The kink-type instability of toroidal stellar magnetic fields with thermal diffusion

TL;DR

This study investigates the stability of toroidal magnetic fields in stellar radiative zones, revealing how thermal diffusion and magnetic strength influence the kink-type instability, with implications for understanding Ap star magnetism.

Contribution

It provides a detailed linear analysis of magnetic field stability considering realistic thermal diffusion and introduces the kink instability as a model for Ap star magnetism.

Findings

Strong fields (>   \

Weak fields show growth rates sensitive to thermal conductivity.

Differential rotation stabilizes the magnetic instability.

Abstract

The stability of toroidal magnetic fields in rotating radiative stellar zones is studied for realistic values of both the Prandtl numbers. The two considered models for the magnetic geometry represent fields with odd and even symmetry with respect to the equator. In the linear theory in Boussinesq approximation the resulting complex eigenfrequency (including growth rate and drift rate) are calculated for a given radial wavenumber of a nonaxisymmetric perturbation with m=1. The ratio of the Alfven frequency, \Omega_A, to the rate of the basic rotation, \Omega, controls the eigenfrequency of the solution. For strong fields with \Omega_A > \Omega the solutions do not feel the thermal diffusion. The growth rate runs with \Omega_A and the drift rate is close to -\Omega so that the magnetic pattern will rest in the laboratory system. For weaker fields with \Omega_A < \Omega the growth rate strongly depends on the thermal conductivity. For fields with dipolar parity and for typical values of the heat conductivity the resulting very small growth rates are almost identical with those for vanishing gravity. For fields with dipolar symmetry the differential rotation of any stellar radiative zone (like the solar tachocline) is shown as basically stabilizing the instability independent of the sign of the shear. Finally, the current-driven kink-type instability of a toroidal background field is proposed as a model for the magnetism of Ap stars. The recent observation of a lower magnetic field treshold of about 300 Gauss for Ap stars is understood as corresponding to the minimum magnetic field producing the instability.