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Author name code: stix
ADS astronomy entries on 2022-09-14
author:"Stix, Michael"
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Title: Solar Global Parameters; Solar Interior
Authors: Stix, Michael
2009LanB...4B....1S Altcode: 2009LanB...4B.4111S
No abstract at ADS
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Title: Book Review
Authors: Stix, Michael
2008GApFD.102..541S Altcode:
No abstract at ADS
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Title: Meridional Circulation and Global Solar Oscillations
Authors: Roth, M.; Stix, M.
2008SoPh..251...77R Altcode: 2007arXiv0710.1773R; 2008SoPh..tmp..130R
We investigate the influence of large-scale meridional circulation on
solar p modes by quasi-degenerate perturbation theory, as proposed by
Lavely and Ritzwoller (Roy. Soc. Lond. Phil. Trans. Ser. A339, 431,
1992). As an input flow we use various models of stationary meridional
circulation obeying the continuity equation. This flow perturbs the
eigenmodes of an equilibrium model of the Sun. We derive the signatures
of the meridional circulation in the frequency multiplets of solar
p modes. In most cases the meridional circulation leads to negative
average frequency shifts of the multiplets. Further possibly observable
effects are briefly discussed.
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Title: Meridional Circulation and Global Solar Oscillations
Authors: Roth, M.; Stix, M.
2008ESPM...12..3.1R Altcode:
We investigate the influence of large-scale meridional circulation on
solar p-modes by quasi-degenerate perturbation theory, as proposed by
Lavely & Ritzwoller, 1992 (Roy. Soc. Lon. Phil. Trans. Ser. A, 339,
431). As an input flow we use various models of stationary meridional
circulation obeying the continuity equation. This flow perturbs the
eigenmodes of an equilibrium model of the Sun. We derive the signatures
of the meridional circulation in the frequency multiplets of solar
p modes. In most cases the meridional circulation leads to negative
average frequency shifts of the multiplets. Further possibly observable
effects are briefly discussed.
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Title: Effects of rotation and input energy flux on convective
overshooting
Authors: Käpylä, Petri J.; Korpi, M. J.; Stix, M.; Tuominen, I.
2007IAUS..239..437K Altcode: 2006astro.ph..9350K
We study convective overshooting by means of local 3D convection
calculations. Using a mixing length model of the solar convection
zone (CZ) as a guide, we determine the Coriolis number (Co), which
is the inverse of the Rossby number, to be of the order of ten or
larger at the base of the solar CZ. Therefore we perform convection
calculations in the range Co = 0...10 and interpret the value of Co
realised in the calculation to represent a depth in the solar CZ. In
order to study the dependence on rotation, we compute the mixing length
parameters alpha_T and alpha_u relating the temperature and velocity
fluctuations, respectively, to the mean thermal stratification. We
find that the mixing length parameters for the rapid rotation case,
corresponding to the base of the solar CZ, are 3-5 times smaller than
in the nonrotating case. Introducing such depth-dependent alpha into
a solar structure model employing a non-local mixing length formalism
results in overshooting which is approximately proportional to alpha
at the base of the CZ. Although overshooting is reduced due to the
reduced alpha, a discrepancy with helioseismology remains due to the
steep transition to the radiative temperature gradient. In comparison
to the mixing length models the transition at the base of the CZ is
much gentler in the 3D models. It was suggested recently (Rempel 2004)
that this discrepancy is due to the significantly larger (up to seven
orders of magnitude) input energy flux in the 3D models in comparison
to the Sun and solar models, and that the 3D calculations should be
able to approach the mixing length regime if the input energy flux is
decreased by a moderate amount. We present results from local convection
calculations which support this conjecture.
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Title: Reynolds stresses and meridional circulation from rotating
cylinder simulations
Authors: Hupfer, C.; Käpylä, P. J.; Stix, M.
2006A&A...459..935H Altcode:
Aims.The latitude and depth dependences of Reynolds stresses are
obtained from numerical simulations of a solar-type convection zone
where the star is assumed to rotate with a uniform angular velocity.<BR
/> Methods: .A two-dimensional model, using a cylindrical annulus
with axis perpendicular to the axis of rotation, is introduced as an
approximation of a spherical section along the meridional plane. We
solve the fully compressible Navier-Stokes equations numerically and use
Cartesian and cylindrical geometries to simulate convection under the
influence of rotation.<BR /> Results: .For moderate Coriolis numbers
both models yield strong extrema of the Reynolds stress component
Q<SUB>θϕ</SUB> at low latitudes near the equator, and a meridional
cell pattern is found in the cylindrical model. For Coriolis numbers
larger than about 10 the flow becomes aligned with the direction of
the rotation axis.<BR />
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Title: Magnetoconvection and dynamo coefficients. III. α-effect
and magnetic pumping in the rapid rotation regime
Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Stix, M.
2006A&A...455..401K Altcode: 2006astro.ph..2111K
Aims.The α- and γ-effects, which are responsible for the generation
and turbulent pumping of large scale magnetic fields, respectively,
due to passive advection by convection are determined in the rapid
rotation regime corresponding to the deep layers of the solar convection
zone.<BR />Methods.A 3D rectangular local model is used for solving the
full set of MHD equations in order to compute the electromotive force
(emf), E = overline {u × b}, generated by the interaction of imposed
weak gradient-free magnetic fields and turbulent convection with varying
rotational influence and latitude. By expanding the emf in terms of the
mean magnetic field, E<SUB>i</SUB> = a<SUB>ij</SUB> overline B_j, all
nine components of a<SUB>ij</SUB> are computed. The diagonal elements
of a<SUB>ij</SUB> describe the α-effect, whereas the off-diagonals
represent magnetic pumping. The latter is essentially the advection
of magnetic fields by means other than the underlying large-scale
velocity field. Comparisons are made to analytical expressions of the
coefficients derived under the first-order smoothing approximation
(FOSA).<BR />Results.In the rapid rotation regime the latitudinal
dependence of the α-components responsible for the generation of the
azimuthal and radial fields does not exhibit a peak at the poles, as
is the case for slow rotation, but at a latitude of about 30°. The
magnetic pumping is predominantly radially down- and latitudinally
equatorward as in earlier studies. The numerical results compare
surprisingly well with analytical expressions derived under first-order
smoothing, although the present calculations are expected to lie near
the limits of the validity range of FOSA.<BR />
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Title: Alpha-Effect and Turbulent Pumping In The Rapid Rotation
Regime - Implications For Solar Dynamo Models
Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Stix, M.;
Tuominen, I.
2006IAUJD...8E..46K Altcode:
We use local 3D convection calculations to compute the alpha-effect and
turbulent pumping of mean magnetic fields in the rapid rotation regime
corresponding to the deep layers of the solar convection zone. We find
that in this regime the alpha-effect responsible for generating the
poloidal field out of the toroidal one peaks at around latitude 30
degrees, in contrast to the slow rotation case and the often adopted
prescription in mean-field models of the solar dynamo, where the
maximum values are found at the poles. Furthermore, the turbulent
pumping of mean fields is predominantly down- and equatorward. We
find that the downward pumping is decreased near the equator for rapid
rotation and can be upward for the toroidal field component. In order
to investigate the implications of the obtained local results for the
problems in mean-field dynamo theory arising from the helioseismically
determined solar rotation profile, namely the poleward migration of
activity belts at low latitudes and the activity being concentrated at
too high latitudes, we introduce the alpha-effect and turbulent pumping
as they were found in the local calculations into a kinematic mean-field
model of the solar dynamo. We also investigate the effect of a one-cell
counter-clockwise meridional flow pattern on the dynamo solutions. We
find that using the alpha-effect and turbulent pumping adapted from
the results of the local calculations, the migration of the activity
belts is equatorward also at low latitudes. When the meridional flow is
added, the activity belts are shifted further closer to the equator,
and a poleward migration belt appears at high latitudes. With all the
effects included, the activity still appears at too high latitudes
(5...60 degrees). Other remaining problems include the somewhat too
short cycle periods for the solar-like dipole solutions.
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Title: Magnetic Field Generation in Fully Convective Rotating Spheres
Authors: Dobler, Wolfgang; Stix, Michael; Brandenburg, Axel
2006ApJ...638..336D Altcode: 2004astro.ph.10645D
Magnetohydrodynamic simulations of fully convective, rotating spheres
with volume heating near the center and cooling at the surface
are presented. The dynamo-generated magnetic field saturates at
equipartition field strength near the surface. In the interior, the
field is dominated by small-scale structures, but outside the sphere, by
the global scale. Azimuthal averages of the field reveal a large-scale
field of smaller amplitude also inside the star. The internal angular
velocity shows some tendency to be constant along cylinders and is
“antisolar” (fastest at the poles and slowest at the equator).
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Title: Local models of stellar convection. II. Rotation dependence
of the mixing length relations
Authors: Käpylä, P. J.; Korpi, M. J.; Stix, M.; Tuominen, I.
