Electrical Resistivity and Hall Effect in Binary Neutron-Star Mergers

TL;DR

This paper investigates the validity of ideal magnetohydrodynamics in binary neutron-star mergers, finding it generally applicable but highlighting conditions where the Hall effect influences magnetic field evolution.

Contribution

It provides a detailed analysis of magnetic field decay timescales and the significance of the Hall effect in neutron-star merger simulations.

Findings

Magnetic-field decay timescales exceed merger timescales at relevant scales.

Hall effect can cause magnetic field rearrangement at low densities and temperatures.

Ideal-MHD approximation remains valid for most current simulations.

Abstract

We examine the range of rest-mass densities, temperatures and magnetic fields involved in simulations of binary neutron-star mergers and identify the conditions under which the ideal-magnetohydrodynamics approximation breaks down and hence the magnetic-field decay should be accounted for. We use recent calculations of the conductivities of warm correlated plasma in envelopes of compact stars and find that the magnetic-field decay timescales are much larger than the characteristic timescales of the merger process for lengthscales down to a meter. Because these are smaller than the currently available resolution in numerical simulations, the ideal-magnetohydrodynamics approximation is effectively valid for all realistic simulations. At the same time, we find that the Hall effect can be important at low densities and low temperatures, where it can induce a non-dissipative rearrangement of the magnetic field. Finally, we mark the region in temperature and density where the hydrodynamic description breaks down.