Non-ideal magnetohydrodynamics on a moving mesh II: Hall effect

TL;DR

This paper extends a moving mesh MHD solver to include the Hall effect, demonstrating stability improvements, convergence, and applications to magnetic cloud collapse, highlighting the Hall effect's influence on magnetic braking.

Contribution

Introduces a stable, high-resolution moving mesh MHD scheme with Hall effect, enabling realistic simulations of magnetized cloud collapse and magnetic phenomena.

Findings

Achieved second order convergence for C-shock simulations.

Successfully reproduced whistler wave dispersion relations.

Showed Hall effect can either weaken or strengthen magnetic braking.

Abstract

In this work we extend the non-ideal magnetohydrodynamics (MHD) solver in the moving mesh code AREPO to include the Hall effect. The core of our algorithm is based on an estimation of the magnetic field gradients by a least-square reconstruction on the unstructured mesh, which we also used in the companion paper for Ohmic and ambipolar diffusion. In an extensive study of simulations of a magnetic shock, we show that without additional magnetic diffusion our algorithm for the Hall effect becomes unstable at high resolution. We can however stabilise it by artificially increasing the Ohmic resistivity, $\eta_{\rm OR}$, so that it satisfies the condition $\eta_{\rm OR} \geq \eta_{\rm H} /5$, where $\eta_{\rm H}$ is the Hall diffusion coefficient. Adopting this solution we find second order convergence for the C-shock and are also able to accurately reproduce the dispersion relation of the whistler waves. As a first application of the new scheme, we simulate the collapse of a magnetised cloud with constant Hall parameter $\eta_{\rm H}$ and show that, depending on the sign of $\eta_{\rm H}$, the magnetic braking can either be weakened or strengthened by the Hall effect. The quasi-Lagrangian nature of the moving mesh method used here automatically increases the resolution in the forming core, making it well suited for more realistic studies with non-constant magnetic diffusivities in the future.