2005A&A...438..403K Altcode: 2004astro.ph.10584K
We study the mixing length concept in comparison to three-dimensional
numerical calculations of convection with rotation. In a limited range,
the velocity and temperature fluctuations are linearly proportional
to the superadiabaticity, as predicted by the mixing length concept
and in accordance with published results. The effects of rotation
are investigated by varying the Coriolis number, Co = 2 Ω τ,
from zero to roughly ten, and by calculating models at different
latitudes. We find that α decreases monotonically as a function of
the Coriolis number. This can be explained by the decreased spatial
scale of convection and the diminished efficiency of the convective
energy transport, the latter of which leads to a large increase of the
superadibaticity, δ = nabla - nabla_ad as function of Co. Applying a
decreased mixing length parameter in a solar model yields very small
differences in comparison to the standard model within the convection
zone. The main difference is the reduction of the overshooting depth,
and thus the depth of the convection zone, when a non-local version
of the mixing length concept is used. Reduction of α by a factor of
roughly 2.5 is sufficient to reconcile the difference between the model
and helioseismic results. The numerical results indicate reduction of
α by this order of magnitude.
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Title: Reynolds stresses - dependence on latitude
Authors: Hupfer, C.; Käpylä, P.; Stix, M.
2005AN....326..223H Altcode:
We present some results of three-dimensional hydrodynamic simulations of
a compressible flow under the influence of rotation. The code implements
a three-layer (stably-unstably-stably stratified) rectangular box placed
at various latitudes in a convection zone of a star. We focus on the
Reynolds stresses Q<SUB>ij</SUB> = < u'<SUB>i</SUB> u'<SUB>j</SUB>
> which in mean-field models have a crucial influence on angular
momentum transport and differential rotation. Especially we examine
the occurrence of a strong peak of Q<SUB>θφ</SUB> at low latitude
very close to the equator, which may have implications to the theory
of the angular velocity profile observed on the Sun.
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Title: Dynamos of the Sun, Stars, and Planets - Preface
Authors: Stix, M.
2005AN....326..155S Altcode:
The conference “Dynamos of the Sun, Stars, and Planets” was organized
by the Kiepenheuer-Institut für Sonnenphysik Freiburg, and was held
at the University of Freiburg from 4th to 6th October 2004. About
50 participants attended the conference, with 8 review lectures,
20 contributed talks, and 6 posters. With only few exceptions,
these contributions appear in the present issue of Astronomische
Nachrichten. This preface summarizes the discussion of the closing
session.
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Title: Book review
Authors: Stix, Michael
2005GApFD..99..431S Altcode:
No abstract at ADS
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Title: On the effect of convection on solar p modes
Authors: Stix, M.; Zhugzhda, Y. D.
2004A&A...418..305S Altcode:
We investigate the modulation of acoustic wave modes by convection. We
consider a cavity that encloses a layer of convection rolls. The
stratification due to gravity is taken into account. For the acoustic
oscillation we use a harmonic expansion for the horizontal dependence,
while a finite-difference scheme is employed in the vertical
direction. We calculate the eigenfrequencies of the acoustic modes
under adiabatic conditions, as functions of the velocity amplitude of
the convection. The results confirm the frequency decreases found in
earlier non-stratified models with only a vertical component of the
convective velocity.
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Title: Tube waves: Exact and approximate
Authors: Stix, M.
2004A&A...415..751S Altcode:
This note deals with magnetohydrodynamic body waves in a magnetic
cylinder. It is shown that the solution obtained by the thin-tube
expansion is, term by term, identical to the Taylor expansion of the
exact solution. Each level of approximation adds a pair of modes, a slow
and a fast one, and corrects the frequencies and eigenfunctions of the
previous approximation. All eigenfrequencies, approximate and exact, can
be read off from a single graph. All slow modes have phase velocities
between the tube speed c<SUB>T</SUB> and \sqrt{2} c<SUB>T</SUB>,
all fast modes have phase velocities above \sqrt{2} c<SUB>T</SUB>.
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Title: The sun : an introduction
Authors: Stix, Michael
2004suin.book.....S Altcode:
No abstract at ADS
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Title: Helioseismology (With 12 Figures)
Authors: Stix, Michael
2004RvMA...17...51S Altcode:
No abstract at ADS
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Title: Time-dependent coupling of solar oscillations
Authors: Roth, M.; Stix, M.
2003A&A...405..779R Altcode:
We investigate the effects of a large-scale time-dependent flow in the
solar convection zone on the solar p-mode oscillations. The theory of
time-dependent perturbations is applied, and we concentrate on flow
fields that can be described by a single harmonic in space and time. An
iterative method of obtaining approximate analytical solutions to the
equations of the coupled oscillator is outlined. Example calculations
are presented for the special case of two coupling partners. Special
attention is paid to the resonance that occurs when the time dependence
of the flow meets the beat frequency of two p modes.\ We conclude that
time-dependent flow fields in the solar convection zone may diminish
the height of the peaks in the oscillation power spectrum, and may
contribute to their asymmetry, broadening, and effective shift.
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Title: What can we learn from Local Convection Simulations in the
Context of mean Field Models of Stellar Rotation and Magnetism?
Authors: Käpylä, Petri J.; Korpi, Maarit J.; Ossendrijver, Mathieu;
Stix, Michael
2003ANS...324...63K Altcode: 2003ANS...324..I02K
No abstract at ADS
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Title: On the time scale of energy transport in the sun
Authors: Stix, Michael
2003SoPh..212....3S Altcode:
It is pointed out that the time scale of energy transport in the Sun
is the Kelvin-Helmholtz time scale, of order 3×10<SUP>7</SUP> years,
roughly 100 times longer than the photon-diffusion time estimated
by Mitalas and Sills (1992). The difference corresponds to a factor
U<SUB>gas</SUB>/U<SUB>rad</SUB>, the ratio of thermal energy density to
radiation energy density. Thus the heat transport, even when mediated
by photons, is slowed down by the large heat capacity of the star. A
numerical example calculation is presented.
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Title: Magnetoconvection and dynamo coefficients. II. Field-direction
dependent pumping of magnetic field
Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A.; Rüdiger, G.
2002A&A...394..735O Altcode: 2002astro.ph..2299O
We study the pumping of magnetic flux in three-dimensional compressible
magnetoconvection in the context of stellar dynamos. The simulation
domain represents a rectangular section from the lower part of
a stellar convection zone plus the underlying stably stratified
layer, with a total depth of up to five pressure scale heights. Once
convection has attained a statistically stationary state, a magnetic
field is introduced. The magnetic field is subsequently modified
by the convective motions, and the resulting pumping effects are
isolated by calculating various coefficients of the expansion of the
electromotive force, /line{u}x{b}, in terms of components of the mean
magnetic field. The dependence of the pumping effects on rotation,
latitude and other parameters is studied. First numerical evidence
is found for the existence of pumping effects in the horizontal
directions. Evidence is found that the pumping effects act differently
on different components of the mean magnetic field. Latitudinal pumping
is mainly equatorward for a toroidal field, and can be poleward for a
poloidal field. Longitudinal pumping is mainly retrograde for the radial
field but prograde for the latitudinal field. The pumping effect in the
vertical direction is found to be dominated by the diamagnetic effect,
equivalent to a predominating downward advection with a maximum speed in
the turbulent case of about 10% of the rms convective velocity. Where
possible, an attempt is made to identify the physical origin of the
effect. Finally, some consequences of the results for stellar dynamos
are discussed.
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Title: Spectral signature of magnetic flux tubes in sunspot penumbrae
Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M.
2002A&A...393..305M Altcode:
We study the polarization of spectral lines in the penumbra by
integrating the radiative transfer equation of polarized light for a
three-dimensional model atmosphere of a sunspot. In this model, the
Evershed flow is confined to magnetic flux tubes which are embedded
in a static background atmosphere, in accordance with the moving tube
model of Schlichenmaier et al. (\cite{Schlichenmaier1998apjl},b). The
gradients and/or discontinuities in the fluid velocity and the
magnetic field at the flux tube boundaries give rise to asymmetric
Stokes profiles. We concentrate on the Stokes-V profiles and study the
net circular polarization (NCP) of two photospheric spectral lines of
neutral iron, Fe I 630.25 nm and Fe I 1564.8 nm. The different behavior
of these two lines, which are exemplary for atomic spectral lines with
a large Landé factor and significantly different wavelength, is based
on the difference in excitation potential of the corresponding atomic
transitions and the fact that the wavelength dependence of the Doppler
shift is linear, while that of the Zeeman splitting is quadratic. We
find that the azimuthal variation of the NCP, N(psi, is a predominantly
antisymmetric function of psi with respect to the line connecting
disk center and spot center (line-of-symmetry) for the infrared line
of Fe I 1564.8 nm, while the variation is predominantly symmetric for
Fe I 630.25 nm. We show that the antisymmetric variation is caused
by anomalous dispersion (Faraday pulsation) and the discontinuity
in the azimuthal angle of the magnetic field, which is due to the
relative inclination between flux tube and background field. We
then compute synthetic NCP maps of a sunspot and compare them with
observational results. Finally, the center-to-limb variation of the
NCP, N(theta ), of these spectral lines is investigated. We show
that the location of the zero-crossing point of N(theta ) on the
center side of the line-of-symmetry represents a diagnostic tool to
determine the inclination angle of the Evershed flow: A vanishing NCP
on the center-side of the line-of-symmetry is an indirect evidence of
downflows in the penumbra.
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Title: Sunspots: What is interesting?
Authors: Stix, M.
