked was sufficient to
power M-class or X-class flares; hence, the modeling does not appear
to support the hypothesis that the absence of large flares is due to
the region having limited energy.
Title: A Bayesian Approach to Forecasting Solar Cycles Using a
Fokker-Planck Equation
Authors: Noble, P. L.; Wheatland, M. S.
Bibcode: 2012SoPh..276..363N
Altcode: 2011arXiv1111.3084N
A Bayesian method for forecasting solar cycles is presented. The
approach combines a Fokker-Planck description of short-timescale (daily)
fluctuations in sunspot number (Noble and Wheatland, Astrophys. J.732,
5, 2011) with information from other sources, such as precursor and/or
dynamo models. The forecasting is illustrated in application to two
historical cycles (cycles 19 and 20), and then to the current solar
cycle (cycle 24). The new method allows the prediction of quantiles,
i.e. the probability that the sunspot number falls outside large or
small bounds at a given future time. It also permits Monte Carlo
simulations to identify the expected size and timing of the peak
daily sunspot number, as well as the smoothed sunspot number for a
cycle. These simulations show how the large variance in daily sunspot
number determines the actual reliability of any forecast of the smoothed
maximum of a cycle. For cycle 24 we forecast a maximum daily sunspot
number of 166±24, to occur in March 2013, and a maximum value of the
smoothed sunspot number of 66±5, indicating a very small solar cycle.
Title: Non-Linear Force-Free Modeling With The Aid of Coronal
Observations
Authors: Malanushenko, A. V.; DeRosa, M. L.; Schrijver, C. J.;
Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2011AGUFMSH43B1956M
Altcode:
Currently many models of coronal magnetic field rely on vector
magnetograms and other kinds of information drawn from the
photosphere. Magnetic fields in the corona, however, manifest themselves
in the shapes of coronal loops, providing a constraint that at the
present stage receives little use due to mathematical complications of
incorporating such input into the numeric models. Projection effects
and the limited number of usable loops further complicate their
use. We present a possible way to account for coronal loops in the
models of magnetic field. We first fit the observed loops with lines
of constant-alpha fields and thus approximate three-dimensional
distribution of currents in the corona along a sparse set of
trajectories. We then apply a Grad-Rubin-like averaging technique
to obtain a volume-filling non-linear force-free model of magnetic
field, modified from the method presented in Wheatland & Regnier
(2009). We present thorough tests of this technique on several known
magnetic fields that were previously used for comparing different
extrapolation techniques (Schrijver et. al., 2006; Metcalf et. al.,
2008; Schrijver et. al., 2008; DeRosa et. al., 2009), as well as on
solar data and compare the results with those obtained by the currently
developed methods that rely completely on the photospheric data.
Title: Modeling the Sunspot Number Distribution with a Fokker-Planck
Equation
Authors: Noble, P. L.; Wheatland, M. S.
Bibcode: 2011ApJ...732....5N
Altcode: 2011arXiv1102.5158N
Sunspot numbers exhibit large short-timescale (daily-monthly)
variation in addition to longer-timescale variation due to solar
cycles. A formal statistical framework is presented for estimating
and forecasting randomness in sunspot numbers on top of deterministic
(including chaotic) models for solar cycles. The Fokker-Planck approach
formulated assumes a specified long-term or secular variation in sunspot
number over an underlying solar cycle via a driver function. The model
then describes the observed randomness in sunspot number on top of this
driver function. We consider a simple harmonic choice for the driver
function, but the approach is general and can easily be extended to
include other drivers which account for underlying physical processes
and/or empirical features of the sunspot numbers. The framework is
consistent during both solar maximum and minimum, and requires no
parameter restrictions to ensure non-negative sunspot numbers. Model
parameters are estimated using statistically optimal techniques. The
model agrees both qualitatively and quantitatively with monthly sunspot
data even with the simplistic representation of the periodic solar
cycle. This framework should be particularly useful for solar cycle
forecasters and is complementary to existing modeling techniques. An
analytic approximation for the Fokker-Planck equation is presented,
which is analogous to the Euler approximation, which allows for
efficient maximum likelihood estimation of large data sets and/or when
using difficult to evaluate driver functions.
Title: Simulating Coronal Emission in Six AIA Channels Using
Quasi-Static Atmosphere Models and Non-Linear Magnetic Field Models
Authors: Malanushenko, Anna; Schrijver, C.; DeRosa, M.; Aschwanden,
M.; Wheatland, M. S.; van Ballegooijen, A. A.
Bibcode: 2011SPD....42.2116M
Altcode: 2011BAAS..43S.2116M
We present the results of simulations of the EUV coronal emission in
AIA channels. We use a non-linear force-free model of magnetic field
constructed in such a way that its field lines resemble the observed
coronal loops in EUV. We then solve one-dimensional quasi-steady
atmosphere model along the magnetic field lines (Schrijver &
Ballegooijen, 2005). Using coronal abundances from CHIANTI and AIA
response functions we then simulate the emission that would be observed
in AIA EUV channels. The resulting intensities are compared against the
real observations in a manner similar to that in Aschwanden et. al.,
2011. The study is similar to those by Lindquist et. al., 2008, with a
few important differences. We use a model of the coronal magnetic field
that resembles the topology observed in EUV, we study EUV emission of
cool loops (rather than SXR) and we make use of high resolution and
cadence AIA and HMI data.
Title: Achieving Self-consistent Nonlinear Force-free Modeling of
Solar Active Regions
Authors: Wheatland, M. S.; Leka, K. D.
Bibcode: 2011ApJ...728..112W
Altcode: 2010arXiv1012.3503W
A nonlinear force-free solution is constructed for the coronal magnetic
field in NOAA solar active region (AR) 10953 based on a photospheric
vector magnetogram derived from Hinode satellite observations on
2007 April 30, taking into account uncertainties in the boundary data
and using improved methods for merging multiple-instrument data. The
solution demonstrates the "self-consistency" procedure of Wheatland
& Régnier, for the first time including uncertainties. The
self-consistency procedure addresses the problem that photospheric
vector magnetogram data are inconsistent with the force-free model,
and in particular that the boundary conditions on vertical electric
current density are overspecified and permit the construction of two
different nonlinear force-free solutions. The procedure modifies the
boundary conditions on current density during a sequence of cycles until
the two nonlinear force-free solutions agree. It hence constructs an
accurate single solution to the force-free model, with boundary values
close, but not matched exactly, to the vector magnetogram data. The
inclusion of uncertainties preserves the boundary conditions more
closely at points with smaller uncertainties. The self-consistent
solution obtained for AR 10953 is significantly non-potential, with
magnetic energy E/E 0 ≈ 1.08, where E 0 is the
energy of the reference potential (current-free) magnetic field. The
self-consistent solution is shown to be robust against changes in
the details of the construction of the two force-free models at each
cycle. This suggests that reliable nonlinear force-free modeling of
ARs is possible if uncertainties in vector magnetogram boundary data
are included.
Title: A current sheet traced from the Sun to interplanetary space
Authors: Zhou, G. P.; Xiao, C. J.; Wang, J. X.; Wheatland, M. S.;
Zhao, H.
Bibcode: 2011A&A...525A.156Z
Altcode:
Context. Magnetic reconnection is a central concept for understanding
solar activity, including filament eruptions, flares, and coronal mass
ejections (CMEs). The existence of transverse and vertical current
sheets, sites where reconnection takes place in the solar atmosphere,
is frequently proposed as a precondition for flare/CME models, but is
rarely identified in observations.
Aims: We aim at identifying
a transverse current sheet that existed in the pre-CME structure and
persisted from the CME solar source to interplanetary space.
Methods: STEREO A/B provide us a unique opportunity to calculate the
interplanetary current sheets for the magnetic cloud. We analyze
such a structure related to the fast halo CME of 2006 December 13
with assembled observations. A current sheet at the front of the
magnetic cloud is analyzed to its origin in a transverse current
sheet in the CME solar source, which can be revealed in the magnetic
field extrapolations, XRT, and LASCO observations.
Results:
An interplanetary current sheet is identified as coming from the CME
solar source by carefully mapping and examining multiple observations
from the Sun to interplanetary space, along with nonlinear force-free
magnetic field extrapolations of the active region NOAA 10930.
Conclusions: The structure identified in the pre-flare state is a global
transverse current sheet, which plays a role in the CME initiation,
and propagates from the corona to interplanetary space.
Title: Solar physics research in Australia
Authors: Cally, P. S.; Wheatland, M. S.; Cairns, I. H.; Melrose, D. B.
Bibcode: 2011ASInC...2..397C
Altcode:
Australia has a small but world-class solar physics research community,
with strong international ties, working in areas of particular
strength defined by the research interests of individuals and small
groups. Most research occurs at the major universities, and a small
number of Ph.D. students are trained in the field each year. This paper
surveys Australia's current contribution to solar physics research,
and the prospects for future development of the field.
Title: Modelling magnetic fields in the corona using nonlinear
force-free fields
Authors: Wheatland, M. S.; Leka, K. D.
Bibcode: 2011ASInC...2..203W
Altcode:
Force-free magnetic fields, in which the magnetic or Lorentz force is
self-balancing and hence zero, provide a simple model for fields in
the Sun's corona. In principle the model may be solved using boundary
values of the field derived from observations, e.g. data from the Hinode
spectro-polarimeter. In practise the boundary data is inconsistent
with the model, because fields at the photospheric level are subject
to non-magnetic forces, and because of substantial uncertainties in the
boundary data. The `self-consistency' procedure tep{2009ApJ...700L..88W}
provides an approach to resolving the problem. This talk reports
on results achieved with the procedure, in particular new results
obtained for active region AR 10953 using Hinode data incorporating
uncertainties in the boundary conditions tep{2011ApJ...728..112W}.
Title: The free energy of NOAA active region AR 11029
Authors: Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2010AGUFMSH53B..02G
Altcode:
Active region AR 11029 was a small but highly active sunspot region
that produced over 70 GOES soft X-ray flares during its transit
of the disk in late October 2009, during a period of deep solar
minimum. The flares appear to show a departure from the well known
flare power-law frequency-size distribution. Specifically, too few
GOES C class and no M class flares were observed by comparison with a
simple power-law distribution (Wheatland 2010). This was conjectured
to be due to the region having insufficient magnetic energy to
power large events (Wheatland 2010). We perform nonlinear force-free
modeling of the coronal magnetic field of the region on 24, 25 and 26
October using three photospheric magnetograms provided by the SOLIS
vector spectromagnetograph. We find the free magnetic energy of the
region is ≤ 1030 ergs which is consistent with the region having
insufficient energy to produce large flares. A recently developed
self-consistency procedure (Wheatland and Régnier 2009) is applied
to overcome the incompatibility between the force-free model and the
forced photospheric data. Force-free model of the coronal magnetic field
(black field lines) of AR 11029 on 24 October superimposed on SOLIS
magnetogram data. The magnetogram shows the line-of-sight magnetic
field on the photosphere. Positive polarity regions are colored blue
and negative polarity regions are colored red.
Title: Time-Dependent Stochastic Modeling of Solar Active Region
Energy
Authors: Kanazir, M.; Wheatland, M. S.
Bibcode: 2010SoPh..266..301K
Altcode: 2010arXiv1008.0459K; 2010SoPh..tmp..162K
A time-dependent model for the energy of a flaring solar active region
is presented based on an existing stochastic jump-transition model
(Wheatland and Glukhov in Astrophys. J.494, 858, 1998; Wheatland
in Astrophys. J.679, 1621, 2008 and Solar Phys.255, 211, 2009). The
magnetic free energy of an active region is assumed to vary in time due
to a prescribed (deterministic) rate of energy input and prescribed
(random) jumps downwards in energy due to flares. The existing model
reproduces observed flare statistics, in particular flare frequency -
size and waiting-time distributions, but modeling presented to date has
considered only the time-independent choices of constant energy input
and constant flare-transition rates with a power-law distribution
in energy. These choices may be appropriate for a solar active
region producing a constant mean rate of flares. However, many solar
active regions exhibit time variation in their flare productivity, as
exemplified by NOAA active region (AR) 11029, observed during October
- November 2009 (Wheatland in Astrophys. J.710, 1324, 2010). Time
variation is incorporated into the jump-transition model for two
cases: (1) a step change in the rates of flare transitions, and (2)
a step change in the rate of energy supply to the system. Analytic
arguments are presented describing the qualitative behavior of the
system in the two cases. In each case the system adjusts by shifting
to a new stationary state over a relaxation time which is estimated
analytically. The model exhibits flare-like event statistics. In
each case the frequency - energy distribution is a power law for
flare energies less than a time-dependent rollover set by the largest
energy the system is likely to attain at a given time. The rollover
is not observed if the mean free energy of the system is sufficiently
large. For Case 1, the model exhibits a double exponential waiting-time
distribution, corresponding to flaring at a constant mean rate during
two intervals (before and after the step change), if the average energy
of the system is large. For Case 2 the waiting-time distribution is a
simple exponential, again provided the average energy of the system is
large. Monte Carlo simulations of Case 1 are presented which confirm the
estimate for the relaxation time and the expected forms of the frequency
- energy and waiting-time distributions. The simulation results provide
a qualitative model for observed flare statistics in AR 11029.
