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.
Methods. We performed local, direct numerical simulations of stably stratified homogeneous sheared turbulence using the Boussinesq approximation. The domain of low Péclet numbers found in stellar interiors is currently inaccessible to numerical simulations without approximation. It is explored here thanks to a suitable asymptotic form of the Boussinesq equations. The turbulent transport of a passive scalar is determined in statistical steady states.
Results. We provide a first quantitative determination of the turbulent diffusion coefficient and find that the form proposed by Zahn is in good agreement with the results of the numerical simulations.
We investigate simulated turbulent flow within thermally driven stellar convection zones. Different driving sources are studied, including cooling at the top of the convectively unstable region, as occurs in surface convection zones; and heating at the base by nuclear burning. The transport of enthalpy and kinetic energy, and the distribution of turbulent kinetic energy dissipation are studied. We emphasize the importance of global constraints on shaping the quasi-steady flow characteristics, and present an analysis of turbulent convection which is posed as a boundary value problem that can be…
Combined action of helical motions of plasma (the $α$ effect) and non-uniform (differential) rotation is a key dynamo mechanism of solar and galactic large-scale magnetic fields. Dynamics of magnetic helicity of small-scale fields is a crucial mechanism in a nonlinear dynamo saturation where turbulent magnetic helicity fluxes allow to avoid catastrophic quenching of the $α$ effect. The convective zone of the Sun and solar-like stars as well as galactic discs are the source for production of turbulent magnetic helicity fluxes. In the framework of the mean-field approach and the spectral $τ$ app…
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…
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…
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…
In a density-stratified turbulent medium the cross helicity <u'.B'> is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations we find the cross helicity and the mean vertical magnetic field anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface exceeds the value of 1 Gauss …
We study the effect of turbulent drift of a large-scale magnetic field that results from the interaction of helical convective motions and differential rotation in the solar convection zone. The principal direction of the drift corresponds to the direction of the large-scale vorticity vector. Thus, the effect produces a latitudinal transport of the large-scale magnetic field in the convective zone wherever the angular velocity has a strong radial gradient. The direction of the drift depends on the sign of helicity and it is defined by the Parker-Yoshimura rule. The analytic calculations are do…
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）
Theoretical modeling of the driving processes of solar-like oscillations is a powerful way of understanding the properties of the convective zones of solar-type stars. In this framework, the description of the temporal correlation between turbulent eddies is an essential ingredient to model mode amplitudes. However, there is a debate between a Gaussian or Lorentzian description of the eddy-time correlation function (Samadi et al. 2003, Chaplin et al. 2005). Indeed, a Gaussian description reproduces the low-frequency shape of the mode amplitude for the Sun, but is unsatisfactory from a theoreti…
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…
The impressive development of global numerical simulations of turbulent stellar interiors unveiled a variety of possible differential rotation (solar or anti-solar), meridional circulation (single or multi-cellular), and dynamo states (stable large scale toroidal field or periodically reversing magnetic fields). Various numerical schemes, based on the so-called anelastic set of equations, were used to obtain these results. It appears today mandatory to assess their robustness with respect to the details of the numerics, and in particular to the treatment of turbulent sub-grid scales. We report…
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…
A turbulent transport of radiation in the solar convective zone is investigated. The mean-field equation for the irradiation intensity is derived. It is shown that due to the turbulent effects, the effective penetration length of radiation can be increased in several times in comparison with the mean penetration length of radiation (defined as an inverse mean absorption coefficient). Using the model of the solar convective zone based on the mixing length theory, where the mean penetration length of radiation is usually much smaller than the turbulent correlation length, it is demonstrated that…
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…
We investigate a massive ($\varSigma \sim 10000 g cm^{-2}$ at 1 AU) protoplanetary disc model by means of 3D radiation magnetohydrodynamics simulations. The vertical structure of the disc is determined self-consistently by a balance between turbulent heating caused by the MRI and radiative cooling. Concerning the vertical structure, two different regions can be distinguished: A gas-pressure dominated, optically thick midplane region where most of the dissipation takes place, and a magnetically dominated, optically thin corona which is dominated by strong shocks. At the location of the photosph…