2002AN....323..178S Altcode:
There are two kinds of questions that must be asked in the context
of sunspots: those concerning the 22-year magnetic cycle, and those
concerning individual spots. The magnetic cycle is probably the result
of an alpha Omega dynamo, but the nature and the magnitude of the
alpha coefficient is not clear. The shear layer at the base of the
convection zone plays an essential role in dynamo models, but it is
not clear whether there is sufficient shearing for an alpha Omega
dynamo. Further, several mechanisms have been proposed that yield a
butterfly diagram, and at least two ways are possible for the generation
of long-term variation. Sunspots show an enigmatic variation of darkness
during the cycle. Other questions concerning individual spots are:
Are current sheets essential? Where in the spot do convective or
fluting instabilities develop? How intense is the convective energy
transport in the umbra? What is the best description of sunspot decay -
diffusion over the whole spot, or erosion at the boundary? And why is
the variation of the frequency of sunspots in phase with the global
cyclic variation of the solar luminosity?
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Title: Net circular polarization of sunspot penumbrae - symmetry
breaking by anomalous dispersion
Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M.
2002ESASP.508..141M Altcode: 2002soho...11..141M
We examine the polarization of spectral lines in the penumbra of
sunspots by solving the radiative transfer equation of polarized
light for a three-dimensional axially symmetric model atmosphere
of a sunspot. The Evershed flow is confined to horizontal magnetic
flux tubes obtained from MHD calculations. These are embedded in
an inclined background magnetic field. In this work, we concentrate
on the Stokes-V profiles and examine the net circular polarization
(NCP), N = ∫V(λ)dλ, of two photospheric spectral lines of neutral
iron, Fe I 630.25 nm and Fe I 1564.8 nm. Analyzing spectra at a fixed
distance from the spot center, we find that the azimuthal variation
of N, N(ψ), is an antisymmetric function of ψ w.r.t. to the line
connecting disk center and spot center for Fe I 1564.8 nm, while
the variation is predominantly symmetric for Fe I 630.25 nm. We show
that the antisymmetric variation is caused by anomalous dispersion
(rotation of the polarization vector in a magnetized plasma). The
different inclination angles lead to a discontinuity in the azimuth
of the magnetic field along the line-of-sight. We show that this
discontinuity together with the effect of anomalous dispersion produced
an antisymmetric component in N(ψ) which outweighs the symmetric
component from the discontinuity for Fe I 1564.8 nm, while it is
negligible for Fe I 630.25 nm. We finally compute synthetic NCP maps of
a sunspot which offer an explanation for recent observational results.
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Title: Net circular polarization of sunspot penumbrae. Symmetry
breaking through anomalous dispersion
Authors: Schlichenmaier, R.; Müller, D. A. N.; Steiner, O.; Stix, M.
2002A&A...381L..77S Altcode:
The net circular polarization, N, is used as a measure for the
asymmetry of Stokes-V profiles: Nequiv int V(lambda ) d lambda ,
integrated over an absorption line. Exemplary for Fe I 630.2 nm and
Fe I 1564.8 nm, we synthesize penumbral V-profiles that stem from a
model atmosphere in which the Evershed flow is confined to horizontal
flux tubes which are embedded in a magnetic field that has the same
magnetic field strength as the flow channel, but is less inclined
w.r.t. the surface normal. At the two points where a line-of-sight
enters and leaves the flow channel, discontinuities in the inclination,
gamma , the velocity v, and the azimuth, phi , of the magnetic field
vector w.r.t. the plane perpendicular to the line-of-sight produce
V-asymmetries. Assuming an axially symmetric penumbra, we investigate
the azimuthal dependence N(psi ) for a mid-penumbral radius. We find:
(1) Without including anomalous dispersion, N(psi ) is symmetric
w.r.t. the line that connects disk center to the center of the spot. (2)
Including anomalous dispersion, this symmetry is broken. We demonstrate
that this is due to the difference in azimuth, triangle phi (psi ),
between the flow channel and the background that varies along the
penumbral circle. For Fe I 630.2 nm this effect is found to be of
minor relevance leading to essentially symmetric N-maps, whereas strong
asymmetries are predicted for Fe I 1564.8 nm. Our results provide an
explanation for recent observational findings.
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Title: The sun: an introduction
Authors: Stix, Michael
2002tsai.book.....S Altcode:
No abstract at ADS
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Title: Physics of the solar dynamo: Outstanding problems
Authors: Stix, M.
2001A&AT...20..417S Altcode:
No abstract at ADS
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Title: Joint 9th European and 5th national astronomical meeting
(Jenam-2000), 'European astronomy at the turn of the millennium'
Authors: Stix, M.
2001A&AT...20..415S Altcode:
No abstract at ADS
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Title: Magnetoconvection and dynamo coefficients:. Dependence of
the alpha effect on rotation and magnetic field
Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A.
2001A&A...376..713O Altcode: 2001astro.ph..8274O
We present numerical simulations of three-dimensional compressible
magnetoconvection in a rotating rectangular box that represents
a section of the solar convection zone. The box contains a
convectively unstable layer, surrounded by stably stratified layers
with overshooting convection. The magnetic Reynolds number, Rm, is
chosen subcritical, thus excluding spontaneous growth of the magnetic
field through dynamo action, and the magnetic energy is maintained by
introducing a constant magnetic field into the box, once convection
has attained a statistically stationary state. Under the influence
of the Coriolis force, the advection of the magnetic field results
in a non-vanishing contribution to the mean electric field, given by
<vec{u}xvec{b}>. From this electric field, we calculate the alpha
-effect, separately for the stably and the unstably stratified layers,
by averaging over time and over suitably defined volumes. From the
variation of alpha we derive an error estimate, and the dependence of
alpha on rotation and magnetic field strength is studied. Evidence is
found for rotational quenching of the vertical alpha effect, and for
a monotonic increase of the horizontal alpha effect with increasing
rotation. For Rm~ 30, our results for both vertical and horizontal
alpha effect are consistent with magnetic quenching by a factor [1+Rm
(B<SUB>0</SUB>/B<SUB>eq</SUB>)<SUP>2</SUP>]<SUP>-1</SUP>. The signs
of the small-scale current helicity and of the vertical component of
alpha are found to be opposite to those for isotropic turbulence.
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Title: Differential rotation of the present and the pre-main-sequence
Sun
Authors: Küker, M.; Stix, M.
2001A&A...366..668K Altcode:
We present a model for the differential rotation of the present Sun as
well as a solar-type star during its pre-main-sequence evolution. The
model is based on the mixing-length theory of convective heat
transport and a standard solar model. The resulting rotation law is
in good agreement with observations and only weakly dependent on the
mixing-length parameter. For the present Sun, the normalized horizontal
shear decreases with increasing rotation rate, but the total shear is
roughly constant. We then follow the Sun's evolutionary track from the
beginning of the contraction to the arrival on the ZAMS. While at an
age of 30 Myr the total shear is very similar to that of the present
Sun, it is much smaller on the Hayashi track.
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Title: Effect of time-dependent velocity fields on solar oscillations
Authors: Roth, Markus; Stix, Michael
2001ESASP.464..243R Altcode: 2001soho...10..243R
Velocity fields in the solar convection zone have various influences on
the solar oscillations. Besides the excitation they lead to splittings
into multiplets in the case of differential rotation and to frequency
shifts of the multiplets components in the case of convection cells. As
the velocity fields are time-dependent, these frequency shifts must be
time-dependent as well. Moreover, the amplitudes and therefore the mode
energies of the solar oscillations are affected. We use time-dependent
perturbation theory to show how the p-mode frequencies and energies
are influenced by non-stationary velocity fields and present possible
effects on the line profiles in the power spectra.
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Title: Sun: Basic Properties
Authors: Stix, M.
2000eaa..bookE1977S Altcode:
The standard star...
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Title: Modulation of Acoustic Waves by Solar Convection
Authors: Stix, M.
2000SoPh..196...19S Altcode:
Amplitude and phase of an acoustic oscillation in the solar convection
zone vary in response to the local variation of the speed of sound
and the convection velocity. Such wave modulation is considered by
means of a two-dimensional periodic model, with alternating vertical
channels of hot rising and cool sinking gas. According to this model,
vertically propagating waves show only amplitude modulation. For low
wave frequencies the amplitude is larger in the upflow channels,
for high frequencies it is larger in the downflow channels. The
transition occurs at a frequency for which the vertical wavelength is
approximately equal to the horizontal period of the model. Waves with
an inclined propagation direction show a similar amplitude modulation
but, in addition, a modulation of their phase. The present results are
compared with recent observational studies. There is evidence that wave
modulation indeed occurs on the Sun, on the granular as well as on the
mesogranular scale, in addition to the episodic amplitude enhancement
that has been interpreted in terms of local acoustic events.
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Title: Wave modulation and wave sources in the solar convection zone
Authors: Kiefer, M.; Stix, M.; Balthasar, H.
2000A&A...359.1175K Altcode:
We investigate the behavior of upward running sound waves in the lower
photosphere by means of a 2-hour time series of FPI-filtergrams and a
corresponding series of white-light images. From the FPI-filtergrams
we obtain velocities in two heights in the solar photosphere. Using
specific filters in the k_h-nu -space, we extract running sound waves
from the velocity time series and the granulation from the white-light
series. The relation between granular structure and wave amplitude
is examined. To this end the granulation images are subdivided into
intensity classes. The amplitudes of the waves are extracted on the
pixel maps corresponding to these classes. We find hints for wave
modulation due to the inhomogeneities in the solar convection zone:
The behavior of the wave amplitudes meets theoretical predictions
with respect to frequency- and height-dependence. The dependence
on the horizontal wave number meets the predictions too, but due
to low wave coherence at high wave numbers no definitive statement
is possible. Further the darkest locations in the granulation are
preferred by waves of increased amplitudes. There also seems to
be a preference for the brightest granular regions. In both cases
the behavior of the waves can be well described by subsurface sound
sources. This is confirmed by comparison of the data with a simple
model of a subsurface sound source.