Title: Modelling the Coronal Magnetic Field Using Hinode (and
Future) Data
Authors: Wheatland, M. S.; Gilchrist, S. A.; Régnier, S.
Bibcode: 2010aogs...21..327W
Altcode:
There is considerable interest in accurate modelling of the solar
coronal magnetic field using photospheric vector magnetograms
as boundary data, and the nonlinear force-free model is often
used. However, recent studies using Hinode data have demonstrated that
this modelling fails in basic ways, with the failure attributable to the
departure of the inferred photospheric magnetic field from a force-free
state. The solar boundary data are inconsistent with the model, which
leads to inconsistencies in calculated force-free solutions. A method
for constructing a self-consistent nonlinear force-free solution is
described, which identifies a force-free solution that is close to the
observed boundary data. Steps towards developing more sophisticated
magnetohydrostatic modelling — taking into account pressure and
gravitational forces at the level of the solar boundary data — are
also outlined.
Title: Evidence for Departure from a Power-Law Flare Size Distribution
for a Small Solar Active Region
Authors: Wheatland, M. S.
Bibcode: 2010ApJ...710.1324W
Altcode: 2010arXiv1001.1464W
Active region 11029 was a small, highly flare-productive solar active
region observed at a time of extremely low solar activity. The region
produced only small flares: the largest of the >70 Geostationary
Observational Environmental Satellite (GOES) events for the region
has a peak 1-8 Å flux of 2.2 × 10-6 W m-2
(GOES C2.2). The background-subtracted GOES peak-flux distribution
suggests departure from power-law behavior above 10-6
W m-2, and a Bayesian model comparison strongly favors
a power-law plus rollover model for the distribution over a simple
power-law model. The departure from the power law is attributed to
this small active region having a finite amount of energy. The rate
of flaring in the region varies with time, becoming very high for 2
days coinciding with the onset of an increase in complexity of the
photospheric magnetic field. The observed waiting-time distribution
for events is consistent with a piecewise-constant Poisson model. These
results present challenges for models of flare statistics and of energy
balance in solar active regions.
Title: On The Brightness and Waiting-Time Distributions of a Type
III Radio Storm Observed By Stereo/Waves
Authors: Eastwood, J. P.; Wheatland, M. S.; Hudson, H. S.; Krucker,
S.; Bale, S. D.; Maksimovic, M.; Goetz, K.; Bougeret, J. -L.
Bibcode: 2010ApJ...708L..95E
Altcode: 2009arXiv0911.4131E
Type III solar radio storms, observed at frequencies below ~16 MHz
by space-borne radio experiments, correspond to the quasi-continuous,
bursty emission of electron beams onto open field lines above active
regions. The mechanisms by which a storm can persist in some cases
for more than a solar rotation whilst exhibiting considerable radio
activity are poorly understood. To address this issue, the statistical
properties of a type III storm observed by the STEREO/WAVES radio
experiment are presented, examining both the brightness distribution
and (for the first time) the waiting-time distribution (WTD). Single
power-law behavior is observed in the number distribution as a function
of brightness; the power-law index is ~2.1 and is largely independent of
frequency. The WTD is found to be consistent with a piecewise-constant
Poisson process. This indicates that during the storm individual type
III bursts occur independently and suggests that the storm dynamics are
consistent with avalanche-type behavior in the underlying active region.
Title: A Self-Consistent Nonlinear Force-Free Solution for a Solar
Active Region Magnetic Field
Authors: Wheatland, M. S.; Régnier, S.
Bibcode: 2009ApJ...700L..88W
Altcode: 2009arXiv0906.4414W
Nonlinear force-free solutions for the magnetic field in the solar
corona constructed using photospheric vector magnetic field boundary
data suffer from a basic problem: the observed boundary data are
inconsistent with the nonlinear force-free model. Specifically, there
are two possible choices of boundary conditions on vertical current
provided by the data, and the two choices lead to different force-free
solutions. A novel solution to this problem is described. Bayesian
probability is used to modify the boundary values on current density,
using field-line connectivity information from the two force-free
solutions and taking into account uncertainties, so that the
boundary data are more consistent with the two nonlinear force-free
solutions. This procedure may be iterated until a set of self-consistent
boundary data (the solutions for the two choices of boundary conditions
are the same) is achieved. The approach is demonstrated to work in
application to Hinode/Solar Optical Telescope observations of NOAA
active region 10953.
Title: Nonlinear Force-Free Magnetic Field Modeling of AR 10953:
A Critical Assessment
Authors: De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.;
Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan,
J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.;
Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.;
Inhester, B.; Tadesse, T.
Bibcode: 2009SPD....40.3102D
Altcode:
Nonlinear force-free field (NLFFF) modeling seeks to provide accurate
representations of the structure of the magnetic field above solar
active regions, from which estimates of physical quantities of interest
(e.g., free energy and helicity) can be made. However, the suite of
NLFFF algorithms have failed to arrive at consistent solutions when
applied to (thus far, two) cases using the highest-available-resolution
vector magnetogram data from Hinode/SOT-SP (in the region of the
modeling area of interest) and line-of-sight magnetograms from
SOHO/MDI (where vector data were not available). One issue is that
NLFFF models require consistent, force-free vector magnetic boundary
data, and vector magnetogram data sampling the photosphere do not
satisfy this requirement. Consequently, several problems have arisen
that are believed to affect such modeling efforts. We use AR 10953
to illustrate these problems, namely: (1) some of the far-reaching,
current-carrying connections are exterior to the observational field
of view, (2) the solution algorithms do not (yet) incorporate the
measurement uncertainties in the vector magnetogram data, and/or (3)
a better way is needed to account for the Lorentz forces within the
layer between the photosphere and coronal base. In light of these
issues, we conclude that it remains difficult to derive useful and
significant estimates of physical quantities from NLFFF models.
Title: A Critical Assessment of Nonlinear Force-Free Field Modeling
of the Solar Corona for Active Region 10953
Authors: De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham;
Leka, K. D.; Lites, Bruce W.; Aschwanden, Markus J.; Amari, Tahar;
Canou, Aurélien; McTiernan, James M.; Régnier, Stéphane; Thalmann,
Julia K.; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas;
Cheung, Mark C. M.; Conlon, Paul A.; Fuhrmann, Marcel; Inhester,
Bernd; Tadesse, Tilaye
Bibcode: 2009ApJ...696.1780D
Altcode: 2009arXiv0902.1007D
Nonlinear force-free field (NLFFF) models are thought to be viable
tools for investigating the structure, dynamics, and evolution of
the coronae of solar active regions. In a series of NLFFF modeling
studies, we have found that NLFFF models are successful in application
to analytic test cases, and relatively successful when applied
to numerically constructed Sun-like test cases, but they are less
successful in application to real solar data. Different NLFFF models
have been found to have markedly different field line configurations
and to provide widely varying estimates of the magnetic free energy in
the coronal volume, when applied to solar data. NLFFF models require
consistent, force-free vector magnetic boundary data. However,
vector magnetogram observations sampling the photosphere, which is
dynamic and contains significant Lorentz and buoyancy forces, do not
satisfy this requirement, thus creating several major problems for
force-free coronal modeling efforts. In this paper, we discuss NLFFF
modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT,
STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process
illustrate three such issues we judge to be critical to the success of
NLFFF modeling: (1) vector magnetic field data covering larger areas
are needed so that more electric currents associated with the full
active regions of interest are measured, (2) the modeling algorithms
need a way to accommodate the various uncertainties in the boundary
data, and (3) a more realistic physical model is needed to approximate
the photosphere-to-corona interface in order to better transform the
forced photospheric magnetograms into adequate approximations of nearly
force-free fields at the base of the corona. We make recommendations
for future modeling efforts to overcome these as yet unsolved problems.
Title: Monte Carlo Simulation of Solar Active-Region Energy
Authors: Wheatland, M. S.
Bibcode: 2009SoPh..255..211W
Altcode: 2009arXiv0902.0424W
A Monte Carlo approach to solving a stochastic-jump transition model
for active-region energy (Wheatland and Glukhov: Astrophys. J.494,
858, 1998; Wheatland: Astrophys. J.679, 1621, 2008) is described. The
new method numerically solves the stochastic differential equation
describing the model, rather than the equivalent master equation. This
has the advantages of allowing more efficient numerical solution, the
modeling of time-dependent situations, and investigation of details of
event statistics. The Monte Carlo approach is illustrated by application
to a Gaussian test case and to the class of flare-like models presented
in Wheatland (Astrophys. J.679, 1621, 2008), which are steady-state
models with constant rates of energy supply, and power-law distributed
jump transition rates. These models have two free parameters: an index
(δ), which defines the dependence of the jump transition rates on
active-region energy, and a nondimensional ratio ( \overline{r} )
of total flaring rate to rate of energy supply. For \overline{r}≪
1 the nondimensional mean energy \langle \overline{E}\rangle of the
active-region satisfies \langle \overline{E}\rangle ≫ 1 , resulting
in a power-law distribution of flare events over many decades of
energy. The Monte Carlo method is used to explore the behavior of
the waiting-time distributions for the flare-like models. The models
with δ≠0 are found to have waiting times that depart significantly
from simple Poisson behavior when \langle \overline{E}\rangle ≫ 1
. The original model from Wheatland and Glukhov (Astrophys. J.494,
858, 1998), with δ=0 (i.e., no dependence of transition rates on
active-region energy), is identified as being most consistent with
observed flare statistics.
Title: Nonlinear Force-Free Magnetic Field Modeling of the Solar
Corona: A Critical Assessment
Authors: De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.;
Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.;
Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung,
M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
Bibcode: 2008AGUFMSH41A1604D
Altcode:
Nonlinear force-free field (NLFFF) modeling promises to provide accurate
representations of the structure of the magnetic field above solar
active regions, from which estimates of physical quantities of interest
(e.g., free energy and helicity) can be made. However, the suite of
NLFFF algorithms have so far failed to arrive at consistent solutions
when applied to cases using the highest-available-resolution vector
magnetogram data from Hinode/SOT-SP (in the region of the modeling
area of interest) and line-of-sight magnetograms from SOHO/MDI (where
vector data were not been available). It is our view that the lack of
robust results indicates an endemic problem with the NLFFF modeling
process, and that this process will likely continue to fail until (1)
more of the far-reaching, current-carrying connections are within the
observational field of view, (2) the solution algorithms incorporate
the measurement uncertainties in the vector magnetogram data, and/or
(3) a better way is found to account for the Lorentz forces within
the layer between the photosphere and coronal base. In light of these
issues, we conclude that it remains difficult to derive useful and
significant estimates of physical quantities from NLFFF models.
Title: The Energetics of a Flaring Solar Active Region and Observed
Flare Statistics
Authors: Wheatland, M. S.
Bibcode: 2008ApJ...679.1621W
Altcode: 2008arXiv0802.3931W
A stochastic model for the energy of a flaring solar active region is
presented, generalizing and extending the approach of Wheatland and
Glukhov. The probability distribution for the free energy of an active
region is described by the solution to a master equation involving
deterministic energy input and random jump transitions downward in
energy (solar flares). It is shown how two observable distributions,
the flare frequency-energy distribution and the flare waiting-time
distribution, may be derived from the steady state solution to the
master equation, for given choices for the energy input and for the
rates of flare transitions. An efficient method of numerical solution
of the steady state master equation is presented. Solutions appropriate
for flaring, involving a constant rate of energy input and power-law
distributed jump transition rates, are numerically investigated. The
flarelike solutions exhibit power-law flare frequency-energy
distributions below a high-energy rollover, set by the largest energy
the active region is likely to have. The solutions also exhibit
approximately exponential (i.e., Poisson) waiting-time distributions,
despite the rate of flaring depending on the free energy of the system.
Title: Non-Linear Force-Free Field Modeling of a Solar Active Region
Around the Time of a Major Flare and Coronal Mass Ejection
Authors: De Rosa, M. L.; Schrijver, C. J.; Metcalf, T. R.; Barnes,
G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann,
T.; Wheatland, M.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann,
M.; Kusano, K.; Régnier, S.; Thalmann, J.
