General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests

TL;DR

This paper introduces a robust numerical implementation of general-relativistic resistive MHD in three dimensions, capable of handling a wide range of conductivities and tested through various astrophysical scenarios including star collapse.

Contribution

The authors develop a new numerical method using implicit-explicit Runge-Kutta schemes for resistive MHD in general relativity, demonstrating its robustness and accuracy across multiple tests and astrophysical applications.

Findings

Implementation recovers ideal-MHD limit at high conductivities.

Code accurately describes a wide conductivity range.

Results on star collapse match perturbative studies within acceptable errors.

Abstract

We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe testbed for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the l=1 mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.