---------------------------------------------------------
Title: Solar Oscillation Transitions in Time-Dependent Perturbation
Theory
Authors: Roth, M.; Stix, M.
2000SPD....31.0110R Altcode: 2000BAAS...32..803R
Time-dependent and stationary velocity fields in the solar convection
zone lead to coupling of solar oscillations, which result in
splittings of the degenerate p-mode frequencies into multiplets. These
splittings are antisymmetric in the case of differential rotation,
i.e., pure toroidal fields, and asymmetric in the case of overturning
convection cells, i.e., poloidal fields. The reason for these effects
are intermixtures of the p-mode eigenfunctions expressed in a linear
expansion of the coupling unperturbed eigenstates. In analogy to a
perturbed quantum-mechanical system of discrete eigenstates, where the
squares of the expansion coefficients are related to the transition
probability between the states, we use time-dependent perturbation
theory to derive an expression for the expansion coefficients of the
p-mode coupling. There the square of the coefficients is regarded
as energy distribution of the perturbed sytem. We conclude that a
time-dependent velocity field has not only effects on the p-mode
splitting, but has also influence on the lifetime and therefore the
linewidth of the power spectra.
---------------------------------------------------------
Title: Convective overshooting on the Sun: radiative effects
Authors: Kiefer, M.; Grabowski, U.; Mattig, W.; Stix, M.
2000A&A...355..381K Altcode:
We calculate solar models with convective overshooting at the top
and at the base of the outer convection zone, and test the models
by comparing their eigenfrequencies to the observed solar p-mode
frequencies. Radiative temperature relaxation is included in form of a
characteristic time that describes both optically thick and thin cases,
and a modified mixing-length formalism is used, with gas parcels
traveling varying path lengths. These modifications to the common
mixing-length theory generally change the efficiency of the convective
energy transport, and therefore the stratification at and immediately
below the surface of the Sun. Radiative relaxation lowers the
convective efficiency and so leads to a steeper temperature gradient,
with the consequence that the temperature becomes somewhat larger in the
near-surface layer, but slightly lower in the upper convection zone; due
to the latter effect there is a negative correction to eigenfrequencies
above ~ 2 mHz. The effect of convective parcels with varying path
lengths is opposite. In the solar interior, radiative relaxation is in
the diffusion limit and therefore has no immediate effect at the base of
the convection zone. However, the larger mixing-length to scale-height
ratio caused by the near-surface effect leads to farther overshooting
at the base. The effect of the multiple-path models is in the same
direction. For most of our models the extent of the overshooting is
larger than permitted by the helioseismic constraint of ~ 0.1 pressure
scale heights, but for some models it is marginal. At the surface the
efficient optically thin radiative relaxation smoothes the temperature
gradient. Both the radiation and the multiple-path effects lead to
more extended overshooting. The models reach ~ 200 km of overshooting,
with temperature fluctuations of up to several hundred Kelvin. We
compare the results with spectroscopic investigations, and with recent
three-dimensional hydrodynamic numerical simulations. A general result
is that mixing-length theory appears unable to reproduce in detail
the properties of solar convection that are directly observed at the
surface or inferred by helioseismology. The improvements based on even
sophisticated modifications remain limited.
---------------------------------------------------------
Title: Commission 12: Solar Radiation and Structure (Radiation et
Structure Solaires)
Authors: Foukal, Peter; Solanki, Sami; Mariska, J.; Baliunas, S.;
Dravins, D.; Duvall, T.; Fang, C.; Gaizauskas, V.; Heinzel, P.;
Kononovich, E.; Koutchmy, S.; Melrose, D.; Stix, M.; Suematsu, Y.;
Deubner, F.
2000IAUTA..24...73F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Coupling of solar p modes: quasi-degenerate perturbation theory
Authors: Roth, M.; Stix, M.
1999A&A...351.1133R Altcode:
The interaction of a large-scale stationary poloidal velocity field
(as a simple model for possibly existing giant cells) with solar p-mode
oscillations is described by quasi-degenerate perturbation theory,
as proposed by Lavely & Ritzwoller (1992). For oscillations of low
degree (l <= 12) and sectoral velocity fields we obtain numerical
solutions of the eigenvalue problem, and derive an approximate formula
for the ensuing frequency splitting. The coupling of the oscillation
modes leads to asymmetric frequency multiplets, with splittings of up to
~ 100 nHz for a velocity with amplitude v = 100 m s<SUP>-1</SUP>. The
splitting scales with v<SUP>2</SUP>, with the oscillation frequency
itself, and with the inverse difference of the squared frequencies
of the coupling partners. Possible observable effects are briefly
discussed.
---------------------------------------------------------
Title: Jagd auf die Sonnen-Neutrinos.
Authors: Stix, M.
1999S&WSp...4...98S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Center-to-limb variation of the solar oscillation. New results
from MDI data
Authors: Schmidt, W.; Stix, M.; Wöhl, H.
1999A&A...346..633S Altcode:
{Using 17 hours of full-disk MDI Doppler data we have investigated the
center-to-limb variation of the oscillatory wave spectrum of the solar
photosphere. Power distributions in the k_hnu -plane are calculated
for fields of 20(deg) x 20(deg) on the Sun, centered at every 10(deg)
heliographic latitude. From the center-to-limb variation of the power
in the f mode and the lowest 7 p modes we obtain information about the
mean inclination of the oscillatory velocity vector with respect to
the vertical direction. We find qualitative agreement with a model of
adiabatic waves in an isothermal atmosphere, but generally the solar
oscillations appear to be less inclined than the model oscillations. We
find no indication for the existence of horizontal sound waves on
the Sun.}
---------------------------------------------------------
Title: Die Sonne im Computer.
Authors: Schleicher, H.; Stix, M.
1999A&R....36Q...4S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Ein Blick in das Innere der Sonne.
Authors: Schleicher, H.; Stix, M.
1999A&R....36....8S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Coupling of Solar Oscillations in Quasi-Degenerate Perturbation
Theory
Authors: Roth, M.; Stix, M.
1999AGAb...15...92R Altcode: 1999AGM....15..P11R
We investigate the coupling of the solar p-modes, caused by a
stationary poloidal velocity field in the solar convection zone,
via quasi-degenerate perturbation theory, as suggested by Lavely and
Ritzwoller (Phil. Trans. R. Soc. Lond. A (1992) 339, 431-496). As a
consequence of the Wigner-Eckhart theorem oscillations couple if they
satisfy several selection rules. The result is the lifting of the
degeneracy. But in contrast to the rotational splitting, coupling
between different multiplets is possible leading to asymmetric
frequency multiplets. For illustration we examine the effect of
sectoral velocity fields, similar to giant convective cells. We find
an approximate solution of the general equations for the coupling of
two p-modes with a degree l <= 12. The individual frequency shifts
scale with the frequency itself, with the square of the velocity,
and with the inverse difference of the squared frequencies of the two
involved modes. The relative deviation of this estimate from the exact
result is less than 10 %. Finally, we show that the splittings are up
to ~100 nHz for a velocity with amplitude 100 m/s. Hence, large scale
poloidal velocity fields lead to an additional line broadening and to
an asymmetric line profile in the power spectra.
---------------------------------------------------------
Title: Waves in structured media: non-radial solar P modes
Authors: Stix, M.; Zhugzhda, Y. D.
1998A&A...335..685S Altcode:
For non-radial solar p modes we calculate corrections to the
eigenfrequencies arising from the sound speed and velocity inhomogeneity
of the convection zone. We use a simple periodic model, and obtain the
frequency corrections by solving a Hill determinant. The frequency
shifts are significant, and in most cases negative; they increase
in magnitude with increasing frequency and harmonic degree l. The
dependence on degree scales with the mode inertia. For large degree
l this trend reverses. For very large degree coupling occurs between
the p modes and “vibrational” modes that only exist because of the
horizontal structure in sound speed and velocity.
---------------------------------------------------------
Title: Solar models with convective overshoot
Authors: Stix, M.; Kiefer, M.
1997ASSL..225...69S Altcode: 1997scor.proc...69S
We calculate models of the Sun possessing a layer of convective
overshoot at the base of their outer convection zones. There is a
small effect on the overshoot layer from the change in the equation of
state. A conspicuous decrease of the layer thickness arises from the
replacement of the Los Alamos opacity tables by tables from Lawrence
Livermore. For the calculated models the thickness lies between 0.13 and
0.19 of a pressure scale height. We also propose a model with a smoothed
transition from the overshoot layer to the radiative core, obtained
by a limitation of the temperature excess of the convection eddies.
---------------------------------------------------------
Title: Comments on the "analytic theory of P modes" by Dzhalilov
and Staude.
Authors: Zhugzhda, Y.; Stix, M.
1997A&A...322..982Z Altcode:
Dzhalilov & Staude (1995A&A...303..561D; hereinafter DS)
have proposed a new "analytic theory" of p modes for the atmospheres
of the Sun and Sun-like stars, which explains the p-mode spectrum in
terms of "resonant transmission" of acoustic waves. It is shown that
this result is mistaken because of an incorrect fit of the piecewise
analytic solutions at the boundaries between the diverse layers of the
atmosphere. Apart from this incorrect treatment of wave propagation,
the interpretation in terms of resonant transmission appears to arise
from a mix-up of resonance and interference phenomena. There is also
some confusion about the concepts of tunnel effect and turning point.