Bibcode: 2008AGUSMSP31A..06D
Altcode:
Solar flares and coronal mass ejections are associated with rapid
changes in coronal magnetic field connectivity and are powered by
the partial dissipation of electrical currents that run through
the solar corona. A critical unanswered question is whether the
currents involved are induced by the advection along the photosphere
of pre-existing atmospheric magnetic flux, or whether these currents
are associated with newly emergent flux. We address this problem by
applying nonlinear force-free field (NLFFF) modeling to the highest
resolution and quality vector-magnetographic data observed by the
recently launched Hinode satellite on NOAA Active Region 10930 around
the time of a powerful X3.4 flare in December 2006. We compute 14
NLFFF models using 4 different codes having a variety of boundary
conditions. We find that the model fields differ markedly in geometry,
energy content, and force-freeness. We do find agreement of the best-fit
model field with the observed coronal configuration, and argue (1)
that strong electrical currents emerge together with magnetic flux
preceding the flare, (2) that these currents are carried in an ensemble
of thin strands, (3) that the global pattern of these currents and
of field lines are compatible with a large-scale twisted flux rope
topology, and (4) that the ~1032~erg change in energy associated with
the coronal electrical currents suffices to power the flare and its
associated coronal mass ejection. We discuss the relative merits of
these models in a general critique of our present abilities to model
the coronal magnetic field based on surface vector field measurements.
Title: Nonlinear Force-free Field Modeling of a Solar Active Region
around the Time of a Major Flare and Coronal Mass Ejection
Authors: Schrijver, C. J.; DeRosa, M. L.; Metcalf, T.; Barnes, G.;
Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.;
Wheatland, M. S.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann,
M.; Kusano, K.; Régnier, S.; Thalmann, J. K.
Bibcode: 2008ApJ...675.1637S
Altcode: 2007arXiv0712.0023S
Solar flares and coronal mass ejections are associated with rapid
changes in field connectivity and are powered by the partial dissipation
of electrical currents in the solar atmosphere. A critical unanswered
question is whether the currents involved are induced by the motion of
preexisting atmospheric magnetic flux subject to surface plasma flows or
whether these currents are associated with the emergence of flux from
within the solar convective zone. We address this problem by applying
state-of-the-art nonlinear force-free field (NLFFF) modeling to the
highest resolution and quality vector-magnetographic data observed
by the recently launched Hinode satellite on NOAA AR 10930 around
the time of a powerful X3.4 flare. We compute 14 NLFFF models with
four different codes and a variety of boundary conditions. We find
that the model fields differ markedly in geometry, energy content,
and force-freeness. We discuss the relative merits of these models in
a general critique of present abilities to model the coronal magnetic
field based on surface vector field measurements. For our application
in particular, we find a fair agreement of the best-fit model field
with the observed coronal configuration, and argue (1) that strong
electrical currents emerge together with magnetic flux preceding the
flare, (2) that these currents are carried in an ensemble of thin
strands, (3) that the global pattern of these currents and of field
lines are compatible with a large-scale twisted flux rope topology,
and (4) that the ~1032 erg change in energy associated with
the coronal electrical currents suffices to power the flare and its
associated coronal mass ejection.
Title: Analysis and Packaging of Radiochemical Solar Neutrino Data:
A Bayesian Approach
Authors: Sturrock, P. A.; Wheatland, M. S.
Bibcode: 2008SoPh..247..217S
Altcode: 2007arXiv0706.2192S; 2008SoPh..tmp....4S
According to current practice, the results of each run of a
radiochemical solar neutrino experiment comprise an estimate of the
flux and upper and lower error estimates. These estimates are derived
by a maximum-likelihood procedure from the times of decay events in
the analysis chamber. This procedure has the following shortcomings:
(a) published results sometimes include negative flux estimates; (b)
even if the flux estimate is non-negative, the probability distribution
function implied by the flux and error estimates will extend into
negative territory; and (c) the overall flux estimate derived from
the results of a sequence of runs may differ substantially from an
estimate made by a "global" analysis of all of the timing data taken
together. These defects indicate that the usual "packaging" of data
in radiochemical solar neutrino experiments provides an inadequate
summary of the data, which implies a loss of information. This article
reviews this problem from a Bayesian perspective, and we suggest an
alternative scheme for the packaging of radiochemical solar neutrino
data, which we believe is free from these shortcomings.
Title: Nonlinear Force-Free Modeling of Coronal Magnetic
Fields. II. Modeling a Filament Arcade and Simulated Chromospheric
and Photospheric Vector Fields
Authors: Metcalf, Thomas R.; De Rosa, Marc L.; Schrijver, Carolus J.;
Barnes, Graham; van Ballegooijen, Adriaan A.; Wiegelmann, Thomas;
Wheatland, Michael S.; Valori, Gherardo; McTtiernan, James M.
Bibcode: 2008SoPh..247..269M
Altcode: 2008SoPh..tmp...17M
We compare a variety of nonlinear force-free field (NLFFF) extrapolation
algorithms, including optimization, magneto-frictional, and Grad -
Rubin-like codes, applied to a solar-like reference model. The model
used to test the algorithms includes realistic photospheric Lorentz
forces and a complex field including a weakly twisted, right helical
flux bundle. The codes were applied to both forced "photospheric" and
more force-free "chromospheric" vector magnetic field boundary data
derived from the model. When applied to the chromospheric boundary data,
the codes are able to recover the presence of the flux bundle and the
field's free energy, though some details of the field connectivity are
lost. When the codes are applied to the forced photospheric boundary
data, the reference model field is not well recovered, indicating
that the combination of Lorentz forces and small spatial scale
structure at the photosphere severely impact the extrapolation of the
field. Preprocessing of the forced photospheric boundary does improve
the extrapolations considerably for the layers above the chromosphere,
but the extrapolations are sensitive to the details of the numerical
codes and neither the field connectivity nor the free magnetic energy in
the full volume are well recovered. The magnetic virial theorem gives
a rapid measure of the total magnetic energy without extrapolation
though, like the NLFFF codes, it is sensitive to the Lorentz forces in
the coronal volume. Both the magnetic virial theorem and the Wiegelmann
extrapolation, when applied to the preprocessed photospheric boundary,
give a magnetic energy which is nearly equivalent to the value derived
from the chromospheric boundary, but both underestimate the free
energy above the photosphere by at least a factor of two. We discuss
the interpretation of the preprocessed field in this context. When
applying the NLFFF codes to solar data, the problems associated with
Lorentz forces present in the low solar atmosphere must be recognized:
the various codes will not necessarily converge to the correct, or
even the same, solution.
Title: Calculating and Testing Nonlinear Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2007SoPh..245..251W
Altcode:
Improvements to an existing method for calculating nonlinear force-free
magnetic fields (Wheatland, Solar Phys. 238, 29, 2006) are described. In
particular a solution of the 3-D Poisson equation using 2-D Fourier
transforms is presented. The improved nonlinear force-free method
is demonstrated in application to linear force-free test cases with
localized nonzero values of the normal component of the field in the
boundary. These fields provide suitable test cases for nonlinear
force-free calculations because the boundary conditions involve
localized nonzero values of the normal components of the field and
of the current density, and because (being linear force-free fields)
they have more direct numerical solutions. Despite their simplicity,
fields of this kind have not been recognized as test cases for
nonlinear methods before. The examples illustrate the treatment of
the boundary conditions on current in the nonlinear force-free method,
and in particular the limitations imposed by field lines that connect
outside of the boundary region.
Title: Non-linear Force-free Modeling Of Coronal Magnetic Fields
Authors: Metcalf, Thomas R.; De Rosa, M. L.; Schrijver, C. J.; Barnes,
G.; van Ballegooijen, A.; Wiegelmann, T.; Wheatland, M. S.; Valori,
G.; McTiernan, J. M.
Bibcode: 2007AAS...210.9102M
Altcode: 2007BAAS...39..204M
We compare a variety of nonlinear force-free field (NLFFF)
extrapolation algorithms, including optimization, magneto-frictional,
and Grad-Rubin-like codes, applied to a solar-like reference
model. The model used to test the algorithms includes realistic
photospheric Lorentz forces and a complex field including a weakly
twisted, right helical flux bundle. The codes were applied to both
forced "photospheric'' and more force-free "chromospheric'' vector
magnetic field boundary data derived from the model. When applied to
the chromospheric boundary data, the codes are able to recover
the presence of the flux bundle and the field's free energy, though
some details of the field connectivity are lost. When the codes are
applied to the forced photospheric boundary data, the reference
model field is not well recovered, indicating that the Lorentz
forces on the photosphere severely impact the extrapolation of the
field. Preprocessing of the photospheric boundary does improve the
extrapolations considerably, although the results depend sensitively
on the details of the numerical codes. When applying the NLFFF codes
to solar data, the problems associated with Lorentz forces present in
the low solar atmosphere must be recognized: the various codes will
not necessarily converge to the correct, or even the same, solution.
Title: Reconstruction of Nonlinear Force-Free Fields and Solar
Flare Prediction
Authors: Wheatland, M. S.
Bibcode: 2007aogs....8..123W
Altcode:
A brief review is presented of methods for calculating nonlinear
force-free fields, with emphasis on a new, fast current-field iteration
procedure. The motivation is to reconstruct coronal magnetic fields
using high-resolution vector magnetic field boundary data from a new
generation of spectro-polarimetric instruments. Methods of solar flare
prediction are also reviewed, with focus on the need to reproduce
observed solar flare statistics. The event statistics method is
described, as well as an extension of the method to incorporate
additional information, based on Bayesian predictive discrimination.
Title: A Fast Current-Field Iteration Method for Calculating Nonlinear
Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2006SoPh..238...29W
Altcode: 2006SoPh..tmp...55W
Existing methods for calculating nonlinear force-free magnetic fields
are slow, and are likely to be inadequate for reconstructing coronal
magnetic fields based on high-resolution vector magnetic field data
from a new generation of spectro-polarimetric instruments. In this
paper a new implementation of the current-field iteration method is
presented, which is simple, fast, and accurate. The time taken by the
method scales as N4, for a three-dimensional grid with
N3 points. The method solves the field-updating part of
the iteration by exploiting a three-dimensional Fast Fourier Transform
solution of Ampere's law with a current density field constructed to
satisfy the required boundary conditions, and uses field line tracing
to solve the current-updating part of the iteration. The method is
demonstrated in application to a known nonlinear force-free field and
to a bipolar test case.
Title: Including Flare Sympathy in a Model for Solar Flare Statistics
Authors: Wheatland, M. S.; Craig, I. J. D.
Bibcode: 2006SoPh..238...73W
Altcode: 2006SoPh..tmp...34W
There is a variety of observational evidence for solar flare sympathy,
i.e., the triggering of a flare in one active region by a flare in
another region. Models for solar flare statistics, however, usually
ignore sympathy by assuming that flares occur as independent events. In
this paper, we argue that statistical flare models should be robust
to the effects of sympathetic flaring. Further, we investigate the
consequences of flare sympathy for a specific model of flare statistics,
the M. S. Wheatland and I. J. D. Craig (Astrophys. J.595, 458, 2003)
model. The original treatment describes an assembly of reconnecting
structures (labelled separators) that flare independently according
to simple rules consistent with magnetohydrodynamic flare models. This
description is modified by allowing a flare at one separator to increase
the probability of flaring at all other separators for a period of
time following the flare, by an amount proportional to the energy of
the flare. Simulations illustrate the transition of the model from weak
to strong sympathy. In the limit of weak sympathy, the model reproduces
observed flare frequency-energy and waiting-time distributions.
Title: A Rate-Independent Test for Solar Flare Sympathy
Authors: Wheatland, M. S.
Bibcode: 2006SoPh..236..313W
Altcode:
Solar flare sympathy is the triggering of a flare in one active
region by a flare in another. Statistical tests for flare sympathy
have returned varying results. However, existing tests have relied on
flaring rates in active regions being constant in time, or else have
attempted to model the rate variation, which is a difficult task. A
simple test is described which is independent of flaring rates. The test
generalizes the approach of L. Fritzová-Švestkova, R.C. Chase, and
Z. Švestka [Solar Phys.48, 275, 1976], and examines the distribution
of flare coincidences in pairs of active regions as a function of
coincidence interval τ. The test is applied to available soft X-ray
and Hα flare event listings. The soft X-ray events exhibit a deficit
of flare coincidences for τ≤;20 min, which is most likely due to an
event-selection effect whereby the increased soft X-ray emission due
to one flare prevents a second flare being identified. The Hα events
show an excess of flare coincidences for τ≤; 10 min, suggesting
flare sympathy. The number of Hα event pairs occurring within 10 min
of one another is higher than that expected on the basis of random
coincidence by a fraction 0.12± 0.02. Nearby active regions (spatial
separation <50˚) show a greater excess of coincidences for τ≤;
10 min than do active regions which are far apart (spatial separation
≥50˚). However, the active regions which are far apart still show
some evidence for an excess of coincidences at very short coincidence
intervals (τ≤; 2 min), which appears to exclude the possibility of
a coronal disturbance propagating from one region to another.
