Instability-driven evolution of poloidal magnetic fields in relativistic stars

TL;DR

This study investigates the nonlinear evolution of purely poloidal magnetic fields in non-rotating relativistic neutron stars, revealing an instability that generates toroidal fields and leads to complex, oscillatory configurations with potential astrophysical implications.

Contribution

It demonstrates the nonlinear development of magnetic field instability in relativistic stars and the formation of mixed poloidal-toroidal fields through numerical simulations.

Findings

Instability develops in the closed magnetic field line region within an Alfven timescale.

A toroidal magnetic component is generated and grows to comparable strength with the poloidal component.

The star relaxes into a non-axisymmetric state with large-amplitude oscillations.

Abstract

The problem of the stability of magnetic fields in stars has a long history and has been investigated in detail in perturbation theory. Here we consider the nonlinear evolution of a non-rotating neutron star with a purely poloidal magnetic field, in general relativity. We find that an instability develops in the region of the closed magnetic field lines and over an Alfven timescale, as predicted by perturbation theory. After the initial unstable growth, our evolutions show that a toroidal magnetic field component is generated, which increases until it is locally comparable in strength with the poloidal one. On longer timescales the system relaxes to a new non-axisymmetric configuration with a reorganization of the stellar structure and large-amplitude oscillations, mostly in the fundamental mode. We discuss the energies involved in the instability and the impact they may have on the phenomenology of magnetar flares and on their detectability through gravitational-wave emission.