---------------------------------------------------------
Title: Kiepenheuer-Institut für Sonnenphysik. Jahresbericht für
1996.
Authors: Stix, M.
1997MitAG..80..177S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Adaptive Optics at the German VTT on Tenerife
Authors: Soltau, D.; Acton, D. S.; Kentischer, Th.; Roser, M.; Schmidt,
W.; Stix, M.; von der Luhe, O.
1997ASPC..118..351S Altcode: 1997fasp.conf..351S
Experiences and considerations are presented which play an important
role for an Adaptive Optics system at our telescope.
---------------------------------------------------------
Title: The depth of the solar convection zone: two models with
overshoot.
Authors: Stix, M.
1996NAWG.1996..230S Altcode:
Two models of the present Sun are calculated: one with a Los Alamos
opacity table, and one with an opacity table form the Lawrence Livermore
Laboratory. Both models have a layer of convective overshoot at the base
of their outer convection zones, calculated with a non-local version
of the mixing-length theory. The total depth of the convection zones
in the two models is 0.274 R<SUB>sun</SUB> and 0.286 R<SUB>sun</SUB>,
respectively; the second of these values is within the limits set by
helioseismic results.
---------------------------------------------------------
Title: Distribution of starspots on cool stars. I. Young and main
sequence stars of 1M<SUB>sun</SUB>_.
Authors: Schuessler, M.; Caligari, P.; Ferriz-Mas, A.; Solanki, S. K.;
Stix, M.
1996A&A...314..503S Altcode:
Sunspots are restricted to a latitude band within 30degof the solar
equator. In contrast, the latitudes of spots on the surfaces of
rapidly rotating cool stars can range from their polar regions, for
RS CVn systems and for T Tauri stars leaving the Hayashi track, to
mid latitudes for stars close to or on the main sequence. In order to
find an explanation for these observed spot latitudes we have applied
the criteria for the undulatory instability (Parker instability) of
a toroidal magnetic flux tube embedded in the convective overshoot
layer below the outer convection zone and calculated the non-linear
evolution of the rising magnetic loops formed by this instability. We
describe the results for a star of one solar mass in different phases
of its evolution before and on the main sequence. We find that there
usually is a range of latitudes at which magnetic flux can emerge on
the stellar surface. The mean latitude of emergence shifts towards
the poles for increasingly rapid rotation. The internal structure
of the star, however, plays an almost equally important role in
determining the latitude of magnetic emergence. For stars of solar
mass only the youngest objects, with extremely deep convection zones,
should show spots emerging at the stellar poles. Pre-main sequence
stars at an age of 10^7^ y (convection zone reaching down half-way to
the centre) exhibit high latitude, but not truly polar spots, while
a main sequence star of one solar mass, even at high rotation rates,
only shows intermediate latitude spots. These results are found to be
in good agreement with Doppler images of young rapid rotators.
---------------------------------------------------------
Title: Wave propagation in inhomogeneous media: shifts of solar
p-mode frequencies.
Authors: Stix, M.; Zhugzhda, Y. D.
1996AGAb...12..166S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Wave trapping in intergranular lanes
Authors: Stix, M.; Zhugzhda, Y. D.
1996ASPC..109..163S Altcode: 1996csss....9..163S
No abstract at ADS
---------------------------------------------------------
Title: Adaptive optics for a 70 cm solar telescope.
Authors: Soltau, D.; Acton, D. S.; Kentischer, T.; Röser, M.; Schmidt,
W.; Stix, M.; von der Lühe, O.
1996AGAb...12...92S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Flux Tube Dynamics in Active Stars
Authors: Caligari, P.; Schüssler, M.; Solanki, S. K.; Schaerer, D.;
Stix, M.
1996ApL&C..34...17C Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Kiepenheuer-Institut für Sonnenphysik. Jahresbericht für
1995.
Authors: Stix, M.
1996MitAG..79..173S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The phase of the radial mean field in the solar dynamo.
Authors: Schlichenmaier, R.; Stix, M.
1995A&A...302..264S Altcode:
Observations indicate that the radial and azimuthal components of the
mean solar magnetic field oscillate with a phase shift of approximately
180deg during the 22-year cycle. In order to calculate such phase shifts
we construct a simple two-dimensional, nonlinear α^2<SUP>OMEGA</SUP>
dynamo, which operates in the overshoot region beneath the convection
zone. Like previous models, our model predicts an almost in-phase
oscillation for most parameter choices. Special configurations, in which
the two components of the mean field have different distributions in
latitude, may resolve the dilemma. Alternative conclusions are that our
knowledge of the α effect is insufficient, or that the observational
result is not reliable.
---------------------------------------------------------
Title: Acoustic Waves in Structured Media and Helioseismology
Authors: Zhugzhda, Y. D.; Stix, M.
1995ASPC...76..326Z Altcode: 1995gong.conf..326Z
No abstract at ADS
---------------------------------------------------------
Title: Convective Efficiency and its Influence on Eigenfrequencies
of the Sun
Authors: Kiefer, M.; Grabowski, U.; Stix, M.
1995LIACo..32..379K Altcode: 1995sews.book..379K
No abstract at ADS
---------------------------------------------------------
Title: Kiepenheuer-Institut für Sonnenphysik. Jahresbericht für
1994.
Authors: Stix, M.
1995MitAG..78..125S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Models with Convective Overshoot
Authors: Stix, M.
1995somo.conf..171S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: p-mode frequency corrections due to convection
Authors: Stix, M.
1995HiA....10..331S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Acoustic waves in structured media and helioseismology.
Authors: Zhugzhda, Y. D.; Stix, M.
1994A&A...291..310Z Altcode:
A simple two-stream model of alternating hot and cool vertical layers,
with uniform upwards and downwards velocities, respectively, was
studied to investigate the influence of convection on solar global
oscillations. The effect on vertically propagating acoustic waves is
small at low frequency, but leads to a significant decrease of the mean
phase velocity of high-frequency modes which are more confined to the
cool layers. As our main result we thus find frequency corrections
for solar p modes of low degree and high order which may reconcile
the calculated with the observed eigenfrequencies. Our model also
yields high-frequency modes with more or less horizontal propagation,
representing the distortion of the wave fronts due to the horizontal
structure, and a "slow mode", a surface wave propagating along the
boundaries between the layers of different vertical velocity.
---------------------------------------------------------
Title: The δ Scuti instability strip: effects of opacity enhancement
and wave reflections
Authors: Li, Y.; Stix, M.
1994A&A...286..815L Altcode:
Theoretical blue edges of the δ Scuti instability strip generally lie
at a lower effective temperature than the observed one. It was hoped
that the recent opacity enhancement found by the OPAL project could
provide more excitation to the pulsations and bring the theoretical
prediction to a better agreement with the observations. However,
calculations in the present research shatter this hope. Instead
of this, the position of the outer pulsation boundary was found to
have a strong effect on the location of the blue edge; the blue edge
becomes hotter when the outer boundary is at a place of smaller optical
depth. Reflections of the pulsation waves at the outer boundary and at a
steep density-inversion zone, which is a result of strong ionization of
hydrogen, are suggested to be responsible for this relationship. When
the outer boundary is at τ= 0.01, the resulting blue edges enclose
all observed δ Scuti stars within the instability strip.
---------------------------------------------------------
Title: Modelling Solar Irradiance Variations with an Area Dependent
Photometric Sunspot Index
Authors: Brandt, P. N.; Stix, M.; Weinhardt, H.
1994SoPh..152..119B Altcode: 1994IAUCo.143..119B; 1994svs..coll..119B
The He 1083 nm line equivalent width and the 10.7 cm radio flux are
employed to model the total solar irradiance corrected for sunspot
deficit. A new "area dependent photometric sunspot index" (APSI)
based on sunspot photometry by Steinegger et al. (1990) is used to
correct the irradiance data for sunspot deficits. Two periods of time
are investigated: firstly, the 1980-1989 period between the maxima of
solar cycles 21 and 22; this period is covered by ACRIM I irradiance
data. Secondly, the 1978-92 period which includes both maxima; here,
the revised Nimbus-7 ERB data are used.
---------------------------------------------------------
Title: Distribution of Magnetic Flux on the Surface of Rapidly
Rotating Stars
Authors: Caligari, P.; Schussler, M.; Stix, M.; Solanki, S. K.
1994ASPC...64..387C Altcode: 1994csss....8..387C
No abstract at ADS
---------------------------------------------------------
Title: Kiepenheuer-Institut für Sonnenphysik. Jahresbericht für
1993.
Authors: Schröter, E. H.; Stix, M.
1994MitAG..77..121S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The phase of the radial field in the solar dynamo
Authors: Schlichenmaier, R.; Stix, M.
1994smf..conf..107S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the Depletion of Lithium in the Sun
Authors: Ahrens, J.; Stix, M.; Thorn, M.
1994snft.book...61A Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Damping of solar p-mode oscillations. 1. Radial modes with
eddy viscosity
Authors: Stix, M.; Rudiger, G.; Knolker, M.; Grabowski, U.