Title: Nonlinear Force-Free Modeling of Coronal Magnetic Fields Part
I: A Quantitative Comparison of Methods
Authors: Schrijver, Carolus J.; De Rosa, Marc L.; Metcalf, Thomas R.;
Liu, Yang; McTiernan, Jim; Régnier, Stéphane; Valori, Gherardo;
Wheatland, Michael S.; Wiegelmann, Thomas
Bibcode: 2006SoPh..235..161S
Altcode:
We compare six algorithms for the computation of nonlinear force-free
(NLFF) magnetic fields (including optimization, magnetofrictional,
Grad-Rubin based, and Green's function-based methods) by evaluating
their performance in blind tests on analytical force-free-field models
for which boundary conditions are specified either for the entire
surface area of a cubic volume or for an extended lower boundary
only. Figures of merit are used to compare the input vector field to
the resulting model fields. Based on these merit functions, we argue
that all algorithms yield NLFF fields that agree best with the input
field in the lower central region of the volume, where the field and
electrical currents are strongest and the effects of boundary conditions
weakest. The NLFF vector fields in the outer domains of the volume
depend sensitively on the details of the specified boundary conditions;
best agreement is found if the field outside of the model volume is
incorporated as part of the model boundary, either as potential field
boundaries on the side and top surfaces, or as a potential field in
a skirt around the main volume of interest. For input field (B) and
modeled field (b), the best method included in our study yields an
average relative vector error En = « |B−b|»/« |B|» of
only 0.02 when all sides are specified and 0.14 for the case where only
the lower boundary is specified, while the total energy in the magnetic
field is approximated to within 2%. The models converge towards the
central, strong input field at speeds that differ by a factor of one
million per iteration step. The fastest-converging, best-performing
model for these analytical test cases is the Wheatland, Sturrock, and
Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann
(2004).
Title: Quantifying the Performance of Force-free Extrapolation
Methods Using Known Solutions
Authors: Barnes, G.; Leka, K. D.; Wheatland, M. S.
Bibcode: 2006ApJ...641.1188B
Altcode:
We outline a method for quantifying the performance of extrapolation
methods for magnetic fields. We extrapolate the field for two
model cases, using a linear force-free approach and a nonlinear
approach. Each case contains a different topological feature of
the field that may be of interest in solar energetic events. We are
able to determine quantitatively whether either method is capable
of reproducing the topology of the field. In one of our examples, a
subjective evaluation of the performance of the extrapolation suggests
that it has performed quite well, while our quantitative score shows
that this is not the case, indicating the importance of being able
to quantify the performance. Our method may be useful in determining
which extrapolation techniques are best able to reproduce a force-free
field and which topological features can be recovered.
Title: An Improved Virial Estimate of Solar Active Region Energy
Authors: Wheatland, M. S.; Metcalf, Thomas R.
Bibcode: 2006ApJ...636.1151W
Altcode: 2005astro.ph..9652W
The MHD virial theorem may be used to estimate the magnetic energy of
active regions on the basis of vector magnetic fields measured at the
photosphere or chromosphere. However, the virial estimate depends on
the measured vector magnetic field being force-free. Departure from the
force-free condition leads to an unknown systematic error in the virial
energy estimate and an origin dependence of the result. We present a
method for estimating the systematic error by assuming that magnetic
forces are confined to a thin layer near the photosphere. If vector
magnetic field measurements are available at two levels in the low
atmosphere (e.g., the photosphere and the chromosphere), the systematic
error may be directly calculated using the observed horizontal and
vertical field gradients, resulting in an energy estimate that is
independent of the choice of origin. If (as is generally the case)
measurements are available at only one level, the systematic error
may be approximated using the observed horizontal field gradients
together with a simple linear force-free model for the vertical
field gradients. The resulting ``improved'' virial energy estimate
is independent of the choice of origin but depends on the choice of
the model for the vertical field gradients, i.e., the value of the
linear force-free parameter α. This procedure is demonstrated for
five vector magnetograms, including a chromospheric magnetogram.
Title: Understanding Solar Flare Statistics
Authors: Wheatland, M. S.
Bibcode: 2005AGUFMSM33E..06W
Altcode:
A review is presented of work aimed at understanding solar flare
statistics, with emphasis on the well known flare power-law size
distribution. Although avalanche models are perhaps the favoured model
to describe flare statistics, their physical basis is unclear, and
they are divorced from developing ideas in large-scale reconnection
theory. An alternative model, aimed at reconciling large-scale
reconnection models with solar flare statistics, is revisited. The
solar flare waiting-time distribution has also attracted recent
attention. Observed waiting-time distributions are described, together
with what they might tell us about the flare phenomenon. Finally,
a practical application of flare statistics to flare prediction is
described in detail, including the results of a year of automated
(web-based) predictions from the method.
Title: Power-spectrum analyses of Super-Kamiokande solar neutrino
data: Variability and its implications for solar physics and neutrino
physics
Authors: Sturrock, P. A.; Caldwell, D. O.; Scargle, J. D.; Wheatland,
M. S.
Bibcode: 2005PhRvD..72k3004S
Altcode: 2004hep.ph....8017S
Since rotational or similar modulation of the solar neutrino flux
would seem to be incompatible with the currently accepted theoretical
interpretation of the solar neutrino deficit, it is important to
determine whether or not such modulation occurs. There have been
conflicting claims as to whether or not power-spectrum analysis
of the Super-Kamiokande solar neutrino data yields indication of
variability. Comparison of these claims is complicated by the fact that
the relevant articles may use different data sets, different methods of
analysis, and different procedures for significance estimation. The
purpose of this article is to clarify the role of power-spectrum
analysis. To this end, we analyze primarily the Super-Kamiokande 5-day
data set, and we use a standard procedure for significance estimation as
used by the Super-Kamiokande collaboration. We then analyze this data
set, with this method of significance estimation, using six methods
of power-spectrum analysis. Five of these have been used in published
articles, and the other is a method that might have been used. We
find that, with one exception, the results of these calculations are
consistent with those of previously published analyses. We find that
the power of the principal modulation (that at 9.43yr-1)
is greater in analyses that take account of error estimates than in
the basic Lomb-Scargle analysis that does not take account of error
estimates. The corresponding significance level ranges between 98%
and 99.3%, depending on the details of the analysis. Concerning the
recent article by Koshio, we find that we can reproduce the results
of his power-spectrum analysis but not the results of his Monte
Carlo simulations, and we have a suggestion that may account for
the difference. We also comment on a recent article by Yoo et al. We
discuss, in terms of subdominant processes, possible neutrino-physics
interpretations of the apparent variability of the Super-Kamiokande
measurements, and we suggest steps that could be taken to resolve the
question of variability of the solar neutrino flux.
Title: A Simple Dynamical Model for Filament Formation in the
Solar Corona
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2005ApJ...630..587L
Altcode:
Filament formation in the solar atmosphere is considered. In the limit
of sub-Alfvénic but supersonic motion, plasma flow in the solar corona
is driven via the induction equation by a slow evolution of force-free
magnetic fields. Methods for solving the relevant magnetohydrodynamic
equations are presented and applied to filament modeling in two and
three dimensions. An illustrative two-dimensional example is given,
which is based on a potential magnetic field with a dip. The example
describes the formation of a normal filament between two bipolar
regions on the Sun. Next a detailed three-dimensional calculation is
presented, which uses linear force-free magnetic fields. The boundary
conditions are chosen to resemble the qualitative ``head-to-tail''
linkage model for the formation of filaments, suggested by Martens &
Zwaan. Consistent with this model, dense formations, reminiscent of
filament pillars, are shown to appear in the corona above the region of
converging and canceling magnetic bipoles. The numerical results are
consistent with the principal role of magnetic field in the dynamical
processes of dense plasma accumulation and support in filaments,
advocated by Martens & Zwaan.
Title: A statistical solar flare forecast method
Authors: Wheatland, M. S.
Bibcode: 2005SpWea...3.7003W
Altcode: 2005SpWea...307003W; 2005astro.ph..5311W
A Bayesian approach to solar flare prediction has been developed which
uses only the event statistics of flares already observed. The method
is simple and objective and makes few ad hoc assumptions. It is argued
that this approach should be used to provide a baseline prediction for
certain space weather purposes, upon which other methods, incorporating
additional information, can improve. A practical implementation of
the method for whole-Sun prediction of Geostationary Observational
Environment Satellite (GOES) events is described in detail and is
demonstrated for 4 November 2003, the day of the largest recorded GOES
flare. A test of the method is described on the basis of the historical
record of GOES events (1975-2003), and a detailed comparison is made
with U.S. National Oceanic and Atmospheric Administration (NOAA)
predictions for 1987-2003. Although the NOAA forecasts incorporate
a variety of other information, the present method outperforms the
NOAA method in predicting mean numbers of event days for both M-X
and X events. Skill scores and other measures show that the present
method is slightly less accurate at predicting M-X events than the
NOAA method but substantially more accurate at predicting X events,
which are important contributors to space weather.
Title: Combined and Comparative Analysis of Power Spectra
Authors: Sturrock, P. A.; Scargle, J. D.; Walther, G.; Wheatland, M. S.
Bibcode: 2005SoPh..227..137S
Altcode: 2005astro.ph..2050S
In solar physics, especially in exploratory stages of research,
it is often necessary to compare the power spectra of two or more
time series. One may, for instance, wish to estimate what the power
spectrum of the combined data sets might have been, or one may wish to
estimate the significance of a particular peak that shows up in two
or more power spectra. One may also on occasion need to search for a
complex of peaks in a single power spectrum, such as a fundamental and
one or more harmonics, or a fundamental plus sidebands, etc. Visual
inspection can be revealing, but it can also be misleading. This
leads one to look for one or more ways of forming statistics,
which readily lend themselves to significance estimation, from two
or more power spectra. We derive formulas for statistics formed from
the sum, the minimum, and the product of two or more power spectra. A
distinguishing feature of our formulae is that, if each power spectrum
has an exponential distribution, each statistic also has an exponential
distribution. The statistic formed from the minimum power of two or more
power spectra is well known and has an exponential distribution. The
sum of two or more powers also has a well-known distribution that is
not exponential, but a simple operation does lead to an exponential
distribution. Concerning the product of two or more power spectra,
we find an analytical expression for the case n = 2, and a procedure
for computing the statistic for n > 2. We also show that some quite
simple expressions give surprisingly good approximations.
Title: Initial Test of a Bayesian Approach to Solar Flare Prediction
Authors: Wheatland, Michael S.
Bibcode: 2005PASA...22..153W
Altcode: 2004astro.ph.10723W
A test of a new Bayesian approach to solar flare prediction is
presented. The approach uses the past history of flaring together
with phenomenological rules of flare statistics to make a prediction
for the probability of occurrence of a large flare within an interval
of time, or to refine an initial prediction (which may incorporate
other information). The test of the method is based on data from the
Geostationary Observational Environmental Satellites, and involves
whole-Sun prediction of soft X-ray flares for 1976-2003. The results
show that the method somewhat over-predicts the probability of all
events above a moderate size, but performs well in predicting large
events.
Title: A Parallel Approach to Nonlinear Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2004ASPC..325..131W
Altcode:
A new procedure for calculating nonlinear force-free fields is briefly
described, which is similar in approach to Sakurai (1981) but which
differs in the method of solution of the problem. The present method is
designed to be implemented on parallel computers. Preliminary results
are shown.
Title: Parallel Construction of Nonlinear Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2004SoPh..222..247W
Altcode:
A numerical approach to calculating nonlinear force-free fields
is presented. The approach is similar to Sakurai (1981) being a
current-field iteration scheme using the integral solution to Ampere's
law (the Biot-Savart law). However, the method of solution presented
here is simpler than Sakurai's approach, in that the field is directly
constructed on a grid without the intermediate solution of a large
system of nonlinear equations. The method also permits straightforward
implementation on parallel computers. Results of applying the method
to a number test cases, including boundary conditions with substantial
currents, are presented.
Title: A Bayesian Approach to Solar Flare Prediction
Authors: Wheatland, M. S.
Bibcode: 2004ApJ...609.1134W
Altcode: 2004astro.ph..3613W
A number of methods of flare prediction rely on classification of
physical characteristics of an active region, in particular optical
classification of sunspots, and historical rates of flaring for a
given classification. However, these methods largely ignore the number
of flares the active region has already produced, in particular the
number of small events. The past history of occurrence of flares (of
all sizes) is an important indicator of future flare production. We
present a Bayesian approach to flare prediction, which uses the flaring
record of an active region together with phenomenological rules of flare
statistics to refine an initial prediction for the occurrence of a big
flare during a subsequent period of time. The initial prediction is
assumed to come from one of the extant methods of flare prediction. The
theory of the method is outlined, and simulations are presented to
show how the refinement step of the method works in practice.
Title: Comparative Analysis of Super-Kamiokande 10-day-bin and
5-day-bin Datasets
Authors: Sturrock, P. A.; Caldwell, D. O.; Scargle, J. D.; Walther,
G.; Wheatland, M. S.