We study the combined effects of convection and radiative diffusion on the evolution of thin magnetic flux tubes in the solar interior. Radiative diffusion is the primary supplier of heat to convective motions in the lower convection zone, and it results in a heat input per unit volume of magnetic flux tubes that has been ignored by many previous thin flux tube studies. We use a thin flux tube model subject to convection taken from a rotating spherical shell of turbulent, solar-like convection as described by Weber, Fan, and Miesch (2011, Astrophys. J., 741, 11; 2013, Solar Phys., 287, 239), n…
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…
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…
Macroturbulence, introduced as a fudge to reproduce the width and shape of stellar absorption lines, reflects gas motions in stellar atmospheres. While in cool stars, it is thought to be caused by convection zones immediately beneath the stellar surface, the origin of macroturbulence in hot stars is still under discussion. Recent works established a correlation between the turbulent-to-total pressure ratio inside the envelope of stellar models and the macroturbulent velocities observed in corresponding Galactic stars. To probe this connection further, we evaluated the turbulent pressure that a…
The dynamical evolution of protoplanetary disks is of key interest for building a comprehensive theory of planet formation and to explain the observational properties of these objects. Using the magnetohydrodynamics code Athena++, with an isothermal shearing box setup, we study the boundary between the active and dead zone, where the accretion rate changes and mass can accumulate. We quantify how the turbulence level is affected by the presence of a non uniform ohmic resistivity in the radial-x direction that leads to a region of inhibited turbulence (or dead zone). Comparing the turbulent act…
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 $ν$…
Radiation transport plays important roles in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent deca…
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…
In this paper, we calibrate the coefficients for the one-dimensional Reynolds stress model with the data generated from the three-dimensional numerical simulations of upward overshooting in turbulent compressible convection. It has been found that the calibrated convective and isotropic coefficients are almost the same as those calibrated in the pure convection zone. However, the calibrated diffusive coefficients differ significantly from those calibrated in the pure convection zone. We suspect that the diffusive effect induced by the boundary is stronger than by the adjacent stable zone. We h…
Chemical composition is an important factor that affects stellar evolution. The element abundance on the stellar surface evolves along the lifetime of the star because of transport processes, including atomic diffusion. However, models of stars with masses higher than about 1.2Msun predict unrealistic variations at the stellar surface. This indicates the need for competing transport processes that are mostly computationally expensive for large grids of stellar models. The purpose of this study is to implement turbulent mixing in stellar models and assess the possibility of reproducing the effe…
Recent 3D-simulations have shown that the turbulent kinetic flux (TKF) is significant. We discuss the effects of TKF on the size of convection zone and find that the TKF may help to solve the solar abundance problem. The solar abundance problem is that, with new abundances, the solar convection zone depth, sound speed in the radiative interior, the helium abundance and density in the convective envelope are not in agreement with helioseismic inversions. We have done Monte Carlo simulations on solar convective envelope models with different profile of TKF to test the effects. The solar abundanc…
Obtaining observational evidence of the turbulent component of solar dynamo operating in the convective zone is a challenging problem because the dynamo action is hidden below the photosphere. Here we present results of a statistical study of flaring active regions (ARs) that produced strong solar flares of an X-ray class X1.0 and higher during a time period that covered solar cycles 23 and 24. We introduced a magneto-morphological classification (MMC) of ARs, which allowed us to estimate possible contribution of the turbulent component of the dynamo into the structure of an AR. We found that …
Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from stellar radiation zones over the whole Hertzsprung-Russell diagram. Turbulent transport in differentially rotating stably stratified stellar radiation zones should be carefully modeled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. Only phenomenological prescriptions have been proposed for the transport in the horizontal direction, which however constitutes a corners…
The major mass fraction of the envelope of hot luminous stars is radiatively stable. However, the partial ionisation of hydrogen, helium and iron gives rise to extended sub-surface convection zones in all of them. In this work, we investigate the effect of the pressure induced by the turbulent motion in these zones based on the mixing length theory, and search for observable consequences. We find that the turbulent pressure fraction can amount up to ~5% in OB supergiants, and to ~30% in cooler supergiants. The resulting structural changes are, however, not significantly affecting the evolution…
