Global simulations of Tayler instability in stellar interiors: the stabilizing effect of gravity

Abstract

Unveiling the evolution of toroidal field instability, known as Tayler instability, is essential to understand the strength and topology of the magnetic fields observed in early-type stars, in the core of the red giants, or in any stellar radiative zone. We want to study the non-linear evolution of the instability of a toroidal field stored in a stably stratified layer, in spherical symmetry and in the absence of rotation. In particular, we intend to quantify the suppression of the instability as a function of the Brunt-Väisäla (ω BV ) and the Alfvén (ω A ) frequencies. We use the MHD equations as implemented in the anelastic approximation in the EULAG-MHD code and perform a large series of numerical simulations of the instability exploring the parameter space for the ω BV and ω A . We show that beyond a critical value gravity strongly suppress the instability, in agreement with the linear analysis. The intensity of the initial field also plays an important role: weaker fields show much slower growth rates. Moreover, in the case of very low gravity, the fastest growing modes have a large characteristic radial scale, at variance with the case of strong gravity, where the instability is characterized by horizontal displacements. Our results illustrate that the anelastic approximation can efficiently describe the evolution of toroidal field instability in stellar interiors. The suppression of the instability as a consequence of increasing values of ω BV might play a role to explain the magnetic desert in Ap/Bp stars, since weak fields are only marginally unstable in the case of strong gravity.

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

“…However, the important effects of stable stratification are omitted in the 3D numerical calculations cited above. Only 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 similarly 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.…”

Is the primary CoRoT target HD 43587 under a Maunder minimum phase?

“…Their results also show that the magnetic field is stored in the stable layer where it is prone to magnetoshear instabilities (see e.g., Miesch et al 2007), in turn developing helical non-axisymmetric motions and currents (source of magnetic field via the so-called α-effect). As demonstrated in Guerrero et al (2019a), these instabilities are highly dependent on the stratification of the atmosphere. For this reason we calibrate the ambient state to reproduce the Brunt-Väisälä frequency profile of TGEC in the stable stratified layer.…”

Global simulations of stellar dynamos

“…On the other hand, the level of subadiabaticity in the stable layer determines the Brunt-Väisäla frequency and therefore the development of gravity waves in the stable layer. These waves might be fundamental for the development of the instability of toroidal fields in radiative zones (Guerrero et al 2019a). We have implemented these ideas in the simulations of the solar analog HD43568 (Ferreira et al 2020).…”