Bibcode: 2004AAS...204.5301S
Altcode: 2004BAAS...36..755S
The Super-Kamiokande Collaboration has released two datasets suitable
for time-series analysis: one packaged in 10-day bins and, more
recently, one packaged in 5-day bins. We have analyzed both datasets by
a likelihood power-spectrum procedure that is to be preferred over the
more usual Lomb-Scargle procedure since it takes account of all of the
available data, whereas the Lomb-Scargle procedure uses only a fraction
of the data. Analysis of these two datasets yields power spectra that
are similar but have some notable differences. Comparative analysis
of these two datasets shows that the significant differences are due
to aliasing. Since each dataset represents highly regular sampling,
a modulation at frequency vM will be accompanied by alias
periodicities at frequencies ěrt vT - vM
ěrt and at vT + vM, where vT is the
sampling frequency. As indications of real oscillations, we have looked
for peaks in the two power spectra which are strong in both, but for
which the power in the 5-day power spectrum is larger than that in
the 10-day power spectrum. This plot identifies three peaks of special
interest. One of these may be attributed to modulation associated with
solar rotation, and the other two may be attributed to modulation
associated with an internal r-mode oscillation. These periodicities
appear to be statistically significant. We thank the Super-Kamiokande
consortium for making these datasets available. This work was supported
by NSF grant AST-0097128 and DOE grant DE-FG03-91ER40618.
Title: Bayesian refinement of solar flare prediction
Authors: Wheatland, M. S.
Bibcode: 2004AAS...204.5415W
Altcode: 2004BAAS...36..760W
A number of methods of flare prediction rely on classification of
physical characteristics of an active region, in particular optical
classification of sunspots, and historical rates of flaring for a given
classification. However these methods largely ignore how many flares
the active region has already produced, in particular the number of
small events. The past history of occurrence of flares (of all sizes)
is an important indicator to future flare production. We present a
Bayesian approach to flare prediction, which uses the past history
of flaring of an active region together with phenomenological rules
of flare statistics to refine an initial prediction for flaring. The
initial prediction may come from one of the extant prediction schemes,
and appears in the method as a prior probability distribution. The
theory of the new method is outlined, and simulations are presented
to show how the refinement step works in practice. Construction of
appropriate prior distributions is also discussed. The author is
supported by an Australian Research Council QEII Fellowship.
Title: Energy Balance in the Corona over the 22 Year Solar Cycle
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2004SoPh..219..265L
Altcode:
Wheatland and Litvinenko (2001) presented a model for dynamical
energy balance in the flaring solar corona which predicts a time
lag between flare occurrence and the supply of energy to the corona
(`driving'). They also suggested that an observed net lag between
flare numbers and sunspot numbers over cycles 21 and 22 might provide
support for the model. Temmer, Veronig, and Hanslmeier (2003) examined
data for five individual solar cycles (19-23) and confirmed a lag
between flare and sunspot numbers for odd solar cycles, but found no
lag for even cycles. Following the suggestion of Temmer, Veronig, and
Hanslmeier, the energy balance model is here extended to incorporate
22-year driving consistent with the phenomenological Gnevyshev—Ohl
rule. The model is found to exhibit a greater lag for the smaller
(even) cycles, in contradiction with the findings of Temmer, Veronig,
and Hanslmeier. A modification to the model is investigated in which
the flaring rate is proportional to the free energy and to the driving
rate for small driving rates, but is proportional only to the free
energy for large driving rates. The modified model can in principle
account for the observations.
Title: Testing Circuit Models for the Energies of Coronal Magnetic
Field Configurations
Authors: Wheatland, M. S.; Farvis, F. J.
Bibcode: 2004SoPh..219..109W
Altcode: 2003astro.ph.11018W
Circuit models involving bulk currents and inductances are often used
to estimate the energies of coronal magnetic field configurations, in
particular configurations associated with solar flares. The accuracy
of circuit models is tested by comparing calculated energies of linear
force-free fields with specified boundary conditions with corresponding
circuit estimates. The circuit models are found to provide reasonable
(order of magnitude) estimates for the energies of the non-potential
components of the fields, and to reproduce observed functional
dependences of the energies. However, substantial departure from
the circuit estimates is observed for large values of the force-free
parameter, and this is attributed to the influence of the non-potential
component of the field on the path taken by the current.
Title: Toward a Reconnection Model for Solar Flare Statistics
Authors: Wheatland, M. S.; Craig, I. J. D.
Bibcode: 2003ApJ...595..458W
Altcode:
A model to account for observed solar flare statistics in terms of
a superposition of independent random flaring elements (assumed to
be sites of magnetic reconnection in the coronal magnetic field
and hence termed ``separators'') is described. A separator of
length l is assumed to flare as a Poisson process in time, with a
rate ν(l) inversely proportional to the Alfvén transit time for
the structure. It is shown that a relationship E~lκ
between the mean energy of events E at a separator and the separator
length implies a relationship E~τκ between individual
waiting times τ and energies E of events at the separator. The most
plausible κ=2 model is found to be compatible with simple pictures for
magnetohydrodynamic energy storage prior to magnetic reconnection in a
current sheet with anomalous (turbulent) resistivity. Formal inversion
of the observed flare frequency-energy distribution is shown to imply
a distribution P(l)~l-1 of the separator lengths in active
regions. A simulation confirms the basic results of the model. It is
also demonstrated that a model comprising time-dependent separator
numbers N=N(t) can reproduce an observed power-law tail in the flare
waiting-time distribution, for large waiting times.
Title: Statistics of the Chi-Square Type, with Application to the
Analysis of Multiple Time-Series Power Spectra
Authors: Sturrock, P. A.; Wheatland, M. S.
Bibcode: 2003astro.ph..7353S
Altcode:
It is often necessary to compare the power spectra of two or more
time series: one may, for instance, wish to estimate what the power
spectrum of the combined data sets might have been, or one may wish
to estimate the significance of a particular peak that shows up in two
or more power spectra. Also, one may occasionally need to search for a
complex of peaks in a single power spectrum, such as a fundamental and
one or more harmonics, or a fundamental plus sidebands, etc. Visual
inspection can be revealing, but it can also be misleading. This
leads one to look for one or more ways of forming statistics, which
readily lend themselves to significance estimation, from two or more
power spectra. The familiar chi-square statistic provides a convenient
mechanism for combining variables drawn from normal distributions, and
one may generalize the chi-square statistic to be any function of any
number of variables with arbitrary distributions. In dealing with power
spectra, we are interested mainly in exponential distributions. One
well-known statistic, formed from the sum of two or more variables
with exponential distributions, satisfies the gamma distribution. We
show that a transformation of this statistic has the convenient
property that it has an exponential distribution. We introduce two
additional statistics formed from two or more variables with exponential
distributions. For certain investigations, we may wish to study the
minimum power (as a function of frequency) drawn from two or more
power spectra. In other investigations, it may be helpful to study
the product of the powers. We give numerical examples and an example
drawn from our solar-neutrino research.
Title: The Coronal Mass Ejection Waiting-Time Distribution
Authors: Wheatland, M. S.
Bibcode: 2003SoPh..214..361W
Altcode: 2003astro.ph..3019W
The distribution of times Δt between coronal mass ejections (CMEs) in
the Large Angle and Spectrometric Coronagraph (LASCO) CME catalog for
the years 1996-2001 is examined. The distribution exhibits a power-law
tail ∼(Δt)γ with an index γ≈−2.36±0.11 for large
waiting times (Δt>10 hours). The power-law index of the waiting-time
distribution varies with the solar cycle: for the years 1996-1998 (a
period of low activity), the power-law index is γ≈−1.86±0.14,
and for the years 1999-2001 (a period of higher activity), the index
is γ≈−2.98±0.20. The observed CME waiting-time distribution,
and its variation with the cycle, may be understood in terms of CMEs
occurring as a time-dependent Poisson process. The CME waiting-time
distribution is compared with that for greater than C1 class solar
flares in the Geostationary Operational Environmental Satellite (GOES)
catalog for the same years. The flare and CME waiting-time distributions
exhibit power-law tails with very similar indices and time variation.
Title: Interpretation of Statistical Flare Data using Magnetic
Reconnection Models
Authors: Craig, I. J. D.; Wheatland, M. S.
Bibcode: 2002SoPh..211..275C
Altcode:
The ability of magnetic reconnection solutions to explain statistical
flare data is discussed. It is assumed that flares occur at
well-defined, isolated sites within an active region, determined by
the null points and separators of the coronal magnetic field (Craig,
2001). Statistical flare observations then derive from a multiplicity
of independent sites, flaring in parallel, that produce events of
widely varying output (Wheatland, 2002). Given that the `separator
length' at an individual site controls the event frequency and the mean
energy release, it is shown that the observed frequency-energy spectrum
N(E)can be inverted to yield a source function that relates directly
to the distribution of separator lengths. It is also pointed out that,
under the parallel flaring model, inferred waiting-time distributions
are naturally interpreted as a superposition of individual point
processes. Only a modest number of flaring separators is required to
mimic a Poisson process.
Title: Understanding Solar Flare Waiting-Time Distributions
Authors: Wheatland, M. S.; Litvinenko, Y. E.
Bibcode: 2002SoPh..211..255W
Altcode:
The observed distribution of waiting times Δt between X-ray solar
flares of greater than C1 class listed in the Geostationary Operational
Environmental Satellite (GOES) catalog exhibits a power-law tail
∼(Δt)γ for large waiting times (Δt>10 hours). It is
shown that the power-law index γ varies with the solar cycle. For
the minimum phase of the cycle the index is γ=−1.4±0.1, and
for the maximum phase of the cycle the index is −3.2±0.2. For
all years 1975-2001, the index is −2.2±0.1. We present a simple
theory to account for the observed waiting-time distributions
in terms of a Poisson process with a time-varying rate λ(t). A
common approximation of slow variation of the rate with respect to a
waiting time is examined, and found to be valid for the GOES catalog
events. Subject to this approximation the observed waiting-time
distribution is determined by f(λ), the time distribution of the rate
λ. If f(λ) has a power-law form ∼λα for low rates,
the waiting time-distribution is predicted to have a power-law tail
∼(Δt)−(3+α) (α>−3). Distributions f(λ) are
constructed from the GOES data. For the entire catalog a power-law index
α=−0.9±0.1 is found in the time distribution of rates for low rates
(λ<0.1 hours−1). For the maximum and minimum phases
power-law indices α=−0.1±0.5 and α=−1.7±0.2, respectively,
are observed. Hence, the Poisson theory together with the observed time
distributions of the rate predict power-law tails in the waiting-time
distributions with indices −2.2±0.1 (1975-2001), −2.9±0.5
(maximum phase) and −1.3±0.2 (minimum phase), consistent with the
observations. These results suggest that the flaring rate varies in an
intrinsically different way at solar maximum by comparison with solar
minimum. The implications of these results for a recent model for flare
statistics (Craig, 2001) and more generally for our understanding of
the flare process are discussed.
Title: Distribution of Flare Energies Based on Independent
Reconnecting Structures
Authors: Wheatland, M. S.
Bibcode: 2002SoPh..208...33W
Altcode:
A model is presented to explain the observed frequency distribution of
flare energies, based on independent flaring at a number of distinct
topological structures (separators) within active-region magnetic
fields. The model is a modification and generalization of a recent
model due to Craig (2001), and reconciles that model with the observed
flare waiting-time distribution, and the observed absence of a flare
waiting-time versus energy relationship. The basic assumptions of the
model are that flares of energy E∼2 occur at separators
of length , and that the frequency of flaring at a separator is
defined by the Alfvén transit time of the structure. To reproduce
the observed distribution of flare energies the model requires a
probability distribution P()∼−1 of separator lengths
within active regions. This prediction of the model is in principle
testable. A theoretical origin for this distribution is also discussed.
Title: Variability of the Solar Neutrino Flux
Authors: Sturrock, P. A.; Scargle, J. D.; Walther, G.; Weber, M. A.;
Wheatland, M. S.
Bibcode: 2002AAS...200.8904S
Altcode: 2002BAAS...34..791S
Several tests of the available data provide evidence for variability of
the solar neutrino flux. The variance of the Homestake measurements is
larger than expected of a constant flux, and varies with heliographic
latitude. The Homestake power spectrum contains a peak at 12.88
y-1 (period 28.4 days), corresponding to a sidereal
rotation frequency of 440 nHz, close to that of the radiative zone. The
power spectrum of GALLEX-GNO data contains the 12.88 y-1
peak and a stronger peak at 13.59 y-1 (period 26.9 days),
corresponding to a sidereal rotation frequency of 462 nHz, that of the
equatorial convection zone at normalized radius 0.85. Further evidence
for time variation comes from the bimodality of the GALLEX-GNO and SAGE
histograms. Joint spectrum analysis of the Homestake and GALLEX-GNO
data yields evidence for the influence of r-mode oscillations [with
l = 3, m = \{1,2,3\}] associated with the same sidereal rotation rate
(13.88 y-1 or 440 nHz) found previously. The periods of these
oscillations (158, 79, and 53 days, respectively) are close to those of
known Rieger-type oscillations, and therefore point to the radiative
zone as the source of these oscillations. A subset of these tests,
selected to be independent, yield results that could arise by chance
from a constant flux with probabilities ranging from 0.1 to 0.0001. If
there are no relevant experimental systematic effects, and if the tests
are valid and statistically independent, the combined estimates yield a
probability of 10-15 that the results are compatible with a
constant flux. A variable flux implies that neutrinos have a significant
magnetic moment, and that neutrino measurements may be used to probe
the Sun's internal magnetic field and internal dynamics. This work
was supported by NASA grants NAS 8-37334 and NAG 5-9784, NSF grant
AST-0097128, and the NASA Applied Information Systems Research Program.
