On the Stability of a General Magnetic Field Topology in Stellar Radiative Zones

TL;DR

This paper explores the stability of various magnetic field configurations in stellar radiative zones, extending classical instability analyses to include non-axisymmetric fields and proposing a new stability criterion.

Contribution

It introduces a formulation for the global potential energy change in stellar magnetic fields, allowing stability analysis of arbitrary axisymmetric and non-axisymmetric configurations.

Findings

Extension of Tayler instability analysis to non-axisymmetric fields

Development of a new stability criterion for stellar magnetic fields

Framework for assessing magnetic stability in stellar radiative zones

Abstract

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. In particular, a purely magnetic instability can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations as originally studied in Tayler (1973), Markey & Tayler (1973), and Tayler (1980). However, most of the magnetic field configurations observed at the surface of massive stars are non- axisymmetric. Thus, extending earlier studies of the axisymmetric Tayler instability in spherical geometry (Goossens, 1980), we introduce a formulation for the global change in the potential energy contained in a convectively-stable region given an arbitrary Lagrangian perturbation, which permits the inclusion of both axisymmetric and non-axisymmetric magnetic fields. With this tool in hand, a path is shown by which more general stability criterion can be established.