Are there any stable magnetic fields in barotropic stars?

TL;DR

This paper constructs and tests the stability of mixed poloidal-toroidal magnetic fields in barotropic stars, finding that such fields are generally unstable and that boundary conditions significantly influence the dominant field component.

Contribution

It extends previous models by exploring different magnetic and current distributions and provides the first stability tests for mixed fields in barotropic stars.

Findings

All mixed fields tested are unstable due to one component or another.

Boundary conditions influence whether poloidal or toroidal fields dominate.

Rotation only partially stabilizes the magnetic configurations.

Abstract

We construct barotropic stellar equilibria, containing magnetic fields with both poloidal and toroidal field components. We extend earlier results by exploring the effect of different magnetic field and current distributions. Our results suggest that the boundary treatment plays a major role in whether the poloidal or toroidal field component is globally dominant. Using time evolutions we provide the first stability test for mixed poloidal-toroidal fields in barotropic stars, finding that all these fields suffer instabilities due to one of the field components: these are localised around the pole for toroidal-dominated equilibria and in the closed-field line region for poloidal-dominated equilibria. Rotation provides only partial stabilisation. There appears to be very limited scope for the existence of stable magnetic fields in barotropic stars. We discuss what additional physics from real stars may allow for stable fields.