Title: Distribution of Flare Energies Based On Independent
Reconnecting Structures
Authors: Wheatland, M. S.
Bibcode: 2002AAS...200.2909W
Altcode: 2002BAAS...34..682W
An explanation for the observed frequency distribution of flare
energies is given, based on independent flaring at a number of
distinct topological structures (separators) within active region
magnetic fields. The approach modifies and generalises a recent model
due to Craig (2001), and reconciles that model with the observed
flare waiting-time distribution, and the observed absence of a flare
waiting-time vs. energy relationship. The basic assumptions of the
model are that flares of energy E l2 occur at separators
of length l, and that the frequency of flaring at a separator is
defined by the Alfvén transit time of the structure. To reproduce the
observed distribution of flare energies the model requires a probability
distribution P(l) l-1 of separator lengths l within active
regions. This prediction of the model is in principle testable. A
theoretical origin for this distribution is also discussed. The
author acknowledges the support of an Australian Research Council
QEII Fellowship.
Title: Solar Neutrino Flux: Evidence for Intrinsic Variability
Authors: Sturrock, P.; Walther, G.; Weber, M.; Scargle, J.;
Wheatland, M.
Bibcode: 2002APS..APR.X7001S
Altcode:
Analyses of Homestake and GALLEX-GNO data yield persuasive evidence for
rotational modulation and related modulations of the solar neutrino
flux. We find in Homestake data evidence that (1) the variance is
significantly larger than that found in Monte Carlo simulations; (2)
the power spectrum contains a significant peak at 12.88 y-1
(period 28.4 days); (3) the spectrum also contains four sidebands
displaced by ± 1 y-1 and ± 2 y-1; (4) the
variance of the data shows a significant heliographic N/S asymmetry;
(5) a time series reconstructed from power spectrum analysis exhibits a
heliographic-latitude-dependent variance; and (6) the spectrum formed
from the variance of the reconstructed flux has a notable peak at
1 y-1. We find from analysis of GALLEX-GNO data that (7)
there is a significant periodicity at 13.59 y-1 (period
26.9 days); and (8) the histogram is bimodal. From a comparative
analysis of Homestake and GALLEX-GNO data, we find (9) evidence for
variations attributable to r-mode oscillations with l = 3, m = 1,2,3
in a region with synodic rotation rate 12.88 y-1. From
analysis of X-ray data acquired by the SXT instrument on Yohkoh, we
find that the corona exhibits two discrete rotation rates, and that
(10) the coronal rotation frequencies are virtually identical to the
principal frequencies in the Homestake and GALLEX-GNO spectra.
Title: Energy Balance in the Flaring Solar Corona
Authors: Wheatland, M. S.; Litvinenko, Y. E.
Bibcode: 2001AGUFMSH42A0778W
Altcode:
Assuming only that flares derive their energy from a coronal source
and that flaring is the dominant mechanism for depleting that source,
the global coronal response time (time for flares to remove available
coronal energy) is about 9 months. A detailed model for dynamic
energy balance in the solar corona over the solar cycle is presented
to describe how the magnetic free energy in the solar corona varies
in response to changes in the supply of energy to the system and to
changes in the flaring rate. The model predicts that both the flaring
rate and the free energy of the system should lag behind the driving
of the system because of the coronal response time (the model gives a
lag of ~ 11 months). This effect may account for hysteresis phenomena
between certain solar activity indices. For example, analysis of time
series of monthly sunspot numbers and monthly numbers of soft X-ray
flares over the years 1976 to 1999 indicates a tendency for flare
numbers to lag behind sunspot numbers by ~ 6 months.
Title: Rates of Flaring in Individual Active Regions
Authors: Wheatland, M. S.
Bibcode: 2001SoPh..203...87W
Altcode:
Rates of flaring in individual active regions on the Sun during the
period 1981-1999 are examined using United States Air Force/Mount Wilson
(USAF/MWL) active-region observations together with the Geostationary
Operational Environmental Satellite (GOES) soft X-ray flare catalog. Of
the flares in the catalog above C1 class, 61.5% are identified with
an active region. Evidence is presented for obscuration, i.e. that
the increase in soft X-ray flux during a large flare decreases the
likelihood of detection of soft X-ray events immediately following
the large flare. This effect means that many events are missing
from the GOES catalog. It is estimated that in the absence of
obscuration the number of flares above C1 class would be higher by
(75±23) %. A second observational selection effect - an increased
tendency for larger flares to be identified with an active region -
is also identified. The distributions of numbers of flares produced
by individual active regions and of mean flaring rate among active
regions are shown to be approximately exponential, although there are
excess numbers of active regions with low flare numbers and low flaring
rates. A Bayesian procedure is used to analyze the time history of the
flaring rate in the individual active regions. A substantial number
of active regions appear to exhibit variation in flaring rate during
their transit of the solar disk. Examples are shown of regions with
and without rate variation, illustrating the different distributions of
times between events (waiting-time distributions) that are observed. A
piecewise constant Poisson process is found to provide a good model
for the observed waiting-time distributions. Finally, applications of
analysis of the rate of flaring to understanding the flare mechanism
and to flare prediction are discussed.
Title: Energy Balance in the Flaring Solar Corona
Authors: Wheatland, M. S.; Litvinenko, Yuri E.
Bibcode: 2001ApJ...557..332W
Altcode:
Assuming only that flares derive their energy from a coronal source
and that flaring is the dominant mechanism for depleting that source,
the global coronal response time (time for flares to remove available
coronal energy) is about 9 months. A detailed model for dynamic
energy balance in the solar corona over the solar cycle is presented
to describe how the magnetic free energy in the solar corona varies
in response to changes in the supply of energy to the system and to
changes in the flaring rate. The model predicts that both the flaring
rate and the free energy of the system should lag behind the driving
of the system because of the coronal response time (the detailed model
gives a lag of ~11 months). This effect may account for hysteresis
phenomena between certain solar activity indices. A specific example is
presented in support of the model. Analysis of time series of monthly
sunspot numbers and monthly numbers of soft X-ray flares over the
years 1976-1999 indicates a tendency for flare numbers to lag behind
sunspot numbers by ~6 months.
Title: YOHKOH/HXT Evidence for a Hyperhot Loop-Top Source in The
Pre-Impulsive Phase of a Loop Flare
Authors: Uchida, Y.; Wheatland, M. S.; Haga, R.; Yoshitake, I.;
Melrose, D.
Bibcode: 2001SoPh..202..117U
Altcode:
A loop flare that occurred on 22 April 1993 near the disk center is
examined using the Yohkoh Hard X-ray Telescope (HXT). We specifically
looked into the faint early phase of the flare prior to the start of
the strong impulsive phase. The pre-impulsive phase, though weak in
intensity, is expected to contain essential clues to the mechanism
of loop flares according to the causality principle, but it has
not received attention previously, probably due to the insufficient
dynamic range and cadence of observations by the instruments on earlier
satellites. Observations with Yohkoh/HXT can clarify what occurs in
this phase. This flare, like many other flares of this type, shows a
relatively weak emission with a smooth and gradual increase during
this pre-impulsive phase, followed by impulsive bursts, and then
turns into a smooth decay phase without impulsive bursts. First, we
found that the spectrum for the initial smooth rise part is consistent
with a thin-thermal source at a temperature around 80 MK. Imaging of
this phase in the HXT/L and M bands shows a single source between the
footpoint sources that will come up in the impulsive phase following
this phase, suggesting that this hyperhot source is located at a
high part of the loop between the footpoints, since this flare takes
a form of a loop. Furthermore, as we go up to the earliest times of
the flare before this `hyperhot' source phase, two fainter sources
are found near the footpoint sources that will appear later in the
impulsive phase. The spectra of these sources at this earliest time of
the flare, in contrast to the `hyperhot' source, cannot be determined
from the HXT because the instrument was not in flare mode, and HXT/M1,
M2, and H-band data are, unfortunately, not available at this very
initial time. We can guess, however, that they are also of thermal
character because the time profile is smooth without any spikes just as
in the following `hyperhot' thermal phase, and in the post-impulsive
`superhot' thermal phase coming up much later. These findings suggest
that there is an important, and probably dynamic, early phase in loop
flares that has been unnoticed in the still dark pre-impulsive phase,
because the very early footpoint sources change into the loop top
source in a matter of 20-30 s, comparable to the dynamic Alfvén time
scale. Some implications of our new findings are discussed.
Title: The local Poisson hypothesis for solar flares
Authors: Wheatland, M. S.
Bibcode: 2001astro.ph..7147W
Altcode:
The question of whether flares occur as a Poisson process has
important consequences for flare physics. Recently Lepreti et
al. presented evidence for local departure from Poisson statistics
in the Geostationary Operational Environmental Satellite (GOES)
X-ray flare catalog. Here it is argued that this effect arises from
a selection effect inherent in the soft X-ray observations; namely
that the slow decay of enhanced flux following a large flare makes
detection of subsequent flares less likely. It is also shown that the
power-law tail of the GOES waiting-time distribution varies with the
solar cycle. This counts against any intrinsic significance to the
appearance of a power law, or to the value of its index.
Title: Modeling the Rate of Occurrence of Solar Flares
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2001ApJ...550L.109L
Altcode:
Dimensional considerations are used to analyze the distribution of
times between solar flares (the flare waiting-time distribution). An
analytical estimate for the mean flaring rate λ0
is obtained, based on the idea that the rate reflects a balance
between the processes of energy input into the corona and energy
dissipation by flaring. The estimate is shown to be in good agreement
with observations of flares by Geostationary Operational Environmental
Satellite detectors. The analytic result is confirmed using the master
equation (probability balance equation) formalism. Analysis of time
variation leads to a differential equation describing how the free
energy in the corona changes when the rates of driving of the system
and of flaring vary. This equation may be used to describe the global
energy balance in the corona over the solar cycle.
Title: Metastable Magnetic Configurations and Their Significance
for Solar Eruptive Events
Authors: Sturrock, Peter A.; Weber, Mark; Wheatland, Michael S.;
Wolfson, Richard
Bibcode: 2001ApJ...548..492S
Altcode:
Solar flares and coronal mass ejections (CMEs) involve the sudden
release of magnetic energy that can lead to the ejection from the Sun of
large masses of gas with entrained magnetic field. In dynamical systems,
such sudden events are characteristic of metastable configurations that
are stable against small perturbations but unstable to sufficiently
large perturbations. Linear stability analysis indicates whether
or not the first requirement is met, and energetic analysis can
indicate whether or not the second requirement is met: if a magnetic
configuration that is stable against small perturbations can make a
transition to a lower energy state, then it is metastable. In this
paper, we consider a long twisted flux tube, anchored at both ends
in the photosphere and restrained by an overlying magnetic arcade. We
argue from a simple order-of-magnitude calculation that, for appropriate
parameter values, it is energetically favorable for part of the flux
tube to erupt into interplanetary space, even when the configuration
is stable according to linear MHD stability theory. The properties
of metastable magnetic configurations may be relevant to CMEs and to
other explosive astrophysical events such as solar flares.
Title: A Test to Confirm the Source of Energy for Solar Flares
Authors: Wheatland, M. S.
Bibcode: 2001PASA...18..351W
Altcode:
A test of the hypothesis that flares derive their energy from
large scale current systems inferred from active region vector
magnetograms is proposed. The test involves a statistical comparison
of the flare-related change in coronal magnetic energy (based on
the magnetohydrodynamic virial theorem) and an independent measure
of the energy of the flare. A simulation suggests that - assuming
the hypothesis is correct - the test requires around 50 flares with
energy greater than 5×1023 J to return a significant
result. Existing archives of vector magnetograms should provide
sufficient data for such a study.
Title: The Origin of the Solar Flare Waiting-time Distribution
Authors: Wheatland, M. S.
Bibcode: 2000SPD....31.0256W
Altcode: 2000BAAS...32.1291W
It was recently pointed out that the distribution of times between
solar flares (the flare waiting-time distribution) follows a power
law, for long waiting times. Based on 25 years of soft X-ray flares
observed by Geostationary Operational Environmental Satellite (GOES)
instruments it is shown that 1. the waiting-time distribution of
flares is consistent with a time-dependent Poisson process, and
2. the fraction of time the Sun spends with different flaring rates
approximately follows an exponential distribution. The second result
is a new phenomenological law for flares. It is shown analytically how
the observed power-law behavior of the waiting times originates in the
exponential distribution of flaring rates. These results are argued
to be consistent with a non-stationary avalanche model for flares.
