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

Abstract

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.

Axisymmetric investigation of differential rotation in contracting stellar radiative zones

“…For example, Fuller et al (2019) propose a revised mechanism for the saturation of the Tayler instability that reproduces fairly well the core rotation rates along the red giant branch during the red clump and up to the white dwarf phase. The magneto-rotational instability (MRI; Rüdiger et al 2015;Jouve et al 2020) could also be at play in contracting radiative zones.…”

Detecting deep axisymmetric toroidal magnetic fields in stars. The traditional approximation of rotation for differentially rotating deep spherical shells with a general azimuthal magnetic field

“…If the differential rotation remains weak the field will remain stable and fossil-like. However, if a sufficient radial differential rotation builds up, its shear will wind up the poloidal component of the field into a supplementary toroidal field (Aurière et al 2007;Gaurat et al 2015;Jouve et al 2020) that can become unstable because of the Tayler instability. If an efficient dynamo loop takes place, as first proposed by Spruit (2002) and identified by Petitdemange et al (in press), the initial toroidal field can be regenerated.…”

Magnetic signatures on mixed-mode frequencies

“…In the recent literature that tackles this important question, most of the attention has been given to the potential effects of Maxwell stresses triggered by unstable fields in stably stratified radiative regions (e.g. Fuller et al 2019;Eggenberger et al 2020;Den Hartogh et al 2020;Jouve et al 2020). Here we recall the potentially significant efficiency with which a stable axisymmetric field redistributes angular momentum along poloidal field lines, a well-known result since Ferraro (1937), Mestel & Weiss (1987).…”