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…
Turbulence in protoplanetary disks affects planet formation in many ways. While small dust particles are mainly affected by the aerodynamical coupling with turbulent gas velocity fields, planetesimals and larger bodies are more affected by gravitational interaction with gas density fluctuations. For the latter process, a number of numerical simulations have been performed in recent years, but a fully parameter-independent understanding has not been yet established. In this study, we present simple scaling relations for the planetesimal stirring rate in turbulence driven by magnetorotational in…
Sub-mm observations of protoplanetary disks now approach the acuity needed to measure the turbulent broadening of molecular lines. These measurements constrain disk angular momentum transport, and furnish evidence of the turbulent environment within which planetesimal formation takes place. We use local magnetohydrodynamic (MHD) simulations of the magnetorotational instability (MRI) to predict the distribution of turbulent velocities in low mass protoplanetary disks, as a function of radius and height above the mid-plane. We model both ideal MHD disks, and disks in which Ohmic dissipation resu…
We perform global time-dependent simulations of an accretion disc around a young stellar object with a dead zone (a region where the magneto-rotational instability cannot drive turbulence because the material is not sufficiently ionised). For infall accretion rates on to the disc of around 10^-7 Msun/yr, dead zones occur if the critical magnetic Reynolds number is larger than about 10^4. We model the collapse of a molecular gas cloud. At early times when the infall accretion rate is high, the disc is thermally ionised and fully turbulent. However, as the infall accretion rate drops, a dead zon…
Radiative turbulent mixing layers (TMLs) are ubiquitous in astrophysical environments, e.g., the circumgalactic medium (CGM), and are triggered by the shear velocity at interfaces between different gas phases. To understand the shear velocity dependence of TMLs, we perform a set of 3D hydrodynamic simulations with an emphasis on the TML properties at high Mach numbers $\mathcal{M}$. Since the shear velocity in mixing regions is limited by the local sound speed of mixed gas, high-Mach number TMLs develop into a two-zone structure: a Mach number-independent mixing zone traced by significant cool…
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…
Based on the turbulent convection model (TCM) of Li & Yang (2007), we have studied the characteristics of turbulent convection in the envelopes of 2 and 5M stars at the RGB and AGB phases. The TCM has been applied successfully in the whole convective envelopes including the convective unstable zone and the overshooting regions. We find that the convective motions become stronger and stronger when the stellar models are located upper and upper along the Hayashi line. In the convective unstable zone, we find that the turbulent correlations are proportional to functions of a common factor $(\nabl…
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…
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 present the first 3D MHD study in spherical geometry of the non-linear dynamical evolution of magnetic flux tubes in a turbulent rotating convection zone. We study numerically the rise of magnetic toroidal flux ropes from the base of a modelled convection zone up to the top of our computational domain where bipolar patches are formed. We compare the dynamical behaviour of flux tubes in a fully convective shell possessing self-consistently generated mean flows such as meridional circulation and differential rotation, with reference calculations done in a quiet isentropic zone. We find that t…
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…
The turbulent burning of nuclei is a common phenomenon in the evolution of stars. Here we examine a challenging case: the merging of the neon and oxygen burning shells in a 23 M$_{\odot}$ star. A previously unknown quasi-steady state is established by the interplay between mixing, turbulent transport, and nuclear burning. The resulting stellar structure has two burning shells within a single convection zone. We find that the new neon burning layer covers an extended region of the convection zone, with the burning peak occurring substantially below where the Damköhler number first becomes equal…
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…
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…
In order to match observed properties of the solar cycle, flux-transport dynamo models require the toroidal magnetic flux to be stored in a region of low magnetic diffusivity, typically located at or below the bottom of the convection zone. We infer the turbulent magnetic diffusivity affecting the toroidal field on the basis of empirical data. We consider the time evolution of mean latitude and width of the activity belts of solar cycles 12--23 and their dependence on cycle strength. We interpret the decline phase of the cycles as a diffusion process. The activity level of a given cycle begins…
