Evolution of neutron stars with toroidal magnetic fields: Axisymmetric simulation in full general relativity

TL;DR

This study uses full general relativistic magnetohydrodynamic simulations to analyze the stability and evolution of neutron stars with toroidal magnetic fields, revealing conditions under which they become unstable or stable, and the role of rotation.

Contribution

It provides the first detailed axisymmetric simulation of neutron star stability with toroidal magnetic fields in full general relativity, highlighting the effects of magnetic field configuration and rotation.

Findings

Nonrotating stars unstable for certain magnetic field profiles.

Unstable modes grow on Alfvén timescale, leading to magnetic reconfiguration.

Rotation can stabilize stars, but instability persists if magnetic energy exceeds ~20% of rotational energy.

Abstract

We study the stability of neutron stars with toroidal magnetic fields by magnetohydrodynamic simulation in full general relativity under assumption of axial symmetry. Nonrotating and rigidly rotating neutron stars are prepared for a variety of magnetic field configuration. For modeling the neutron stars, the polytropic equation of state with the adiabatic index $\Gamma=2$ is used for simplicity. It is found that nonrotating neutron stars are dynamically unstable for the case that toroidal magnetic field strength varies $\propto \varpi^{2k-1}$ with $k\geq 2$ (here $\varpi$ is the cylindrical radius), whereas for $k=1$ the neutron stars are stable. After the onset of the instability, unstable modes grow approximately in the Alfv\'en time scale and, as a result, a convective motion is excited to change the magnetic field profile until a new state, which is stable against axisymmetric perturbation, is reached. We also find that rotation plays a role in stabilization, although the instability still sets in in the Alfv\'en time scale when the ratio of magnetic energy to rotational kinetic energy is larger than a critical value $\sim 0.2$. Implication for the evolution of magnetized protoneutron stars is discussed.