1993A&A...272..340S Altcode:
A Fourier transform method is used to derive shear and volume
eddy viscosities arising from small-scale turbulent motions
in the solar convection zone. For homogeneous and isotropic
turbulence the volume viscosity exceeds the shear viscosity by a
factor 6. For oscillations with a large-scale spatial structure the
viscosities depend on the frequency of oscillation in the form exp(-
|ω<SUB>osc</SUB>τ<SUB>corr</SUB>|), where τ<SUB>corr</SUB> is the
correlation time of the turbulence. This dependence restricts the
damping effect upon the solar p modes to a layer of at most several
thousand kilometers just below the Sun's surface. <P />The damping
rates of radial solar p modes were calculated with the help of an
energy integral. The result is that turbulent damping may account for
up to 20% of the total damping derived from the observed width of the
lines in the oscillation spectrum. If convective overshoot into the
solar atmosphere is included, the effect increases to 25 - 30%.
---------------------------------------------------------
Title: On the depletion of lithium in the sun.
Authors: Ahrens, B.; Stix, M.; Thorn, M.
1992A&A...264..673A Altcode:
We describe evolutionary sequences of solar models starting in a
fully convective phase at the Hayashi line. An overshoot layer of
about 0.30 pressure scale heights is sufficient for the depletion of
lithium by a factor 100. The destruction of Li occurs almost entirely
during the pre-main-sequence evolution, within a period of 1.5 x 10
exp 7 yr when the star develops a radiative core and departs from the
Hayashi line. For the present sun, the same overshoot layer leads to
a convection zone of about 200,000 km total depth, in good agreement
with the helioseismic evidence and with the needs of the solar dynamo.
---------------------------------------------------------
Title: Book-Review - the Sun - an Introduction
Authors: Stix, M.
1992S&T....83Q.173S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Lithium depletion during the sun's pre-main-sequence phase.
Authors: Ahrens, B.; Stix, M.; Thorn, M.
1992AGAb....7..147A Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - the Sun - an Introduction
Authors: Stix, M.
1991Sci...254R1053S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - the Sun - an Introduction
Authors: Stix, M.; Ambroz, P.
1991BAICz..42..329S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: An alpha-Omega dynamo with order and chaos
Authors: Schmalz, S.; Stix, M.
1991A&A...245..654S Altcode:
A simple alpha-Omega dynamo is presented, including alpha-quenching by
the magnetic field, modeled by a separate differential equation. The
model is cast in spectral form. It is demonstrated that the type
of solution, in particular the transition to chaotic behavior,
critically depends on the number of Fourier components taken into
account. Low-order systems tend to reach chaotic solutions already at
moderate dynamo number, via subharmonic cascades. High-order systems
have limit cycles even at large magnitude of the dynamo number; their
routes to chaos preferentially include two- and three-dimensional tori
in phase space.
---------------------------------------------------------
Title: Book-Review - the Sun - an Introduction
Authors: Stix, M.; Doyle, J. G.
1991IrAJ...20...49S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The overshoot layer at the base of the solar convection zone.
Authors: Skaley, D.; Stix, M.
1991A&A...241..227S Altcode:
Using the nonlocal mixing-length theory of Shaviv and Salpeter
(1973), solar models with overshoot at the base of the convection
zone are calculated. The depth of the overshoot layer is not uniquely
defined because of the unknown statistical properties of the turbulent
convection. Models with an overshoot depth of more than 50 percent
of a pressure scale height are possible. The eigenfrequencies of
these models generally are slightly higher than the eigenfrequencies
of models without overshoot; the difference is most pronounced for
oscillations of intermediate degree. The temperature at the base of
the mixing region reaches 2.8 x 10 to the 6th K; this is of interest
for the destruction of lithium during the sun's main-sequence evolution.
---------------------------------------------------------
Title: The Sun. an Introduction
Authors: Stix, Michael
1991sun..book.....S Altcode:
As in all other fields of astronomy, progress in instrumentation
and observational techniques has in recent years brought a wealth of
new information about the sun. This introduction presents a complete
overview of solar physics, of what we know and would like to know. The
increasing number of observations of solar pheno- mena on neighbouring
stars makes this book valuable not only for students specializing in
solar physics but also for researchers interested in stellar structure
and the solar-stellar connection.
---------------------------------------------------------
Title: The solar dynamo
Authors: Stix, M.
1991GApFD..62..211S Altcode:
This review begins with remarks on contributions by T. G. Cowling to
the problem of the solar magnetism. Then I discuss problems connected
to first-order smoothing in mean-field dynamo theory. Next, the reasons
for a solar dynamo operating near the base of the outer convection zone
will be recalled, and models will be reviewed. Finally, I address the
variety of possible solutions to the dynamo equations: Stationary and
oscillatory, symmetric and antisymmetric with respect to the equator,
axisymmetric and longitude-dependent. Limit cycles and chaotic fields
which appear in the non-linear regime will be mentioned in this context.
---------------------------------------------------------
Title: Book-Review - the Sun
Authors: Stix, M.; Fritze, K.
1990AN....311..304S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The equation of state and the frequencies of solar P modes.
Authors: Stix, M.; Skaley, D.
1990A&A...232..234S Altcode:
Solar interior models are calculated with and without the electrostatic
interaction in the equation of state. The ionization equilibria
of hydrogen and helium and the equation of state are derived in a
consistent manner from a minimization of the free energy, and the
electrostatic effects the pressure and the partition functions for bound
electrons are considered in the Debye-Hueckel treatment, essentially
following Daeppen (1980). It is shown that the eigenfrequencies of the
solar model which includes the electrostatic interaction agree better
with the frequencies of observed solar oscillations than those of the
model without electrostatic interaction.
---------------------------------------------------------
Title: Book-Review - the Sun - an Introduction
Authors: Stix, M.; Mills, A. A.
1989JBAA...99..245S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - the Sun
Authors: Stix, M.
1989S&T....78..606S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - the Sun - an Introduction
Authors: Stix, M.
1989Sci...246..246S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Eigenschwingungen der Sonne.
Authors: Stix, M.
1989PhyBl..45..146S Altcode: 1989PhB....45..146S
No abstract at ADS
---------------------------------------------------------
Title: The Sun's differential rotation.
Authors: Stix, M.
1989amts.conf..248S Altcode:
Equatorial zones of the Sun rotate more rapidly than high-latitude
regions. Modern observational results of this well-known phenomenon
are reviewed. In addition, the author reviews results concerning some
probably related phenomena: meridional circulation, the correlation
between latitudinal and longitudinal motions on the solar surface,
a possible dependence on latitude of the surface temperature, and
direct rotational effects upon solar convection. Temporal variations of
some of these phenomena, notably the "torsional oscillator", are also
mentioned. The theory of the Sun's differential rotation offers mean
and explicit models. The aim of all models is not only to explain the
rotation observed at the solar surface, but also to predict the form
of the angular velocity within the convection zone. Only some of the
mean models have been successful in this respect. The explicit models
continue to yield cylindrical isorotation; possible reasons for this
are briefly discussed.
---------------------------------------------------------
Title: The Sun's Differential Rotation.
Authors: Stix, M.
1989RvMA....2..248S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The sun. an introduction
Authors: Stix, Michael
1989sai..book.....S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Sun. an Introduction
Authors: Stix, Michael
1989sun..book.....S Altcode: 1989QB521.S75......
As in all other fields of astronomy, progress in instrumentation and
observational techniques has brought a wealth of new information about
the Sun in recent years. This introduction presents a complete overview
of solar physics, of what we know and would like to know. The increasing
number of observations of solar phenomena on neighbouring stars makes
this book not only indispensable for students specializing in solar
physics but also for researchers interested in stellar structure and
the solar stellar connection.
---------------------------------------------------------
Title: Electromagnetic core-mantle coupling: The fourier method for
the solution of the induction equation
Authors: Paulus, Michael; Stix, Michael
1989GApFD..47..237P Altcode:
The Gauss coefficients of the geomagnetic field since 1903 are used as a
time-dependent boundary condition for the poloidal field in the Earth's
mantle. The coefficients are Fourier transformed, and the induction
equation for the mantle field is solved in Fourier space. The phase
advance of the poloidal field at the base of the mantle, and of the
ensuing "poloidal" electromagnetic couple, is investigated as a function
of the conductivity profile. Since, except for the phase shift, the
couple behaves essentially as the one calculated by Stix and Roberts
(1984) for each epoch separately, the "toroidal" part of the couple is
calculated according to their instantaneous method. The phase shift is
then obtained from a comparison with the couple required by the decade
fluctuations in the length of the day. This permits a determination
of the electrical conductivity of the mantle, which we find to be a
rather flat function of radius.
---------------------------------------------------------
Title: A review of: "Advances in Helio- and asteroseismology"
Authors: Stix, Michael
1989GApFD..46..266S Altcode:
Edited By J. Christensen-Dalsgaard and S. Frandsen. D. Reidel,
xxi + 604 pp., Hardb. Dfl. 230.00, us 109.00 (ISBN 90-277-2614-0),
Paperb. Dfl. 95.00 US 49.00 (ISBN 90-277-2615-9).
---------------------------------------------------------
Title: Solar oscillations: overshoot at the base of the convection
zone.
Authors: Skaley, D.; Stix, M.
