Magnetic pinch-type instability in stellar radiative zones
G. Ruediger, L. L. Kitchatinov, M. Gellert
备注：
10 pages, 9 figures, Proc. IAU Symp. 259, Cosmic Magnetic Fields: from Planets, to Stars and Galaxies. K.G. Strassmeier, A.G. Kosovichev, J. Beckmann, eds
The solar tachocline is shown as hydrodynamically stable against nonaxisymmetric disturbances if it is true that no cos^{4}θterm exists in its rotation law. We also show that the toroidal field of 200 Gauss amplitude which produces the tachocline in the magnetic theory of Ruediger & Kitchatinov (1997) is stable against nonaxisymmetric MHD disturbances -- but it becomes unstable for rotation periods slightly slower than 25 days. The instability of such weak fields lives from the high thermal diffusivity of stellar radiation zones compared with the magnetic diffusivity. The growth times, however, result as very long (of order of 10\^5 rotation times). With estimations of the chemical mixing we find the maximal possible field amplitude to be ~500 Gauss in order to explain the observed lithium abundance of the Sun. Dynamos with such low field amplitudes should not be relevant for the solar activity cycle. With nonlinear simulations of MHD Taylor-Couette flows it is shown that for the rotation-dominated magnetic instability the resulting eddy viscosity is only of the order of the molecular viscosity. The Schmidt number as the ratio of viscosity and chemical diffusion grows to values of ~20. For the majority of the stellar physics applications, the magnetic-dominated Tayler instability will be quenched by the stellar rotation.
Helioseismology puts strong constraints on the internal sound speed and on the rotation profile in the radiative zone. Young stars of solar type are more active and faster rotators than the Sun. So we begin to build models which include different rotation histories and compare the results with all the solar observations. The profiles of the rotation we get have interesting consequence for the introduction of magnetic field in the radiative zone. We discuss also the impact of mass loss deduced from measured flux of young stars. We deduce from these comparisons some quantitative effect of the dy…
Convection in the cores of massive stars becomes anisotropic when they rotate. This anisotropy leads to a misalignment of the thermal gradient and the thermal flux, which in turn results in baroclinicity and circulation currents in the upper radiative zone. We show that this induces a much stronger meridional flow in the radiative zone than previously thought. This drives significantly enhanced mixing, though this mixing does not necessarily reach the surface. The extra mixing takes on a similar form to convective overshooting, and is relatively insensitive to the rotation rate above a thresho…
Asteroseismology has reached a level of accuracy that may allow us to detect the effect of a deep magnetic field on oscillation modes. We thus aim to develop an asymptotic theory for short-wavelength waves in radiative zones of rotating stars with a general magnetic field topology (toroidal and poloidal). A dispersion relation is derived for a uniformly rotating star with a low-amplitude, axisymmetric magnetic field. The parameter space of this model is explored with a Hamiltonian ray-tracing method. The features of the gravito-inertial waves modified by the magnetic field are studied with dif…
We present a series of numerical simulations of the quiet Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun's atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of ele…
Effects of the radiative interior on solar inertial modes
Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系统研究所）；Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen（哥廷根大学天体物理与地球物理研究所）
The solar convection zone exhibits a strong level of differential rotation, whereby the rotation period of the polar regions is about 25-30% longer than the equatorial regions. The Coriolis force associated with these zonal flows perpetually "pumps" the convection zone fluid, and maintains a quasi-steady circulation, poleward near the surface. What is the influence of this meridional circulation on the underlying radiative zone, and in particular, does it provide a significant source of mixing between the two regions? In Paper I, we began to study this question by assuming a fixed meridional f…
The dynamics of the solar radiative interior are still poorly constrained by comparison to the convective zone. This disparity is even more marked when we attempt to derive meaningful temporal variations. Many data sets contain a small number of modes that are sensitive to the inner layers of the Sun, but we found that the estimates of their uncertainties are often inaccurate. As a result, these data sets allow us to obtain, at best, a low resolution estimate of the solar core rotation rate down to approximately 0.2R. We present inferences based on mode determination resulting from an alternat…
Some contracting or expanding stars are thought to host a large-scale magnetic field in their radiative interior. By interacting with the contraction-induced flows, such fields may significantly alter the rotational history of the star. They thus constitute a promising way to address the problem of angular momentum transport during the rapid phases of stellar evolution. In this work, we aim at studying the interplay between flows and magnetic fields in a contracting radiative zone. We propose a scenario that may account for the post-main sequence evolution of solar-like stars, in which a quasi…
Internal waves propagating in stellar radiative zones can lead to efficient angular momentum transport, that should occur throughout the whole lifetime of stars. They thus play a key role in shaping the internal rotation profile of these regions, that can be probed by asteroseismology. We present a new analytical study of their propagation and dissipation near the equatorial plane. We include the effects of rotation and differential rotation without making any assumption on their relative strength relative to that of the background stable stratification. This analytical framework allows in pri…
