Beyond ideal magnetohydrodynamics: From fibration to 3+1 foliation

TL;DR

This paper develops a resistive multi-fluid framework within the 3+1 space-time foliation, addressing numerical challenges and applying it to hot neutron star models with relative flows among components.

Contribution

It introduces a new formulation for multi-fluid systems in relativistic astrophysics, incorporating multi-parameter equations of state and addressing inversion issues from evolved to primitive variables.

Findings

Highlights numerical issues in multi-fluid relativistic systems.

Applies the framework to a neutron star model with relative flows.

Provides a hierarchy of models for advanced astrophysical simulations.

Abstract

We consider a resistive multi-fluid framework from the 3+1 space-time foliation point-of-view, paying particular attention to issues relating to the use of multi-parameter equations of state and the associated inversion from evolved to primitive variables. We highlight relevant numerical issues that arise for general systems with relative flows. As an application of the new formulation, we consider a three-component system relevant for hot neutron stars. In this case we let the baryons (neutrons and protons) move together, but allow heat and electrons to exhibit relative flow. This reduces the problem to three momentum equations; overall energy-momentum conservation, a generalised Ohm's law and a heat equation. Our results provide a hierarchy of increasingly complex models and prepare the ground for new state-of-the-art simulations of relevant scenarios in relativistic astrophysics.