1988ESASP.286..525S Altcode: 1988ssls.rept..525S
Solar models are calculated with the non-local form of mixing length
theory, as proposed by Shaviv and Salpeter, applied to the lower part
of the convection zone. The resulting overshoot layer has a depth
of 16 Mm, this is about 30% of the local pressure scale height. The
parameters α = Λ/H<SUB>p</SUB> (mixing length/pressure scale height)
and the initial He-abundance Y<SUB>0</SUB> are obtained by calculating
a full model sequence in time to α = 1.505 and Y<SUB>0</SUB> =
0.25637. The total convection zone has the depth d = 197 Mm at a
temperature T = 2.166 MK compared to d = 181 Mm and T = 1.927 MK
in the local case. This fact may have implications on the observed
low Li-abundance. The influence of the obershoot layer on low-l modes
shows an incrase in the frequencies of the order of about 1 μHz, thus
lowing the difference to the observed frequencies. For intermediate-l
modes where the reflection boundary is just below the overshoot region
the effect is strongest, up to about 4 μHz. High-l modes are slightly
lowered by the overshoot effect. Nevertheless in all frequency ranges
a discrepancy of several μHz remains.
---------------------------------------------------------
Title: Corrections to first order smoothing in mean-field
electrodynamics
Authors: Nicklaus, Bernhard; Stix, Michael
1988GApFD..43..149N Altcode:
We employ the method of ordered cumulants to calculate corrections to
the first order smoothing approximations of the transport coefficients
and appearing in the mean-field dynamo equation. Special results are
derived for the case of stationary, isotropic Gaussian turbulence,
and explicit formulae are given for (4) and (4), the terms arising
when fourth order correlations are involved. The order of these terms,
relative to the usual second order correlation terms, is S2, where
S=uc/λc, is the Strouhal number. Two particular examples demonstrate
that the corrections can dominate the original terms, and even change
the sign of α and (or) β. The coefficient β(4) strongly depends on
the helicity of the turbulent flow.
---------------------------------------------------------
Title: Gray's constant and 'swiss cheese' and 'sea serpents' in
stellar convection zones
Authors: Belvedere, G.; Pidatella, R. M.; Stix, M.
1987A&A...177..183B Altcode:
Gray (1985), on the basis of Zeeman broadening measurements on a
sample of G and K darfs found an interesting relation between the
average magnetic field strength, B, and the areal coverage factor,
A<SUB>0</SUB>: the product A<SUB>0</SUB>B is a constant independent
of spectral type and rotational velocity. Pidatella and Stix (1986)
applied a non-local form of the mixing length theory to the lower part
of the solar convection zone to estimate the size of the overshoot layer
and computed the magnetic field strength beyond which thin toroidal
flux tubes, located in the overshoot layer, become unstable. In the
present work the authors extend the calculations of Pidatella and Stix
(1986) to a number of main sequence spectral types, ranging from F5
to K0. A possible explanation of why the Sun does not fit Gray's law
is also proposed.
---------------------------------------------------------
Title: On the frequencies of solar oscillations.
Authors: Stix, M.; Knoelker, M.
1987ppcs.work...67S Altcode:
Solar oscillations, with frequencies between 2 and 5 mHz, can be
identified as p modes with well-determined degree 1 and overtone number
n, but minor discrepancies, of order 10 μHz, between observed and
calculated frequencies remain. The authors describe the computation
of solar models and their frequencies of oscillation, check the
accuracy of the numerical results, and study the influence of the
atmosphere. Attempts to improve the calculated frequencies for
low degree and intermediate order (n = 10...20) have so far been
unsuccessful.
---------------------------------------------------------
Title: On the origin of stellar magnetism
Authors: Stix, Michael
1987LNP...292...13S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the Origin of Stellar Magnetism
Authors: Stix, M.
1987LNP...292...15S Altcode: 1987ssp..conf...15S
The author concentrates on two problems which are related to the origin
of stellar magnetism. The first is the concept of mean fields, which
plays a key role in the theory. The second is a question which has been
discussed recently in particular in the context of the solar dynamo:
namely the transition layer at the base of the convection zone as the
postulated seat of the dynamo.
---------------------------------------------------------
Title: Models for a Differentially Rotating Solar Convection Zone
Authors: Stix, Michael
1987ASSL..137..329S Altcode: 1987isav.symp..329S
Axisymmetric mean field models of the sun's differential rotation are
considered which employ a real solar envelope. The models include
the mixing length theory of convective energy transport of Vitense
(1953). The driving terms included in the mean equations are second
order correlations of velocity and temperature fluctuations. Two classes
of models are investigated: (1) models with anisotropic viscosity,
a special form of driving by Reynolds stresses; and (2) models with
the latitude-dependent heat transport which arises from the influence
of rotation upon convection and which generates meridional circulation
and differential rotation.
---------------------------------------------------------
Title: Convective overshoot at the base of the sun's convection zone
Authors: Pidatella, R. M.; Stix, M.
1986A&A...157..338P Altcode:
The non-local form of mixing length theory, as proposed by Shaviv
and Salpeter (1973), is applied to the deeper part of the solar
convection zone. The result is a layer of convective overshoot
(with inward convective heat transport) which extends over a few
tenths of a scale height, and has a boundary layer at its base where
the temperature gradient suddenly changes from nearly adiabatic
to the radiative value. The overshoot layer is part of a (slightly)
sub-adiabatic region, of approximately one scale height thickness. The
authors argue that this region should be capable to store sufficient
magnetic flux, in the form of thin toroidal flux tubes, to account
for the flux observed at the solar surface.
---------------------------------------------------------
Title: The role of inhomogeneous heat transport and anisotropic
momentum exchange in the dynamics of stellar convection zones -
Application to models of the sun's differential rotation
Authors: Pidatella, R. M.; Stix, M.; Belvedere, G.; Paterno, L.
1986A&A...156...22P Altcode:
We propose mean field models of the Sun's differential rotation which
fully include the mixing-length formalism, ionization and inertial
terms due to rotation. We assume that differential rotation can be
generated by two distinct mechanisms: (i) latitude-dependent heat
transport, HT, modelled through the perturbation of the mixing-length;
(ii) anisotropy of viscosity, AV, modelled through a special form of
the viscous tensor. in the former case the perturbation parameter ɛ
represents the strength of the rotation-convection interaction process,
in the latter case ɛ represents the deviation from isotropy of the
viscous momentum exchange. In both cases ɛ is determined by comparison
of the calculations with the observed differential rotation. We
test the response of the models to changes of the input parameters,
as the depth of the convection zone, the kinematic viscosity, and
the boundary conditions imposed at the lower edge of the convection
zone. One of the most interesting results is that the AV mechanism is
more effective than the HT mechanism, especially for deep convection
zones. Furthermore, all the AV models require a small scale horizontal
momentum exchange more effective than the vertical one to reproduce
the observed differential rotation. The influence of rotation on the
latitude- dependent energy transport depends strongly on the choice
of the lower boundary conditions. When the lower boundary conditions
are imposed in the radiative layers immediately below the convection
zone, the models become independent of the choice of the lower boundary
conditions. There is a general good agreement of the models with the
observable quantities. Also, our internal rotation curve is compatible
with that deduced from the analysis of the rotational splittings of
5 min oscillation modes.
---------------------------------------------------------
Title: Electromagnetic core-mantle coupling.
Authors: Paulus, M.; Stix, M.
1986ersu.conf..259P Altcode:
Electromagnetic core-mantle coupling can account for the decade
fluctuations of the Earth's rotation. The essential physical quantity is
the electrical conductivity of the mantle. Observational requirements
are best satisfied by a conductivity which steeply drops off outwards
from the core-mantle boundary. Results for the geomagnetic field based
on such a conductivity profile are presented for the period 1903.5
to 1975.5 and are compared with the decade fluctuations of the Earth'
rotation.
---------------------------------------------------------
Title: Zur Dynamotheorie des Erdmagnetfeldes.
Authors: Stix, M.
1985PhyBl..41..152S Altcode: 1985PhB....41..152S
No abstract at ADS
---------------------------------------------------------
Title: Schwankungen der Erdrotation und elektromagnetische
Kern-Mantel-Kopplung.
Authors: Stix, M.
1985S&W....24...87S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Time-dependent electromagnetic core-mantle coupling
Authors: Stix, M.; Roberts, P. H.
1984PEPI...36...49S Altcode:
The magnetic field in the Earth's mantle is computed using a
depth-dependent electrical conductivity, of form σ = σ<SUB>a</SUB>(
r/ a) <SUP>- α</SUP>, and an approximation scheme in which the
electromagnetic time constant of the mantle is assumed small compared
with the time scales of the secular variation, and in which the induced
currents and fields are obtained iteratively. We first associate the
toroidal fields in the mantle with motions at the core surface ( r =
a) which create the observed geomagnetic field by flux rearrangement,
and compute the resulting couple, Γ, parallel to the geographical
axis. Using only zonal core motions, and values σ<SUB>a</SUB> =
3 × 10 <SUP>3</SUP>ω<SUP>-1</SUP>m<SUP>-1</SUP>, α = 30 for the
conductivity profile, we find that the toroidal induced fields create a
couple, Γ<SUB>T</SUB>, that over most of this century has been roughly
ten times greater than the poloidal part, Γ<SUB>S</SUB>, of Γ, and
has the same sign. The total couple, Γ, has fluctuations of order 10
<SUP>18</SUP> Nm as required for the observed decade fluctuations in
the length of the day. Its average is ∼ -1.5 × 10 <SUP>18</SUP>
Nm, i.e., it is too large to remain unbalanced. We suppose that an
equally important couple in the opposite sense is created by flux
leakage from the core, and we estimate the necessary gradient of
toroidal field in the core to be of order -0.5 Gs km <SUP>-1</SUP>
at the core surface. During the course of the data analysis needed
for the present work, we found some evidence for a torsional wave in
the Earth's core with a period of ∼ 60 y.
