Author name code: stix ADS astronomy entries on 2022-09-14 author:"Stix, Michael" ------------------------------------------------------------------------ Title: Solar Global Parameters; Solar Interior Authors: Stix, Michael Bibcode: 2009LanB...4B....1S Altcode: 2009LanB...4B.4111S No abstract at ADS Title: Book Review Authors: Stix, Michael Bibcode: 2008GApFD.102..541S Altcode: No abstract at ADS Title: Meridional Circulation and Global Solar Oscillations Authors: Roth, M.; Stix, M. Bibcode: 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. Title: Meridional Circulation and Global Solar Oscillations Authors: Roth, M.; Stix, M. Bibcode: 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. Title: Effects of rotation and input energy flux on convective overshooting Authors: Käpylä, Petri J.; Korpi, M. J.; Stix, M.; Tuominen, I. Bibcode: 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. Title: Reynolds stresses and meridional circulation from rotating cylinder simulations Authors: Hupfer, C.; Käpylä, P. J.; Stix, M. Bibcode: 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.
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.
Results: .For moderate Coriolis numbers both models yield strong extrema of the Reynolds stress component Qθϕ 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.
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. Bibcode: 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.
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, Ei = aij overline B_j, all nine components of aij are computed. The diagonal elements of aij 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).
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.
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. Bibcode: 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. Title: Magnetic Field Generation in Fully Convective Rotating Spheres Authors: Dobler, Wolfgang; Stix, Michael; Brandenburg, Axel Bibcode: 2006ApJ...638..336D Altcode: 2004astro.ph.10645D Magnetohydrodynamic simulations of fully convective, rotating spheres with volume heating near the center and cooling at the surface are presented. The dynamo-generated magnetic field saturates at equipartition field strength near the surface. In the interior, the field is dominated by small-scale structures, but outside the sphere, by the global scale. Azimuthal averages of the field reveal a large-scale field of smaller amplitude also inside the star. The internal angular velocity shows some tendency to be constant along cylinders and is ``antisolar'' (fastest at the poles and slowest at the equator). Title: Local models of stellar convection. II. Rotation dependence of the mixing length relations Authors: Käpylä, P. J.; Korpi, M. J.; Stix, M.; Tuominen, I. Bibcode: 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. Title: Reynolds stresses - dependence on latitude Authors: Hupfer, C.; Käpylä, P.; Stix, M. Bibcode: 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 Qij = < u'i u'j > 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 Qθφ at low latitude very close to the equator, which may have implications to the theory of the angular velocity profile observed on the Sun. Title: Dynamos of the Sun, Stars, and Planets - Preface Authors: Stix, M. Bibcode: 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. Title: Book review Authors: Stix, Michael Bibcode: 2005GApFD..99..431S Altcode: No abstract at ADS Title: On the effect of convection on solar p modes Authors: Stix, M.; Zhugzhda, Y. D. Bibcode: 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. Title: Tube waves: Exact and approximate Authors: Stix, M. Bibcode: 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 cT and \sqrt{2} cT, all fast modes have phase velocities above \sqrt{2} cT. Title: The sun : an introduction Authors: Stix, Michael Bibcode: 2004suin.book.....S Altcode: No abstract at ADS Title: Helioseismology (With 12 Figures) Authors: Stix, Michael Bibcode: 2004RvMA...17...51S Altcode: No abstract at ADS Title: Time-dependent coupling of solar oscillations Authors: Roth, M.; Stix, M. Bibcode: 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. 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 Bibcode: 2003ANS...324...63K Altcode: 2003ANS...324..I02K No abstract at ADS Title: On the time scale of energy transport in the sun Authors: Stix, Michael Bibcode: 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 3×107 years, roughly 100 times longer than the photon-diffusion time estimated by Mitalas and Sills (1992). The difference corresponds to a factor Ugas/Urad, 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. Title: Magnetoconvection and dynamo coefficients. II. Field-direction dependent pumping of magnetic field Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A.; Rüdiger, G. Bibcode: 2002A&A...394..735O Altcode: 2002astro.ph..2299O We study the pumping of magnetic flux in three-dimensional compressible magnetoconvection in the context of stellar dynamos. The simulation domain represents a rectangular section from the lower part of a stellar convection zone plus the underlying stably stratified layer, with a total depth of up to five pressure scale heights. Once convection has attained a statistically stationary state, a magnetic field is introduced. The magnetic field is subsequently modified by the convective motions, and the resulting pumping effects are isolated by calculating various coefficients of the expansion of the electromotive force, /line{u}x{b}, in terms of components of the mean magnetic field. The dependence of the pumping effects on rotation, latitude and other parameters is studied. First numerical evidence is found for the existence of pumping effects in the horizontal directions. Evidence is found that the pumping effects act differently