Evolution of random initial magnetic fields in stably stratified and barotropic stars

TL;DR

This study uses 3D magnetohydrodynamic simulations to investigate how initially random magnetic fields evolve in different star types, revealing that stable stratification leads to equilibrium states influenced by dissipation mechanisms.

Contribution

It demonstrates that stable stratification enables magnetic fields to reach equilibrium, with the nature of the equilibrium depending on the dominant dissipation process, advancing understanding of stellar magnetic field stability.

Findings

In barotropic stars, magnetic fields decay without reaching equilibrium.

In stably stratified stars, magnetic fields evolve to a stable equilibrium.

The equilibrium's symmetry and wavelength depend on dissipation mechanisms.

Abstract

Long-lived magnetic fields are known to exist in upper main-sequence stars, white dwarfs, and neutron stars. In order to explore possible equilibrium configurations of the magnetic field inside these stars, we have performed 3D-magnetohydrodynamic simulations of the evolution of initially random magnetic fields in stably stratified and barotropic stars with an ideal-gas equation of state using the {\sc Pencil Code}, a high-order finite-difference code for compressible hydrodynamic flows in the presence of magnetic fields. In barotropic (isentropic) stars, we confirm previous results in the sense that all initial magnetic fields we tried decay away, unable to reach a stable equilibrium. In the case of stably stratified stars (with radially increasing specific entropy), initially random magnetic fields appear to always evolve to a stable equilibrium. However, the nature of this equilibrium depends on the dissipation mechanisms considered. If magnetic diffusivity (or hyperdiffusivity) is included, the final state is more axially symmetric and dominated by large wavelengths than the initial state, whereas this is not the case if only viscosity (or hyperviscosity) is present. In real stars, the main mechanism allowing them to relax to an equilibrium is likely to be phase mixing, which we argue is more closely mimicked by viscosity. Therefore, we conclude that, depending on its formation mechanism, the equilibrium magnetic field in these stars could in principle be very asymmetric.