Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone

Context. The interactions between magnetic fields and differential rotation in stellar radiative interiors could play a major role in achieving an understanding of the magnetism of intermediate-mass and massive stars and of the differential rotation profile observed in red-giant stars. Aims. The present study is aimed 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 investigate in detail the effects of the stable stratification and thermal diffusion and we aim, in particular, to assess the role of the stratification at stabilising the system. Methods. We performed 2D and 3D global Boussinesq numerical simulations started from an initial radial or cylindrical differential rotation and a large-scale poloidal magnetic field. Under the conditions of a large rotation frequency compared to the Alfvén frequency, we built a magnetic configuration strongly dominated by its toroidal component. We then perturbed this configuration to observe the development of non-axisymmetric instabilities. Results. The parameters of the simulations were chosen to respect the ordering of time scales of a typical stellar radiative zone. In this framework, the axisymmetric evolution is studied by varying the relative effects of the thermal diffusion, the Brunt-Väisälä frequency, the rotation, and the initial poloidal field strength. After a transient time and using a suitable adimensionalisation, we find that the axisymmetric state only depends on tes/tAp the ratio between the Eddington–Sweet circulation time scale and the Alfvén time scale. A scale analysis of the Boussinesq magnetohydrodynamical equations allows us to recover this result. In the cylindrical case, a magneto-rotational instability develops when the thermal diffusivity is sufficiently high to enable the favored wavenumbers to be insensitive to the effects of the stable stratification. In the radial case, the magneto-rotational instability is driven by the latitudinal shear created by the back-reaction of the Lorentz force on the flow. Increasing the level of stratification then leaves the growth rate of the instability mainly unaffected while its horizontal length scale grows. Conclusions. Non-axisymmetric instabilities are likely to exist in stellar radiative zones despite the stable stratification. They could be at the origin of the magnetic dichotomy observed in intermediate-mass and massive stars. They are also unavoidable candidates for the transport of angular momentum in red giant stars.

Probing the mid-layer structure of red giants

Context. The space-borne missions CoRoT and Kepler have already brought stringent constraints on the internal structure of low-mass evolved stars, a large part of which results from the detection of mixed modes. However, all the potential of these oscillation modes as a diagnosis of the stellar interior has not been fully exploited yet. In particular, the coupling factor or the gravity-offset of mixed modes, q and εg, are expected to provide additional constraints on the mid-layers of red giants, which are located between the hydrogen-burning shell and the neighborhood of the base of the convective zone. The link between these parameters and the properties of this region, nevertheless, still remains to be precisely established. Aims. In the present paper, we investigate the potential of the coupling factor in probing the mid-layer structure of evolved stars. Methods. Guided by typical stellar models and general physical considerations, we modeled the coupling region along with evolution. We subsequently obtained an analytical expression of q based on the asymptotic theory of mixed modes and compared it to observations. Results. We show that the value of q is degenerate with respect to the thickness of the coupling evanescent region and the local density scale height. On the subgiant branch and the beginning of the red giant branch (RGB), the model predicts that the peak in the observed value of q is necessarily associated with the important shrinking and the subsequent thickening of the coupling region, which is located in the radiative zone at these stages. The large spread in the measurement is interpreted as the result of the high sensitivity of q to the structure properties when the coupling region becomes very thin. Nevertheless, the important degeneracy of q in this regime prevents us from unambiguously concluding on the precise structural origin of the observed values. In later stages, the progressive migration of the coupling region toward the convective zone is expected to result in a slight and smooth decrease in q, which is in agreement with observations. At one point just before the end of the first-dredge up and the luminosity bump, the coupling region becomes entirely located in the convective region and its continuous thickening is shown to be responsible for the observed decrease in q. We demonstrate that q has the promising potential to probe the migration of the base of the convective region as well as convective extra-mixing during this stage. We also show that the frequency-dependence of q cannot be neglected in the oscillation spectra of such evolved RGB stars, which is in contrast with what is assumed in the current measurement methods. This fact can have an influence on the physical interpretation of the observed values. In red clump stars, in which the coupling regions are very thin and located in the radiative zone, the small variations and spread observed in q suggest that their mid-layer structure is very stable. Conclusions. A structural interpretation of the global observed variations in q was obtained and the potential of this parameter in probing the dynamics of the mid-layer properties of red giants is highlighted. This analytical study paves the way for a more quantitative exploration of the link of q with the internal properties of evolved stars using stellar models for a proper interpretation of the observations. This will be undertaken in the following papers of this series.

The 2D dynamics of radiative zones of low-mass stars

Context. Helioseismology and asteroseismology allow us to probe the differential rotation deep within low-mass stars. In the solar convective envelope, the rotation varies with latitude with an equator rotating faster than the pole, which results in a shear applied on the radiative zone below. However, a polar acceleration of the convective envelope can be obtained through 3D numerical simulations in other low-mass stars and the dynamical interaction of the surface convective envelope with the radiative core needs to be investigated in the general case. Aim. In the context of secular evolution, we aim to describe the dynamics of the radiative core of low-mass stars to get a deeper understanding of the internal transport of angular momentum in such stars, which results in a solid rotation in the Sun from 0.7R⊙ to 0.2R⊙ 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. Methods. We build 2D numerical models of a radiative core on the top of which we impose a latitudinal shear so as to reproduce a conical or cylindrical differential rotation in a convective envelope. We perform a systematic study over the Rossby number Ro = ΔΩ/2Ω0 measuring the latitudinal differential rotation at the radiative–;convective interface. We provide a 2D description of the differential rotation and the associated meridional circulation in the incompressible and stably stratified cases using the Boussinesq approximation. Results. The imposed shear generates a geostrophic flow implying a cylindrical differential rotation in the case of an isotropic viscosity. When compared to the baroclinic flow that arises from the stable stratification, we find that the geostrophic flow is dominant when the Rossby number is high enough (Ro ≥ 1) with a cylindrical rotation profile. For low Rossby numbers (Ro < 1), the baroclinic solution dominates with a quasi-shellular rotation profile. Using scaling laws from 3D simulations, we show that slow rotators (Ω0 < 30Ω⊙) are expected to have a cylindrical rotation profile. Fast rotators (Ω0 > 30Ω⊙) may have a shellular profile at the beginning of the main sequence in stellar radiative zones. Conclusions. This study enables us to predict different types of differential rotation and emphasizes the need for a new generation of 2D rotating stellar models developed in synergy with 3D numerical simulations. The shear induced by a surface convective zone has a strong impact on the dynamics of the underlying radiative zone in low-mass stars. However, it cannot produce a flat internal rotation profile in a solar configuration calling for additional processes for the transport of angular momentum in both radial and latitudinal directions.