---------------------------------------------------------
Title: Models of solar differential rotation.
Authors: Pidatella, R. M.; Stix, M.; Belvedere, G.; Paterno, L.
1984ESASP.220...33P Altcode: 1984ESPM....4...33P
The models presented give the dependence of the angular velocity at
the Sun's equator on the depth of the convection zone. In order to
drive differential rotation two different mechanisms are considered:
latitude dependence of the mixing length and the anisotropy of the
turbulent viscosity. The influence of boundary conditions at the bottom
of the convection zone on the models are also studied.
---------------------------------------------------------
Title: Solar oscillations as an algebraic eigenvalue problem
Authors: Knoelker, M.; Stix, M.
1984MmSAI..55..305K Altcode:
The 'Cowling approximation', where the Eulerian perturbation of the
gravitational potential is neglected, is used to obtain the frequencies
of adiabatic solar oscillations as eigenvalues of a real symmetric
matrix. The computed p-mode spectra of low and high degree are compared
with observational results. It is suggested that the influence of
the Coulomb interactions on the equation of state, which is presently
neglected, will probably improve the degree of agreement obtained.
---------------------------------------------------------
Title: Sonnenmagnetismus: Beobachtungen und Theorie
Authors: Stix, M.
1984AN....305R.215S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Oscillations and the Equation of State
Authors: Kaisig, M.; Knolker, M.; Stix, M.
1984LIACo..25..239K Altcode: 1984trss.conf..239K; 1984tpss.conf..239K
No abstract at ADS
---------------------------------------------------------
Title: Solar Magnetism : Observation and Theory
Authors: Stix, M.
1984AN....305Q.215S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar magnetism - Observation and theory
Authors: Stix, M.
1984AN....305..215S Altcode:
This introductory review consists of four parts. The first is a
discussion of the concentration of magnetic flux into small elements,
large electrical conductivity and superadiabatic stratification as
the main reasons for these flux tubes, their relationship to the
mean field, and the observational evidence for the latter. The second
briefly repeats the approximations and merits of kinematic mean-field
dynamos. In the form of the alpha-omega dynamo, this theory explains the
reversals, latitude migration, dipolar parity, and other properties of
the mean solar field. The third part treats the question of flux loss
from the convection zone through the buoyancy force, with the conclusion
that the dynamo most probably has its main shear region at the bottom of
the convection zone or in a transition layer beneath it. The last part
discusses further dynamic aspects of the sun's magnetism (e.g., models
of limit cycles and models with chaotic behavior) and in particular
the question of the phase stability of the solar cycle.
---------------------------------------------------------
Title: Helicity and alpha-effect of simple convection cells
Authors: Stix, M.
1983A&A...118..363S Altcode:
The helicity of a rotationally distorted convection cell in a fluid
with spatially varying density was derived in order to calculate
the mean electric current parallel to the mean field of the sun (the
alpha-effect). The alpha-effect occurs in a conducting fluid subjected
to helical motions. A representative convection cell is analyzed in
terms of eight harmonic contributions to the helicity of the rotational
motion. The estimate derived for the alpha term is dependent on the
rotation and density stratification, as was found by Krause (1967).
---------------------------------------------------------
Title: Two comments of the sun's differential rotation
Authors: Schmidt, W.; Stix, M.
1983A&A...118....1S Altcode:
The authors argue that the effect of rotation should be neglected
when the convection velocity is estimated through a comparison of the
kinetic energy with the work done by the superadiabatic temperature
gradient. A recent model of the Sun's differential rotation by Durney
(1981) would thus not be restricted to small rates of rotation. The
authors present a simple model where convection cells elongated
in north-south direction are simulated by means of an anisotropic
turbulent viscosity tensor. The resulting mean flow has equatorial
acceleration, as observed on the Sun, with negligible concomitant
meridional circulation and pole-equator temperature difference.
---------------------------------------------------------
Title: A Convenient Method to Obtain Stellar Eigenfrequencies
Authors: Knoelker, M.; Stix, M.
1983SoPh...82..331K Altcode: 1983IAUCo..66..331K
The differential equations describing stellar oscillations are
transformed into an algebraic eigenvalue problem. Frequencies
of adiabatic oscillations are obtained as the eigenvalues of a
banded real symmetric matrix. We employ the Cowling-approximation,
i.e. neglect the Eulerian perturbation of the gravitational potential,
and, in order to preserve selfadjointness, require that the Eulerian
pressure perturbation vanishes at the outer boundary. For a solar model,
comparison of first results with results obtained from a Henyey method
shows that the matrix method is convenient, accurate, and fast.
---------------------------------------------------------
Title: Theoretical Problems - Solar and Stellar Magnetic Fields
Authors: Stix, M.
1983IAUS..102..509S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solare Oszillationen als algebraisches Eigenwertproblem
Authors: Knoelker, M.; Stix, M.
1983MitAG..60..221K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A review of: "Solar magnetohydrodynamics"
Authors: Stix, M.
1983GApFD..24..327S Altcode:
By E. R. Priest, Geophys. and Astrophys. Monographs, Vol. 21, D. Reidel,
Dordrecht, 1982. xx + 469 pp, Dfl. 235, US $99.00 (ISBN 90-277-1374-x).
---------------------------------------------------------
Title: Solar type dynamos in late main sequence stars
Authors: Stix, M.
1983spm..conf..197S Altcode:
αω-dynamos are calculated for stellar models representing F5 to M0
stars. Oscillatory fields are found for all the stellar models, with
periods increasing towards later spectral types. It is suggested that -
besides rotation - the main parameters affecting the period and the
amplitude of the oscillatory field are the turbulent diffusivities
and the depth of the outer convection zone.
---------------------------------------------------------
Title: Die differentielle Rotation und der magnetische Zyklus
der Sonne
Authors: Stix, M.
1983MitAG..60...95S Altcode:
Differential rotation originates from Reynolds stresses in the Sun's
convection zone, either via a mean meridional circulation or by direct
transport of angular momentum. The required correlations between
the components of the turbulent velocity field are provided by the
action of rotation upon convection. When a magnetic field is present,
the same interaction generates a mean electric field parallel to the
mean magnetic field. The latter effect cooperates with differential
rotation to yield an oscillatory mean field which propagates along
the surfaces of isorotation. This article reviews some attempts to
describe such processes theoretically including the recently proposed
strange attractor model of the solar cycle.
---------------------------------------------------------
Title: On electromagnetic core-mantle coupling
Authors: Stix, M.
1982GApFD..21..303S Altcode:
The induced magnetic field in the Earth's mantle is computed for an
electrical conductivity of the mantle of form = a(a/r) where a is the
core radius. When the inducing core motion is a uniform westward drift
of -10-10s-1 relative to the mantle, the retarding couple reaches -1019
Nm. This result can be obtained with values and α such that the time
scale of screening, μσa2/α2, is still below 10 years. The retarding
couple, and in particular the contribution from the higher field
harmonics, increases with increasing concentration of the conducting
layer towards the core-mantle boundary. Deviations from the average
torque balance of order 10% of the retarding couple can account for the
"decade fluctuations" in the Earth's rate of rotation.
---------------------------------------------------------
Title: Eine bequeme Methode zur Berechnung stellarer Eigenfrequenzen -
Anwendungen auf Sonnenmodelle
Authors: Knölker, M.; Stix, M.
1982MitAG..55..138K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Rotation-Magnetism-Convection Coupling in the Sun (Invited
Review Paper)
Authors: Stix, M.
1982ASSL...96...63S Altcode: 1982spls.meet...63S
The rotational and magnetic evolution of a star depends on its initial
mass and angular momentum, but not directly on its initial magnetic
field if the star has an outer convection zone. The present field is
generated by a self-excited dynamo. Rotation influences convection
and so generates the two main ingredients of the dynamo process,
nonuniform rotation and helicity. Several competing descriptions have
been proposed: A two-level picture where first single convective cells
are distorted by rotation and then the net effect on the mean flow
and field is considered, and a direct numerical approach, including
rotational effects, where small-scale motions enter only as isotropic
diffusivities of heat, momentum, and field. Difficulties arise in
particular from the fact that the magnetic field is concentrated
into fibrils of large field strength. Predictions of a quantitative
relationship between a star's rate of rotation and its magnetic field
amplitude are also difficult, although observations of late-type
stars suggest such a relationship. A transition between two modes
of dynamo operation may occur as the star's rotation slows down by
magnetic braking.
---------------------------------------------------------
Title: The Rotation and the Magnetic Field of the Earth
Authors: Stix, M.
1982tfer.conf...98S Altcode:
Contents: Weak or strong toroidal fields? Electromagnetic core-mantle
coupling.
---------------------------------------------------------
Title: Theory of the Solar Cycle
Authors: Stix, M.
1981SoPh...74...79S Altcode:
The properties of kinematic αω-dynamos are briefly reviewed. The mean
field concept, including turbulent diffusivity, is defended against
recent criticism. It is pointed out that although the Maunder minimum
cannot be explained by kinematic dynamo theory alone, this does not
invalidate dynamo theory in general. A special discussion is devoted
to attempts to evaluate the coefficients of the mean field induction
equation in the case of very large conductivity. The field then behaves
intermittent, in the form of locally concentrated flux tubes, and the
α-effect and the turbulent diffusivity may be determined by asymptotic
techniques or with the help of an exact solution of the non-dissipative
induction equation in Lagrangian co-ordinates.