on different components of the mean magnetic field. Latitudinal pumping is mainly equatorward for a toroidal field, and can be poleward for a poloidal field. Longitudinal pumping is mainly retrograde for the radial field but prograde for the latitudinal field. The pumping effect in the vertical direction is found to be dominated by the diamagnetic effect, equivalent to a predominating downward advection with a maximum speed in the turbulent case of about 10% of the rms convective velocity. Where possible, an attempt is made to identify the physical origin of the effect. Finally, some consequences of the results for stellar dynamos are discussed. Title: Spectral signature of magnetic flux tubes in sunspot penumbrae Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M. Bibcode: 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. Title: Sunspots: What is interesting? Authors: Stix, M. Bibcode: 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? Title: Net circular polarization of sunspot penumbrae - symmetry breaking by anomalous dispersion Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M. Bibcode: 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. Title: Net circular polarization of sunspot penumbrae. Symmetry breaking through anomalous dispersion Authors: Schlichenmaier, R.; Müller, D. A. N.; Steiner, O.; Stix, M. Bibcode: 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. Title: The sun: an introduction Authors: Stix, Michael Bibcode: 2002tsai.book.....S Altcode: No abstract at ADS Title: Physics of the solar dynamo: Outstanding problems Authors: Stix, M. Bibcode: 2001A&AT...20..417S Altcode: No abstract at ADS Title: Joint 9th European and 5th national astronomical meeting (Jenam-2000), 'European astronomy at the turn of the millennium' Authors: Stix, M. Bibcode: 2001A&AT...20..415S Altcode: No abstract at ADS Title: Magnetoconvection and dynamo coefficients:. Dependence of the alpha effect on rotation and magnetic field Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A. Bibcode: 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 (B0/Beq)2]-1. The signs of the small-scale current helicity and of the vertical component of alpha are found to be opposite to those for isotropic turbulence. Title: Differential rotation of the present and the pre-main-sequence Sun Authors: Küker, M.; Stix, M. Bibcode: 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. Title: Effect of time-dependent velocity fields on solar oscillations Authors: Roth, Markus; Stix, Michael Bibcode: 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. Title: Sun: Basic Properties Authors: Stix, M. Bibcode: 2000eaa..bookE1977S Altcode: The standard star... Title: Modulation of Acoustic Waves by Solar Convection Authors: Stix, M. Bibcode: 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. Title: Wave modulation and wave sources in the solar convection zone Authors: Kiefer, M.; Stix, M.; Balthasar, H. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 2000IAUTA..24...73F Altcode: No abstract at ADS Title: Coupling of solar p modes: quasi-degenerate perturbation theory Authors: Roth, M.; Stix, M. Bibcode: 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-1. The splitting scales with v2, 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. Bibcode: 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. Bibcode: 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. Bibcode: 1999A&R....36Q...4S Altcode: No abstract at ADS Title: Ein Blick in das Innere der Sonne. Authors: Schleicher, H.; Stix, M. Bibcode: 1999A&R....36....8S Altcode: No abstract at ADS Title: Coupling of Solar Oscillations in Quasi-Degenerate Perturbation Theory Authors: Roth, M.; Stix, M. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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 Rsun and 0.286 Rsun, 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 1Msun_. Authors: Schuessler, M.; Caligari, P.; Ferriz-Mas, A.; Solanki, S. K.; Stix, M. Bibcode: 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. Bibcode: 1996AGAb...12..166S Altcode: No abstract at ADS Title: Wave trapping in intergranular lanes Authors: Stix, M.; Zhugzhda, Y. D. Bibcode: 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. Bibcode: 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. Bibcode: 1996ApL&C..34...17C Altcode: No abstract at ADS Title: Kiepenheuer-Institut für Sonnenphysik. Jahresbericht für 1995. Authors: Stix, M. Bibcode: 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. Bibcode: 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^2OMEGA 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. Bibcode: 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. Bibcode: 1995LIACo..32..379K Altcode: 1995sews.book..379K No abstract at ADS Title: Kiepenheuer-Institut für Sonnenphysik. Jahresbericht für 1994. Authors: Stix, M. Bibcode: 1995MitAG..78..125S Altcode: No abstract at ADS Title: Solar Models with Convective Overshoot Authors: Stix, M. Bibcode: 1995somo.conf..171S Altcode: No abstract at ADS Title: p-mode frequency corrections due to convection Authors: Stix, M. Bibcode: 1995HiA....10..331S Altcode: No abstract at ADS Title: Acoustic waves in structured media and helioseismology. Authors: Zhugzhda, Y. D.; Stix, M. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 1994MitAG..77..121S Altcode: No abstract at ADS Title: The phase of the radial field in the solar dynamo Authors: Schlichenmaier, R.; Stix, M. Bibcode: 1994smf..conf..107S Altcode: No abstract at ADS Title: On the Depletion of Lithium in the Sun Authors: Ahrens, J.; Stix, M.; Thorn, M. Bibcode: 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. Bibcode: 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(- |ωoscτcorr|), where τcorr 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.

