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.
Highlights
Considerable progress has recently been made in the understanding of magnetic fields at the surface of stars, mostly thanks to the ground-based instruments NARVAL at the Pic du Midi observatory in France and ESPaDOnS at the Mauna Kea Observatory in Hawaï
We studied the effects of the stable stratification in the non-adiabatic case on instabilities which can develop when an initial poloidal field is wound up by an initial differential rotation
Two different profiles for the differential rotation were considered, both likely to exist in stellar radiative zones: one, cylindrical, which satisfies the Taylor–Proudman constrain and the other, shellular, which corresponds to what could be expected in a strongly stably stratified layer
Summary
Considerable progress has recently been made in the understanding of magnetic fields at the surface of stars, mostly thanks to the ground-based instruments NARVAL at the Pic du Midi observatory in France and ESPaDOnS at the Mauna Kea Observatory in Hawaï. A few recent 3D global numerical studies have focused on the effect of stable stratification on MHD instabilities in specific cases, like for example Philidet et al (2020) for spherical Couette flows, Guerrero et al (2019) for the Tayler instability in a non-rotating spherical shell or Szklarski & Arlt (2013) for the Tayler instability of a toroidal field produced by the winding-up of an initial poloidal field In this last study, very to what is presented in this paper, the wound-up magnetic field is found to be unstable only if the feedback on the differential rotation is inhibited until the ratio of toroidal Alfvén frequency to rotation frequency becomes sufficiently large that the Tayler instability sets in.
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