Stability of the toroidal magnetic field in rotating stars

TL;DR

This paper investigates how rotation affects the stability of toroidal magnetic fields in stellar radiation zones, revealing that the impact depends on the magnetic field's radial configuration and that rotation can only reduce, not eliminate, certain instabilities.

Contribution

It provides a linear stability analysis of toroidal magnetic fields in rotating stars, highlighting the dependence on magnetic configuration and the limited stabilizing effect of rotation.

Findings

Rotation cannot fully suppress instability if the magnetic field increases with radius.

If the magnetic field decreases with radius, instability can be completely suppressed.

Rotation reduces the growth rate of instabilities but does not eliminate them.

Abstract

The magnetic field in stellar radiation zones can play an important role in phenomena such as mixing, angular momentum transport, etc. We study the effect of rotation on the stability of a predominantly toroidal magnetic field in the radiation zone. In particular we considered the stability in spherical geometry by means of a linear analysis in the Boussinesq approximation. It is found that the effect of rotation on the stability depends on a magnetic configuration. If the toroidal field increases with the spherical radius, the instability cannot be suppressed entirely even by a very fast rotation. Rotation can only decrease the growth rate of instability. If the field decreases with the radius, the instability has a threshold and can be completey suppressed.