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. Bibcode: 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. Bibcode: 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. Bibcode: 1992AGAb....7..147A Altcode: No abstract at ADS Title: Book-Review - the Sun - an Introduction Authors: Stix, M. Bibcode: 1991Sci...254R1053S Altcode: No abstract at ADS Title: Book-Review - the Sun - an Introduction Authors: Stix, M.; Ambroz, P. Bibcode: 1991BAICz..42..329S Altcode: No abstract at ADS Title: An alpha-Omega dynamo with order and chaos Authors: Schmalz, S.; Stix, M. Bibcode: 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. Bibcode: 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. Bibcode: 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 Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 1989JBAA...99..245S Altcode: No abstract at ADS Title: Book-Review - the Sun Authors: Stix, M. Bibcode: 1989S&T....78..606S Altcode: No abstract at ADS Title: Book-Review - the Sun - an Introduction Authors: Stix, M. Bibcode: 1989Sci...246..246S Altcode: No abstract at ADS Title: Eigenschwingungen der Sonne. Authors: Stix, M. Bibcode: 1989PhyBl..45..146S Altcode: 1989PhB....45..146S No abstract at ADS Title: The Sun's differential rotation. Authors: Stix, M. Bibcode: 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. Bibcode: 1989RvMA....2..248S Altcode: No abstract at ADS Title: The sun. an introduction Authors: Stix, Michael Bibcode: 1989sai..book.....S Altcode: No abstract at ADS Title: The Sun. an Introduction Authors: Stix, Michael Bibcode: 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 Bibcode: 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 Bibcode: 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. Bibcode: 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/Hp (mixing length/pressure scale height) and the initial He-abundance Y0 are obtained by calculating a full model sequence in time to α = 1.505 and Y0 = 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 Bibcode: 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. Bibcode: 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, A0: the product A0B 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. Bibcode: 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 Bibcode: 1987LNP...292...13S Altcode: No abstract at ADS Title: On the Origin of Stellar Magnetism Authors: Stix, M. Bibcode: 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 Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 1985PhyBl..41..152S Altcode: 1985PhB....41..152S No abstract at ADS Title: Schwankungen der Erdrotation und elektromagnetische Kern-Mantel-Kopplung. Authors: Stix, M. Bibcode: 1985S&W....24...87S Altcode: No abstract at ADS Title: Time-dependent electromagnetic core-mantle coupling Authors: Stix, M.; Roberts, P. H. Bibcode: 1984PEPI...36...49S Altcode: The magnetic field in the Earth's mantle is computed using a depth-dependent electrical conductivity, of form σ = σa( r/ a) - α, 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 σa = 3 × 10 3ω-1m-1, α = 30 for the conductivity profile, we find that the toroidal induced fields create a couple, ΓT, that over most of this century has been roughly ten times greater than the poloidal part, ΓS, of Γ, and has the same sign. The total couple, Γ, has fluctuations of order 10 18 Nm as required for the observed decade fluctuations in the length of the day. Its average is ∼ -1.5 × 10 18 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 -1 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. Bibcode: 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. Bibcode: 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. Bibcode: 1984AN....305R.215S Altcode: No abstract at ADS Title: Solar Oscillations and the Equation of State Authors: Kaisig, M.; Knolker, M.; Stix, M. Bibcode: 1984LIACo..25..239K Altcode: 1984trss.conf..239K; 1984tpss.conf..239K No abstract at ADS Title: Solar Magnetism : Observation and Theory Authors: Stix, M. Bibcode: 1984AN....305Q.215S Altcode: No abstract at ADS Title: Solar magnetism - Observation and theory Authors: Stix, M. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 1983IAUS..102..509S Altcode: No abstract at ADS Title: Solare Oszillationen als algebraisches Eigenwertproblem Authors: Knoelker, M.; Stix, M. Bibcode: 1983MitAG..60..221K Altcode: No abstract at ADS Title: A review of: "Solar magnetohydrodynamics" Authors: Stix, M. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 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. Bibcode: 1982MitAG..55..138K Altcode: No abstract at ADS Title: The Rotation-Magnetism-Convection Coupling in the Sun (Invited Review Paper) Authors: Stix, M. Bibcode: 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. Bibcode: 1982tfer.conf...98S Altcode: Contents: Weak or strong toroidal fields? Electromagnetic core-mantle coupling. Title: Theory of the Solar Cycle Authors: Stix, M. Bibcode: 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.