In the context of secular evolution, we describe the dynamics of the radiative core of low-mass stars to understand the internal transport of angular momentum in such stars which results in a solid rotation in the Sun from 0.7R_sun to 0.2R_sun and a weak radial core-envelope differential rotation in solar-type stars. This study requires at least a 2D description to capture the latitudinal variations of the differential rotation. We build 2D numerical models of a radiative core on the top of which we impose a latitudinal shear so as to reproduce a cylindrical differential rotation in a convecti…
The Goldreich-Schubert-Fricke (GSF) instability is a rotational instability that is thought to contribute to the transfer of angular momentum in differentially rotating stars. It has been included in recent codes of stellar evolution in a diffusion-like approximation, under the assumption that the kinematic viscosity $ν$ is unimportant for the development of the instability. As noted previously by other authors, for most stellar applications this may not be a valid approximation. We discuss this issue in detail, solving the dispersion relation of the perturbed modes for realistic values of $ν$…
Context. In stellar interiors, rotation is able to drive turbulent motions, and the related transport processes have a significant influence on the evolution of stars. Turbulent mixing in the radiative zones is currently taken into account in stellar evolution models through a set of diffusion coefficients that are generally poorly constrained. Aims. We want to constrain the form of one of them, the radial diffusion coefficient of chemical elements due to the turbulence driven by radial differential rotation, derived by Zahn (1974, 1992) on phenomenological grounds and largely used since. Meth…
Barotropic rotation and radiative equilibrium are mutually incompatible in stars. The issue is often addressed by allowing for a meridional circulation, but this is not devoid of theoretical complications. Models of rotation in the Sun which maintain strict radiative equilibrium, making use of the observation that the Sun is not in a state of barotropic rotation, have recently been suggested. To investigate the dynamical behaviour of these solutions, we study the local stability of stratified, weakly magnetized, differentially rotating fluids to non-axisymmetric perturbations. Finite heat cond…
Context. Turbulent transport in stellar radiative zones is a key ingredient of stellar evolution theory, but the anisotropy of the transport due to the stable stratification and the rotation of these regions is poorly understood. The assumption of shellular rotation, which is a cornerstone of the so-called rotational mixing, relies on an efficient horizontal transport. However, this transport is included in many stellar evolution codes through phenomenological models that have never been tested. Aims. We investigate the impact of horizontal shear on the anisotropy of turbulent transport. Metho…
Recent numerical simulations suggest that the model by Zahn (1992, A&A, 265, 115) for the turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is valid. We investigate the robustness of this result with respect to the numerical configuration and Reynolds number of the flow. We compare results from simulations performed with two different numerical codes, including one that uses the shearing-box formalism. We also extensively study the dependence of the turbulent diffusion coefficient on the turbulent Reynolds number. The two numerical codes used in this…
The topic of turbulent transport in a stellar radiative zone is vast and poorly understood. Many physical processes can potentially drive turbulence in stellar radiative zone but the limited observational constraints and the uncertainties in modelling turbulent transport make it difficult to identify the most relevant one. Here, we focus on the effect of stable stratification on the radial turbulent transport of chemicals and more particularly on the case where the turbulence is driven by a radial shear. Results of numerical simulations designed to test phenomenological models of turbulent tra…
This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. In particular, a purely magnetic instability can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations as originally studied in Tayler (1973), Markey & Tayler (1973), and Tayler (1980). However, most of the magnetic field configurations observed at the surface of massive stars are non- axisymmetric. Thus, extending earlier studies of the axisymmetric Tayler instabilit…
Turbulent transport of chemical elements in radiative zones of stars is considered in current stellar evolution codes thanks to phenomenologically derived diffusion coefficients. Recent local numerical simulations (Prat & Lignières 2013, A&A, 551, L3) suggest that the coefficient for radial turbulent diffusion due to radial differential rotation satisfies $D_{\rm t}\simeq0.058κ/Ri$, in qualitative agreement with Zahn's model. However, this model does not apply when differential rotation is strong with respect to stable thermal stratification or when chemical stratification has a significant dy…
Context. Stars experience rapid contraction or expansion at different phases of their evolution. Modelling the angular momentum and chemical elements transport occurring during these phases remains an unsolved problem. Aims. We study a stellar radiative zone undergoing radial contraction and investigate the induced differential rotation and meridional circulation. Methods. We consider a rotating spherical layer crossed by an imposed radial velocity field that mimics the contraction and solve numerically the axisymmetric hydrodynamical equations in both the Boussinesq and anelastic approximatio…
The Standard Solar Model (SSM) is no more sufficient to interpret all the observations of the radiative zone obtained with the SoHO satellite. We recall our present knowledge of this internal region and compare the recent results to models beyond the SSM assumptions. Then we discuss the missing processes and quantify some of them in using young analog observations to build a more realistic view of our star. This progress will be useful for solar-like stars observed by COROT and KEPLER.
