Stability of Hall equilibria in neutron star crusts

TL;DR

This paper investigates the stability of magnetic field configurations in neutron star crusts, demonstrating that certain equilibria are stable and evolve predictably under Hall drift and Ohmic diffusion through 2D simulations.

Contribution

It provides the first detailed numerical analysis of the stability of Hall equilibria in neutron star crusts, showing that some configurations are stable and evolve towards attractors.

Findings

Purely poloidal equilibrium is 2D-stable with decay towards an attractor.

Unstable mixed poloidal-toroidal fields evolve into stable configurations.

Decay timescales align with the Ohmic timescale.

Abstract

In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are "Hall equilibria", i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stable configurations, around which damped oscillations occur. For this field, the decay scales with the Ohmic timescale. We also study the case of an unstable equilibrium consisting of both poloidal and toroidal field components that are confined within the crust. This field evolves into a stable configuration, which undergoes damped oscillations superimposed on a slow evolution towards an attractor, just as the purely poloidal one.