Hall equilibria with toroidal and poloidal fields: application to neutron stars

TL;DR

This paper develops analytical and numerical solutions for Hall equilibria in neutron star crusts, exploring various magnetic configurations and their evolution, including the generation of toroidal fields due to Hall effects.

Contribution

It provides the first comprehensive set of solutions for Hall equilibria in neutron star crusts, covering diverse magnetic configurations and their stability.

Findings

External dipole fields require a uniformly rotating electron fluid.

Toroidal magnetic energy is a small fraction of total magnetic energy.

Hall effect induces additional toroidal fields during equilibrium transitions.

Abstract

We present solutions for Hall equilibria applicable to neutron star crusts. Such magnetic configurations satisfy a Grad-Shafranov-type equation, which is solved analytically and numerically. The solutions presented cover a variety of configurations, from purely poloidal fields connected to an external dipole to poloidal-toroidal fields connected to an external vacuum field, or fully confined within the star. We find that a dipole external field should be supported by a uniformly rotating electron fluid. The energy of the toroidal magnetic field is generally found to be a few percent of the total magnetic field energy for the fields with an external component. We discuss the evolution due to Ohmic dissipation which leads to slowing down of the electron fluid. We also find that the transition from an MHD equilibrium to a state governed by Hall effect, generates spontaneously an additional toroidal field in regions where the electron fraction changes.