We introduce two new methods that are designed to improve the realism and utility of large, active region-scale 3D MHD models of the solar atmosphere. We apply these methods to RADMHD, a code capable of modeling the Sun's upper convection zone, photosphere, chromosphere, transition region, and corona within a single computational volume. We first present a way to approximate the physics of optically-thick radiative transfer without having to take the computationally expensive step of solving the radiative transfer equation in detail. We then briefly describe a rudimentary assimilative techniqu…
It is well known that the combination of barotropic rotation and radiative equilibrium are mutually incompatible in stars. The Sun's internal rotation is far from barotropic, however, which allows at least the theoretical possibility that the Sun's thermal balance is one of radiative equilibrium in the region of the tachocline near the outer boundary of the radiative zone. We show here that (i) the constraint of radiative equilibrium leads to a straightforward ordinary differential equation for the Sun's rotation profile, and (ii) solutions of this equation can be found that, to within current…
Transport of angular momentum and chemical elements by the MRI dynamo in stellar radiative zones
Toulouse Univ.（图卢兹大学）；Institut de Recherche en Astrophysique et Planétologie（天体物理学与行星学研究所在）；CNRS（法国国家科学研究中心）；CNES（法国国家空间研究中心）；Département d’Astrophysique/AIM CEA/IRFU（天体物理系/AIM cea/IRFU）；Univ. Paris-Saclay（巴黎萨克雷大学）；Univ. de Paris Cité（巴黎西岱大学）；Institut de Mécanique des Fluides de Toulouse（图卢兹流体力学研究所）
We present a comprehensive radiative magnetohydrodynamic simulation of the quiet Sun and large solar active regions. The 197 Mm wide simulation domain spans from 18 (10) Mm beneath the photosphere to 113 Mm in the solar corona. Radiative transfer assuming local thermal equilibrium, optically-thin radiative losses, and anisotropic conduction transport provide the necessary realism for synthesizing observables to compare with remote sensing observations of the photosphere and corona. This model self-consistently reproduces observed features of the quiet Sun, emerging and developed active regions…
A major outstanding problem in solar physics is the confinement of the solar tachocline, the thin shear layer that separates nearly solid-body rotation in the radiative interior from strong differential rotation in the convection zone. Here, we present the first 3-D, global solar simulation in which a tachocline is confined by a self-excited dynamo. The non-axisymmetric magnetism is initially built in the convection zone and then diffusively imprints downward. Additionally, the field is locally amplified throughout the radiative interior by vigorous horizontal motions that arise from equatoria…
Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dimensional and time-dependent model of stellar radiation zones consisting of an electrically-conductive and stably-stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially-symmetric time-independe…
Recent spectropolarimetric surveys of main-sequence intermediate-mass stars have exhibited a dichotomy in the distribution of the observed magnetic field between the kG dipoles of Ap/Bp stars and the sub-Gauss magnetism of Vega and Sirius. We would like to test whether this dichotomy is linked to the stability versus instability of large-scale magnetic configurations in differentially rotating radiative zones. We computed the axisymmetric magnetic field obtained from the evolution of a dipolar field threading a differentially rotating shell. A full parameter study including various density pro…
The rich harvest of seismic observations over the past decade provides evidence of angular momentum redistribution in stellar interiors that is not reproduced by current evolution codes. In this context, transport by internal gravity waves can play a role and could explain discrepancies between theory and observations. The efficiency of the transport of angular momentum by waves depends on their driving mechanism. While excitation by turbulence throughout the convective zone has already been investigated, we know that penetrative convection into the stably stratified radiative zone can also ge…
Our understanding of large-scale magnetic fields in stellar radiative zones remains fragmented and incomplete. Such magnetic fields, which must be produced by some form of dynamo mechanism, are thought to dominate angular-momentum transport, making them crucial to stellar evolution. A major difficulty is the effect of stable stratification, which generally suppresses dynamo action. We explore the effects of stable stratification on mean-field dynamo theory with a particular focus on a non-helical large-scale dynamo (LSD) mechanism known as the magnetic shear-current effect. We find that the me…
The question of the origin and evolution of magnetic fields in stars possessing a radiative envelope, like the A-type stars, is still regarded as a challenge for stellar physics. Those zones are likely to be differentially rotating, which suggests that strong interactions between differential rotation and magnetic fields could be at play. We numerically compute the joint evolution of the magnetic and velocity fields in a 3D spherical shell starting from an initial profile for the poloidal magnetic field and differential rotation. The poloidal magnetic field is initially wound-up by the differe…