Title: An Optimization Approach to Reconstructing Force-free Fields
Authors: Wheatland, M. S.; Sturrock, P. A.; Roumeliotis, G.
Bibcode: 2000ApJ...540.1150W
Altcode:
A new method for reconstructing force-free magnetic fields from their
boundary values, based on minimizing the global departure of an initial
field from a force-free and solenoidal state, is presented. The method
is tested by application to a known nonlinear solution. We discuss
the obstacles to be overcome in the application of this method to the
solar case: the reconstruction of force-free fields in the corona from
measurements of the vector magnetic field in the low atmosphere.
Title: The Origin of the Solar Flare Waiting-Time Distribution
Authors: Wheatland, M. S.
Bibcode: 2000ApJ...536L.109W
Altcode: 2000astro.ph..5121W
It was recently pointed out that the distribution of times between solar
flares (the flare waiting-time distribution) follows a power law for
long waiting times. Based on 25 years of soft X-ray flares observed by
Geostationary Operational Environmental Satellite instruments, it is
shown that (1) the waiting-time distribution of flares is consistent
with a time-dependent Poisson process and (2) the fraction of time
the Sun spends with different flaring rates approximately follows an
exponential distribution. The second result is a new phenomenological
law for flares. It is shown analytically how the observed power-law
behavior of the waiting times originates in the exponential distribution
of flaring rates. These results are argued to be consistent with a
nonstationary avalanche model for flares.
Title: Flare Frequency-Size Distributions for Individual Active
Regions
Authors: Wheatland, M. S.
Bibcode: 2000ApJ...532.1209W
Altcode:
It is well known that the size (peak count rate of emission, or
inferred energy) distribution of flares observed on the Sun follows
a power law. However, the distributions that are constructed include
flares from different active regions that have a variety of physical
properties. In this paper cumulative peak count rate distributions
are constructed for individual active regions using events listed in
the WATCH solar X-ray burst catalog. The individual distributions are
found to be consistent with the distribution constructed from events
in all active regions named in the catalog. This result suggests that
the flare power-law size distribution reflects an intrinsic property
of the flare mechanism and is not a product of the distributions of
physical parameters between active regions. The result is consistent
with the avalanche model for flares and more generally argues against
macroscopic flare models.
Title: Are Electric Currents in Solar Active Regions Neutralized?
Authors: Wheatland, M. S.
Bibcode: 2000ApJ...532..616W
Altcode:
Models for energy storage in the solar corona due to the twisting of
coronal magnetic fields by subphotospheric flows imply that coronal
currents should be neutralized (i.e., observed currents over a given
polarity of the magnetic field should sum to zero). The neutralized
current hypothesis is quantitatively tested by examining vector
magnetic field data from 21 active regions observed by the Solar
Magnetic Field Telescope of the Huairou Solar Observing Station of
Beijing Astronomical Observatory. For each active region, the current
over the positive polarity of the field, I+, is estimated,
as well as the current over the negative polarity, I-, and
the total current over both polarities, Itot. In no case
is the total current Itot significantly different from
zero. The currents I+ and I- are found to be
significantly different from zero (at the 3 σ level) in more than half
of the active regions studied, implying that large-scale currents in
active regions are typically unneutralized. The implications of this
result and the relationship of this study to related studies (e.g.,
of current helicity) are discussed.
Title: Do Solar Flares Exhibit AN Interval-Size Relationship?
Authors: Wheatland, M. S.
Bibcode: 2000SoPh..191..381W
Altcode:
Some models for flare statistics predict or assume that there is
a relationship between the times between flares and the energy of
flares. This question is examined observationally using the WATCH
solar X-ray burst catalogue. A rank correlation test applied to the
data finds strong evidence for a correlation between the time since the
last event, tb, and the size (peak count rate) of an event,
and for a correlation between the time to the next event, ta,
and the size of an event. A more sophisticated statistical test, taking
into account a probable bias in event selection, does not support the
hypothesis that event size depends on tb or ta.
Title: Models for Flare Statistics and the Waiting-time Distribution
of Solar Flare Hard X-ray Bursts
Authors: Wheatland, M. S.; Edney, S. D.
Bibcode: 1999spro.proc..357W
Altcode:
In a previous study (Wheatland, Sturrock, McTiernan 1998), a
waiting-time distribution was constructed for solar flare hard X-ray
bursts observed by the ICE/ISEE-3 spacecraft. A comparison of the
observed distribution with that of a time-dependent Poisson process
indicated an overabundance of short waiting times (10~s -- 10~min),
implying that the hard X-ray bursts are not independent events. Models
for flare statistics assume or predict that flares are independent
events -- in particular the avalanche model makes this specific
prediction. The results of the previous study may be reconciled with
the avalanche picture if individual flares produce several distinct
bursts of hard X-ray emission. A detailed comparison of the avalanche
model and the ICE/ISEE-3 waiting-time distribution is presented here.
Title: Rotational Signature and Possible R-Mode Signature in the
GALLEX Solar Neutrino Data
Authors: Sturrock, P. A.; Scargle, J. D.; Walther, G.; Wheatland, M. S.
Bibcode: 1999ApJ...523L.177S
Altcode: 1999astro.ph..4278S
Recent analysis of the Homestake data has yielded evidence that the
solar neutrino flux varies in time--more specifically, that it exhibits
a periodic variation that may be attributed to rotational modulation
occurring deep in the solar interior, either in the tachocline or
in the radiative zone. Here we present a spectral analysis of the
GALLEX data that yields supporting evidence for this rotational
modulation. The most prominent peak in the power spectrum occurs
at the synodic frequency of 13.08 yr-1 (cycles per year)
and is estimated to be significant at the 0.1% level. It appears that
the most likely interpretation of this modulation is that the electron
neutrinos have nonzero magnetic moment, so that they oscillate between
left-hand (detectable) and right-hand (nondetectable) chiralities
as they traverse the Sun's internal magnetic field. This oscillation
could account for the neutrino deficit. The second strongest peak in
the GALLEX spectrum has a period of 52 days, and this period occurs
in other solar data as well. We suggest that this periodicity and also
the Rieger 154 day periodicity, which shows up in many solar parameters
and in the Homestake data, are due to r-mode oscillations.
Title: Frequency-energy distributions of flares and active region
transient brightenings
Authors: Wheatland, M. S.; Uchida, Y.
Bibcode: 1999SoPh..189..163W
Altcode:
In 1988, Uchida and Shibata proposed a model for compact loop
flares as due to the collision of two large amplitude torsional
Alfvén wave packets coming up along a coronal magnetic loop,
leaking out from the subphotospheric convective layers of the solar
atmosphere. We investigate the possibility that active region transient
brightenings occur when a single torsional Alfvén wave packet transits
a coronal loop. Assuming this related origin for flares and transient
brightenings, the statistics of the two phenomena must also be closely
related. It is shown that the observed power-law frequency-energy
distributions of flares and transient brightenings may be accounted
for in a natural way if the energy distribution of the underlying
torsional Alfvén wave packets is itself a power law.
Title: A Better Linear Force-free Field
Authors: Wheatland, M. S.
Bibcode: 1999ApJ...518..948W
Altcode:
Linear force-free fields are often used as approximate models for
magnetic fields in the solar corona, calculated on the basis of boundary
values measured in the low atmosphere. The problem that is set up and
solved does not have a unique solution, however, and various particular
solutions--motivated in large part by mathematical convenience--appear
in the literature. A method is presented for calculating the linear
force-free field that is consistent with the observed component of
the magnetic field normal to the solar surface and has a minimum
difference between the components tangent to the surface and the
observed tangential field. The method is tested by application to a
known nonlinear solution.
Title: Topological Differences Between Force-Free Field Models
Authors: Hudson, T. S.; Wheatland, M. S.
Bibcode: 1999SoPh..186..301H
Altcode:
The potential and linear force-free field models for the magnetic field
in the solar corona are often used in the analysis of flares. The
field is calculated using boundary values measured in the low solar
atmosphere. The topology of the field calculated using these models
is then compared to the position of flare emissions. We demonstrate
that the topology of the field according to each of these models,
with the same boundary conditions in place, is not in general even
qualitatively equivalent. An argument is given for a similar discrepancy
between a linear force-free field solution and a nonlinear force-free
field solution.
Title: Rotational and Related Periodicities in the Homestake and
GALLEX Neutrino Data
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1999HEAD....4.3908S
Altcode: 1999BAAS...31..743S
If neutrinos have a sufficiently strong magnetic moment, the solar
neutrino flux will be modulated by the Sun's internal magnetic field. We
have spectrum-analyzed the Homestake data, looking for evidence of
periodic modulation in the range 12.6 - 13.3 y(-1) due to structures
in the radiative zone that has a sidereal rotation rate in the range
13.6 - 14.3 y(-1) . We find a peak at 12.88 y(-1) . The estimated
probability of finding such a peak in the search band by chance is
about 3%. We also find sidebands at 11.88, 12.88, 14.88 and 15.88 y(-1)
, attributable to a seasonal modulation due to the tilt of the solar
axis. The estimated probability of this combination occurring by chance
is about 0.2%. We have more recently examined the GALLEX data and find
that the strongest peak in the range 1 to 20 cycles per year occurs
at 13.10 y(-1) , close to the value found in the Homestake data. The
estimated probability of finding such a periodicity in the search band
by chance is less than 0.1%. There is evidence for some other well
known solar periodicities in the neutrino data: a peak at 2.32 cycles
per year (period = 157 days) in the Homestake data, and a peak at 7.00
cycles per year (period = 52 days) in the GALLEX data. We propose that
these periodicities [together with another well known periodicity at
4.67 cycles per year (period = 78 days)] are due to internal r-mode
oscillations. We suggest that these modulations in the neutrino flux may
be understood in terms of the RSFP (resonant spin flavor precession)
mechanism proposed by Akhmedov and others. This interpretation leads
to an estimate of Delta m(2) and to a lower limit for the neutrino
magnetic moment. This work was supported in part by Air Force grant
F49620-95-1-008 and NASA grants NAS 8-37334 and NAGW-5-4038.
Title: The Waiting-Time Distribution of Solar Flare Hard X-Ray Bursts
Authors: Wheatland, M. S.; Sturrock, P. A.; McTiernan, J. M.
Bibcode: 1998ApJ...509..448W
Altcode:
A waiting-time distribution is constructed for 8 yr of solar flare
hard X-ray bursts observed by the ICE/ISEE 3 spacecraft. The observed
distribution is compared with a simulated waiting-time distribution
produced by a time-dependent Poisson process constructed using rates
estimated from the observations. The observed distribution shows an
overabundance of short waiting times (10 s-10 minutes) in comparison
with the simulation. This result implies that the hard X-ray bursts
are not independent events. The implications of this result for the
existence of sympathetic flaring and to models of flare statistics are
discussed, and the result is compared with previous determinations of
waiting-time distributions for solar hard X-ray events.
Title: Apparent Latitudinal Modulation of the Solar Neutrino Flux
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1998ApJ...507..978S
Altcode:
We examine the solar neutrino flux, as measured by the Homestake
neutrino detector, to search for evidence of a dependence upon the
solar latitude of the Earth-Sun line that varies from 7.25d south in
mid-March to 7.25d north in mid-September. Although the flux does
not obviously show any dependence on latitude, we do find evidence
for a dependence of the variance of the flux upon latitude. When
data from 108 runs of the Homestake experiment are divided into four
quartiles, sorted according to latitude, we find that the northernmost
quartile exhibits a larger variance than the other three. By applying
the shuffle test, we estimate the probability that this could have
occurred by chance to be in the range 1%-2%. For more detailed
information, we examine a ``reconstructed flux'' formed from our recent
maximum likelihood spectrum analysis. This procedure indicates that
the variance is largest at about 6.5d north. We also find that the
spectrum of the variance of the reconstructed flux has a notable peak
at 1 cycle y-1 tending to confirm a latitude dependence of
the variance. We also examine the 12.88 cycle yr periodicity described
in our recent paper and find that the amplitude of the periodicity is
greater for the northernmost quartile than for the other quartiles. We
suggest that these effects may be attributed to resonant spin-flavor
precession of left-hand-helicity electron neutrinos in the magnetic
field of the solar radiative zone.
Title: Flare Frequency Distributions Based on a Master Equation
Authors: Wheatland, M. S.; Glukhov, S.
Bibcode: 1998ApJ...494..858W
Altcode:
The Rosner & Vaiana model for flares is generalized to allow
for flares that do not deplete all free energy from the system, a
step that overcomes a number of objections to the original model. We
obtain a probability balance equation, or master equation, describing
the free energy E of an active region subject to a prescribed growth
rate, Ė, and a prescribed distribution, α(E), of stochastic decay
events. We argue that the solution appropriate to flares involves an
energy-independent growth rate and a power-law form for α(E), which may
be the result of an underlying avalanche process. The resulting model
produces power-law flare frequency distributions below a high-energy
rollover corresponding to the largest energy the system is likely to
attain, which is set by the balance between the rate of growth and the
rate of stochastic decay. There is a close correspondence between the
resulting model and the avalanche model for flares.
