Stability of toroidal magnetic fields in stellar interiors

TL;DR

This paper uses 3D MHD simulations to explore the stability of toroidal and mixed magnetic fields in stellar interiors, revealing how rotation, diffusion, and field configuration influence the Tayler instability.

Contribution

First comprehensive simulation study including rotation and diffusion effects on magnetic field stability in stars, highlighting new unstable axisymmetric modes.

Findings

Fast rotation can suppress instability when axes are aligned and p<1.5.

Diffusion can induce instability in certain regimes.

An unstable axisymmetric mode exists at the stability threshold.

Abstract

We present 3D MHD simulations of purely toroidal and mixed poloidal-toroidal magnetic field configurations to study the behavior of the Tayler instability. For the first time the simultaneous action of rotation and magnetic diffusion are taken into account and the effects of a poloidal field on the dynamic evolution of unstable toroidal magnetic fields is included. In the absence of diffusion, fast rotation (rotation rate compared to Alfv\'en frequency) is able to suppress the instability when the rotation and magnetic axes are aligned and when the radial field strength gradient p < 1.5. When diffusion is included, this system turns unstable for diffusion dominated and marginally diffusive dominated regions. If the magnetic and rotation axes are perpendicular to each other the stabilizing effect induced by the Coriolis force is scale dependent and decreases with increasing wavenumber. In toroidal fields with radial field gradients bigger than p > 1.5, rapid rotation does not suppress the instability but instead introduces a damping factor to the growth rate in agreement with the analytic predictions. For the mixed poloidal-toroidal fields we find an unstable axisymmetric mode, not predicted analytically, right at the stability threshold for the non-axisymmetric modes; it has been argued that an axisymmetric mode is necessary for the closure of the Tayler-Spruit dynamo loop.