[Abridged] Most exoplanets detected so far are close-in planets, which are likely to be affected by tidal dissipation in their host star. To get a complete picture of the evolution of star-planet systems one needs to consider the impact of tides within both stellar radiative and convective zones. We aim to provide a general formalism to assess tidal dissipation in stellar radiative zones for all spectral types, allowing for the study of the dynamics of a given system throughout stellar evolution. We investigate the influence of stellar structure and evolution on tidal dissipation in the radiat…
Continued progress in observational stellar astrophysics requires a deep understanding of the underlying convection dynamics. We present results of realistic 3D radiative hydrodynamic simulations of the outer layers of a moderate mass star (1.47 Msun), including the full convection zone, the overshoot region, and the top layers of the radiative zone. The simulation results show that the surface granulation has a broad range of scales, from 2 to 12 Mm, and that large granules are organized in well-defined clusters, consisting of several granules. Comparison of the mean structure profiles from 3…
Advances in laser and Z-pinch technology, coupled with the development of plasma diagnostics and the availability of high-performance computers, have recently stimulated the growth of high-energy density laboratory astrophysics. In particular a number of experiments have been designed to study radiative shocks and jets with the aim of shedding new light on physical processes linked to the ejection and accretion of mass by newly born stars. Although general scaling laws are a powerful tools to link laboratory experiments with astrophysical plasmas, the phenomena modelled are often too complicat…
The present study aims at studying the flow and field produced by a stellar radiative zone which is initially made to rotate differentially in the presence of a large-scale poloidal magnetic field threading the whole domain. We focus both on the axisymmetric configurations produced by the initial winding-up of the magnetic field lines and on the possible instabilities of those configurations. We aim in particular at assessing the role of the stratification at stabilising the system. We perform 2D and 3D global Boussinesq numerical simulations started from an initial radial or cylindrical diffe…
Key physical ingredients governing the evolution of massive stars are mass losses, convection and mixing in radiative zones. These effects are important both in the frame of single and close binary evolution. The present paper addresses two points: 1) the differences between two families of rotating models, i.e. the family of models computed with and without an efficient transport of angular momentum in radiative zones; 2) The impact of the mass losses in single and in close binary models.
The evolution of a star is influenced by its internal rotation dynamics through transport and mixing mechanisms, which are poorly understood. Magnetic fields can play a role in transporting angular momentum and chemical elements, but the origin of magnetism in radiative stellar layers is unclear. Using global numerical simulations, we identify a subcritical transition to turbulence due to the generation of a magnetic dynamo. Our results have many of the properties of the theoretically-proposed Tayler-Spruit dynamo mechanism, which strongly enhances transport of angular momentum in radiative zo…
We present axisymmetric simulations of the coupled convective and radiative regions in the Sun in order to investigate the angular momentum evolution of the radiative interior. Both hydrodynamic and magnetohydrodynamic models were run. We find an initial rapid adjustment in which the dif- ferential rotation of the convection zone viscously spreads into the radiative interior, thus forming a "tachocline". In polar regions the subsequent spread of the tachocline is halted by a counter-rotating meridional circulation cell which develops in the tachocline. Near the equator such a counter-rotating …
Current state-of-the-art computational modeling makes it possible to build realistic models of stellar convection zones and atmospheres that take into account chemical composition, radiative effects, ionization, and turbulence. The standard 1D mixing-length-based evolutionary models are not able to capture many physical processes of the stellar interior dynamics. Mixing-length models provide an initial approximation of stellar structure that can be used to initialize 3D radiative hydrodynamics simulations which include realistic modeling of turbulence, radiation, and other phenomena. In this p…
Stellar evolution models calculate convective boundaries using either the Schwarzschild or Ledoux criterion, but confusion remains regarding which criterion to use. Here we present a 3D hydrodynamical simulation of a convection zone and adjacent radiative zone, including both thermal and compositional buoyancy forces. As expected, regions which are unstable according to the Ledoux criterion are convective. Initially, the radiative zone adjacent to the convection zone is Schwarzschild-unstable but Ledoux-stable due to a composition gradient. Over many convective overturn timescales the convecti…
Coexisting Tayler instability-driven dynamos in radiative zones: New dynamo solution and its impacts on stellar physics
