# On the importance of resistivity and Hall effect in MHD simulations of binary neutron star mergers

## TL;DR

This paper investigates the conditions under which ideal MHD assumptions hold in binary neutron star merger simulations, emphasizing the roles of resistivity and Hall effect, and delineates the regimes where hydrodynamics fails.

## Contribution

It identifies the plasma conditions where ideal MHD breaks down and highlights the significance of Hall effects at low densities and temperatures in BNSM simulations.

## Key findings

- Ideal MHD applies until hydrodynamic breakdown conditions.
- Hall effect influences magnetic field configuration at low densities.
- Hydrodynamic description fails in specific temperature-density regimes.

## Abstract

We examine the range of rest-mass densities, temperatures and magnetic fields involved in simulations of binary neutron star mergers (BNSM) and identify the conditions under which the ideal magneto-hydrodynamics (MHD) breaks down using recently computed conductivities of warm, magnetized plasma created in such systems. While previous dissipative MHD studies of BNSMs assumed that dissipation sets in due to low conduction at low rest-mass densities, we show that this paradigm must be shifted: the ideal MHD is applicable up to the regime where the hydrodynamic description of matter breaks down. We also 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-density plane where the hydrodynamic description breaks down.