Instability of Magnetic Equilibria in Barotropic Stars

TL;DR

This study demonstrates that stable magnetic equilibria do not exist in barotropic stars, as magnetic fields always decay, highlighting the importance of stable stratification for magnetic stability.

Contribution

It provides numerical evidence that stable magnetic equilibria require stable stratification, challenging previous assumptions and expanding understanding of magnetic field stability in stars.

Findings

Magnetic fields decay in barotropic stars within a few Alfvén times.

Stable equilibria are not found in barotropic stellar models.

Stable stratification is essential for magnetic stability in stars.

Abstract

In stably stratified stars, numerical magneto-hydrodynamics simulations have shown that arbitrary initial magnetic fields evolve into stable equilibrium configurations, usually containing nearly axisymmetric, linked poloidal and toroidal fields that stabilize each other. In this work, we test the hypothesis that stable stratification is a requirement for the existence of such stable equilibria. For this purpose, we follow numerically the evolution of magnetic fields in barotropic (and thus neutrally stable) stars, starting from two different types of initial conditions, namely random disordered magnetic fields, as well as linked poloidal-toroidal configurations resembling the previously found equilibria. With many trials, we always find a decay of the magnetic field over a few Alfv\'en times, never a stable equilibrium. This strongly suggests that there are no stable equilibria in barotropic stars, thus clearly invalidating the assumption of barotropic equations of state often imposed on the search of magnetic equilibria. It also supports the hypothesis that, as dissipative processes erode the stable stratification, they might destabilize previously stable magnetic field configurations, leading to their decay.