Université de Genève（日内瓦大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；IRAP, Université de Toulouse, CNRS, CNES, UPS（图卢兹大学 IRAP 研究所）；Institut Universitaire de France (IUF)（法国高等研究院）
Solar activity and helioseismology show the limitation of the standard solar model and call for the inclusion of dynamical processes in both convective and radiative zones. We concentrate here on the radiative zone and first show the sensitivity of boron neutrinos to the microscopic physics included in solar models. We confront the neutrino predictions of the seismic model to all the detected neutrino fluxes. Then we compute new models of the Sun including a detailed transport of angular momentum and chemicals due to internal rotation that includes meridional circulation and shear induced turb…
Intermediate-mass main sequence stars have large radiative envelopes overlying convective cores. This configuration allows internal gravity waves (IGWs) generated at the convective-radiative interface to propagate towards the stellar surface. The signatures of these waves can be observed in the photometric and spectroscopic data from stars. We have studied the propagation of these IGWs using two-dimensional fully-non-linear hydrodynamical simulations with realistic stellar reference states from the one-dimensional stellar evolution code, Modules for Stellar Astrophysics (MESA). When a single w…
Understanding effects driven by rotation in the solar convection zone is essential for many problems related to solar activity, such as the formation of differential rotation, meridional circulation, and others. We analyze realistic 3D radiative hydrodynamics simulations of solar subsurface dynamics in the presence of rotation in a local domain 80 Mm wide and 25 Mm deep, located at 30 degrees latitude. The simulation results reveal the development of a shallow 10-Mm deep substructure of the Near-Surface Shear Layer (NSSL), characterized by a strong radial rotational gradient and self-organized…
The revolution of helio- and asteroseismology provides access to the detailed properties of stellar interiors by studying the star's oscillation modes. Among them, gravity (g) modes are formed by constructive interferences between progressive internal gravity waves (IGWs), propagating in stellar radiative zones. Our new 3D nonlinear simulations of the interior of a solar-like star allows us to study the excitation, propagation, and dissipation of these waves. The aim of this article is to clarify our understanding of the behavior of IGWs in a 3D radiative zone and to provide a clear overview o…
We present results of the instability analysis of the post-main sequence massive star models against radial and nonradial pulsations. We confirm that both p- and g-modes can be excited by the $κ$-mechanism acting in the metal opacity bump. However, as opposed to the previous claims, we find that an intermediate convective zone (ICZ) related to the hydrogen burning shell is not necessary for excitation of g-modes. These modes can be reflected at a minimum of the Brunt-Väisälä frequency, located at the top of the chemical composition gradient region surrounding the radiative helium core. This mi…
We examine the linear behavior of three-dimensional Lagrangian displacements in a stratified, shearing background. The isentropic and iso-rotation surfaces of the equilibrium flow are assumed to be axisymmetric, but otherwise fully two-dimensional. Three-dimensional magnetic fields are included in the perturbation equations; however the equilibrium is assumed to be well-described by purely hydrodynamic forces. The model, in principle very general, is used to study the behavior of fluid displacements in an environment resembling the solar convection zone. Some very suggestive results emerge. Al…
In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in each layer and cases where wave tunneling occurs. We find that efficient wave transmission can be achieved by `resonant propagation' or `resonant tunneling', even when stable layers are strongly stratified, and we call this phenomenon `enhanced wave transmission'. Enhanced wave transmission only occurs when the total number of layers is odd (embedding stable la…
We study the relation between the internal structures of 10 benchmark main-sequence F-stars and their rotational properties. Stellar rotation of main-sequence F-type stars can be characterised by two distinct rotational regimes. Early-type F-stars are usually rapid rotators with periods typically below 10 days, whereas later-type F-stars have longer rotation periods. Specifically, and since the two rotational regimes are tightly connected to the effective temperatures of the stars, we investigate in detail the characteristics of the partial ionisation zones in the outer convective envelopes of…
The era of detailed asteroseismic analyses opened by space missions such as CoRoT and $\textit{Kepler}$ has highlighted the need for stellar models devoid of numerical inaccuracies, in order to be able to diagnose which physical aspects are being ignored or poorly treated in standard stellar modeling. We tackle here the important problem of fixing convective zones boundaries in the frame of the local mixing length theory. First we show that the only correct way to locate a convective zone boundary is to find, at each iteration step, through interpolations or extrapolations from points $\textit…