Title: Search for Periodicities in the Homestake Solar Neutrino Data
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1997ApJ...491..409S
Altcode:
We evaluate a χ2 statistic to test against the Homestake
data the hypothesis that the neutrino flux from the Sun is constant. We
use estimates of standard deviations derived 1000 simulations of the
sequence of 108 runs, and we also use two procedures for deriving
proxies for the standard deviation from the experimental data. All
tests indicate that the hypothesis should be rejected; the significance
level ranges from 5.8% to 0.1%. We also search for evidence of
periodicities in the neutrino flux by evaluating the log likelihood of
finding the actual count rates in a model in which the neutrino flux
is modulated with a sinusoidal term. We consider a range of values of
the frequency (0-20 cycles yr-1) and, for each frequency,
adjust the modulation parameters to maximize the likelihood. We find
no evidence of modulation at the frequency of the solar cycle. A 1000
shuffle test and 1000 simulations using error estimates taken from the
simulations yield no evidence for either the quasi-biennial (2.2 yr)
periodicity or the Rieger (157 day) periodicity. However, simulations
based on the experimental error estimates yield significance levels
of 1% and 2.7% for the quasi-biennial periodicity, and 2% and 0.2%
for the Rieger periodicity. We have also looked for evidence
of modulation at a frequency that might be related to the solar
rotation frequency. We have adopted a search band of 12.4-13.1 cycles
yr-1, corresponding to the 1 year lower sideband (synodic
frequency) of the rotation frequency of the Sun's radiative zone, as
estimated from helioseismology. There is indeed a peak in that band,
at 12.88 cycles yr-1, that according to the simulation test
is significant at the 3% level. However, we also find evidence of four
sidebands near 10.88, 11.88, 13.88, and 14.88 cycles yr-1
that may be due to the departure of the rotational axis from the
normal to the ecliptic. We introduce a correlation measure formed
from the powers at a ``fundamental'' and at four sidebands. None of
1000 shuffle tests, and only one of 1000 simulations, yield values of
the correlation measure as large as that formed from the experimental
data. These tests offer support, at the 0.1% and 0.2% significance
level, respectively, for the proposition that the neutrino flux
is modulated at a frequency that could be the synodic frequency
corresponding to a sidereal rotational frequency of 13.88 cycles
yr-1 (440 nHz) of the Sun's radiative zone.
Title: Search for Periodicities in the Homestake Solar Neutrino Data
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1997BAAS...29.1121S
Altcode:
No abstract at ADS
Title: Test for Constancy of the Solar Neutrino Flux as Measured by
the Homestake Neutrino Experiment
Authors: Walther, G.; Sturrock, P. A.; Wheatland, M. S.
Bibcode: 1997BAAS...29.1121W
Altcode:
No abstract at ADS
Title: Coronal Heating and the Vertical Temperature Structure of
the Quiet Corona
Authors: Wheatland, M. S.; Sturrock, P. A.; Acton, L. W.
Bibcode: 1997ApJ...482..510W
Altcode:
The radial variation of temperature in the inner corona is examined
using long-exposure Yohkoh images of two regions of diffuse (quiet)
corona. The results indicate a steady radial increase of temperature for
both regions, out to 0.7 and 0.95 solar radii above the limb. We find
that the filter-ratio data for the two regions is well fitted in each
case by integration over the line of sight of a spherically symmetric
model atmosphere in hydrostatic equilibrium and with a temperature
profile due to a conserved inward heat flux. An Abel inversion process
is also applied to the data, and this gives results consistent with
the spherically symmetric, conserved-heat flux model. These results
imply that the nonthermal energy responsible for heating these regions
of the quiet corona is being deposited beyond the observed range of
heights. However, the diffuse regions we examined are believed to be
partly closed-field regions, and so, the radial models require careful
interpretation. We discuss the implications for coronal heating in
these regions.
Title: An optimization approach to reconstructing force-free fields
from boundary data: II. Numerical results
Authors: Wheatland, M. S.; Roumeliotis, G.
Bibcode: 1997SPD....28.1604W
Altcode: 1997BAAS...29..920W
The reconstruction of force-free fields from boundary data is an
important problem in solar physics. Reliable reconstructions of fields
in active regions may allow detailed tests of existing theories of the
physics of solar flares and of coronal heating. A new method, based on
minimizing a global objective function describing the departure from
a force-free and solenoidal state, has been presented in a talk at
this meeting. A computer code to reconstruct arbitrary 3-d fields from
boundary data, based on this approach, has been written and is being
tested. We describe the details of the implementation of the method
and the numerical results obtained. The method has been tested against
known analytic force-free solutions, which highlight the advantages
and shortcomings of our approach. We also describe the application
of the method to real boundary data, and outline particular physical
problems that we hope to address with our code. This work was supported
in part by Air Force grant F49620-95-1-008 and NASA grants NAS 8-37334
and NAGW-2265.
Title: An optimization approach to reconstructing force-free fields
from boundary data: I. Theoretical basis.
Authors: Roumeliotis, G.; Wheatland, M. S.
Bibcode: 1997SPD....28.1603R
Altcode: 1997BAAS...29..920R
The reconstruction of force-free fields from boundary data is an
important problem in solar physics. Reliable reconstructions of fields
in active regions may allow detailed tests of existing theories of the
physics of solar flares and of coronal heating. A new method, based on
minimizing a global objective function describing the departure from
a force-free and solenoidal state, will be presented in this talk. A
computer code to reconstruct arbitrary 3-d fields from boundary data,
based on this approach, has been written and will be described in
another talk at this meeting. This work was supported in part by Air
Force grant F49620-95-1-008 and NASA grants NAS 8-37334 and NAGW-2265.
Title: Avalanche Models of Solar Flares and the Distribution of
Active Regions
Authors: Wheatland, M. S.; Sturrock, P. A.
Bibcode: 1996ApJ...471.1044W
Altcode:
Avalanche models of solar flares successfully reproduce the power-law
distribution of flare frequency as a function of energy. However,
the model distributions have been produced for a single numerical
grid, representing a single active region on the Sun. Here we
convolve the distribution owing to an avalanche grid with each of
two observationally determined active region size distributions. The
resulting energy distributions are power laws (with index α ≍ 1.5)
below about 1031 ergs, but they gradually steepen with
energy. The resulting distributions are compared with a flare energy
distribution derived from International Cometary Explorer satellite
observations. Qualitative agreement is found between the model and
observed distributions, although the observations favor a simple
power-law model distribution with a somewhat steeper index (≍1.71).
Title: Coronal Heating in the Quiet Corona
Authors: Wheatland, M.; Sturrock, P.
Bibcode: 1996AAS...188.3308W
Altcode: 1996BAAS...28Q.869W
The radial variation of temperature in the inner corona is examined
using long exposure Yohkoh images for two regions of diffuse (quiet)
corona. The results indicate a steady radial increase of temperature
for both regions, out to 0.7 and 0.9 solar radii above the limb,
respectively. We find that the filter ratio data for the two regions
is well fitted in each case by integration over the line of sight
of a model radial atmosphere in hydrostatic equilibrium and with
a temperature profile due to a conserved inward heat flux. An Abel
inversion process is also applied to the data, and this gives results
consistent with the radially symmetric, conserved heat flux model. These
results imply that the non-thermal energy responsible for heating these
pieces of the quiet corona is being deposited beyond the observed range
of heights. However, the diffuse regions we examined are believed to be
mainly closed field regions, and so the radial models require careful
interpretation. We discuss the implications for coronal heating in these
regions, and compare this result with other recent determinations of
the temperature in the inner corona. This work was supported in part
by NASA grant NAS 8-37334. The authors acknowledge also support from
Air Force grant F49620-95-1-0008 and NASA grant NAGW-2265.
Title: Yokhoh Soft X-Ray Telescope Images of the Diffuse Solar Corona
Authors: Sturrock, P. A.; Wheatland, M. S.; Acton, L. W.
Bibcode: 1996ApJ...461L.115S
Altcode:
During the interval 1992 May 3--15, an extended region (out to 1.5
solar radii) of diffuse, stable corona crossed the northeast limb
of the Sun. This region underlaid a coronal streamer as revealed by
the Mauna Loa Coronagraph of the High Altitude Observatory. During
this passage, the soft X-ray telescope on Yohkoh obtained a number of
high-quality pairs of images, closely spaced in time, through the two
thinnest analysis filters. Analysis of these data indicates that (1)
the temperature increases steadily with height and (2) the variation
of temperature with radius is consistent with a conserved inward
heat flux. These results imply that the magnetic field configuration
was substantially open out to 1.5 solar radii and that there was no
significant coronal heating below that height in that region. It appears
that this region was being heated by nonthermal energy deposited beyond
1.5 solar radii.
Title: Interpretation of SXT Data Concerning the Diffuse Corona
Authors: Sturrock, P. A.; Wheatland, M. S.; Acton, L. W.
Bibcode: 1996mpsa.conf..417S
Altcode: 1996IAUCo.153..417S
No abstract at ADS
Title: Energy Release in a Prominence-Loaded Flaring Loop
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1995SoPh..159..137W
Altcode:
Zaitsev and Stepanov (1991, 1992) proposed a mechanism for energy
release in solar flares that involves the intrusion of dense prominence
material into a coronal loop. The resulting non-steady state conditions
are claimed to increase the resistance of the loop by 8-10 orders of
magnitude. It is shown here that the dramatic increase in resistance
calculated by Zaitsev and Stepanov depends on a gross overestimate of
the of the magnitude of the magnetic force in the loop prior to the
flare trigger. A more realistic estimate of the increase due to the
mechanism suggests that it is by no more than about four orders of
magnitude. As a consequence, the `prominence-loading` mechanism does
not provide a tenable flare model.
Title: Interpreting YOHKOH Hard and Soft X-Ray Flare Observations
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1995SoPh..158..283W
Altcode:
A simple model is presented to account for theYohkoh flare observations
of Feldmanet al. (1994), and Masuda (1994). Electrons accelerated by
the flare are assumed to encounter the dense, small regions observed
by Feldmanet al. at the tops of impulsively flaring coronal magnetic
loops. The values of electron density and volume inferred by Feldmanet
al. imply that these dense regions present an intermediate thick-thin
target to the energised electrons. Specifically, they present a
thick (thin) target to electrons with energy much less (greater)
thanEc, where 15 keV <Ec < 40 keV. The
electrons are either stopped at the loop top or precipitate down
the field lines of the loop to the footpoints. Collisional losses
of the electrons at the loop top produce the heating observed by
Feldmanet al. and also some hard X-rays. It is argued that this is the
mechanism for the loop-top hard X-ray sources observed in limb flares
by Masuda. Adopting a simple model for the energy losses of electrons
traversing the dense region and the ambient loop plasma, hard X-ray
spectra are derived for the loop-top source, the footpoint sources
and the region between the loop top and footpoints. These spectra
are compared with the observations of Masuda. The model spectra are
found to qualitatively agree with the data, and in particular account
for the observed steepening of the loop-top and footpoint spectra
between 14 and 53 keV and the relative brightnesses of the loop-top
and footpoint sources.
Title: Coronal Hard X-ray Sources in Solar Flares
Authors: Wheatland, M. S.; Sturrock, P. A.
Bibcode: 1995SPD....26.1321W
Altcode: 1995BAAS...27..991W
No abstract at ADS
Title: Some topics in the physics of solar flares
Authors: Wheatland, Michael Scott
Bibcode: 1995PhDT.......189W
Altcode:
No abstract at ADS
Title: Alfvenic fronts and the turning-off of the energy release in
solar flares
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1994PASA...11...25W
Altcode: 1994PASAu..11...25W
The effect of impulsively turning off the dissipation in an existing
model for energy propagation through Alfvenic fronts into the coronal
site of enerrgy release in a solar flare is examined. In the optimum
case of impedance matching, the flux tube re-stresses on a much longer
timescale than it relaxes, suggesting an explanation for the timescales
observed in homologous flares.
Title: Cross-field current closure below the solar photosphere
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1994AuJPh..47..361W
Altcode:
A simple model is developed to describe how an externally imposed
current closes as a function of time below the photosphere. A
vertical current density is assumed to turn on at the photospheric
boundary. The model implies that the subsequent closure of the current
in the sub-photosphere depends only on the ratio RA/R,
where RA = muoVA is the Alfvenic
impedance of the photosphere and R = 1/sigmaP is the
resistance corresponding to the conductivity sigmaP and
a characteristic length l. For RA/R much greater than
1, current closure occurs at a front, propagating with the Alfven
speed. For RA/R much less than 1, current closure is a
diffusive process ahead and behind a slowly propagating Alfvenic
front. The first case is the relevant one for the Sun, where
RA/R as approximately 108/VA, for
VA in kilometers per second.