Impact of the Hall effect in star formation : improving the angular momentum conservation

TL;DR

This paper improves the numerical simulation of star formation by modifying the Hall effect implementation, significantly enhancing angular momentum conservation during protostellar collapse.

Contribution

It introduces a modification to the 2D Riemann solver that reduces angular momentum loss in star formation simulations, maintaining numerical accuracy.

Findings

Enhanced angular momentum conservation by one order of magnitude.

Reproduced previous simulation results with consistent resistivities and effects.

Negligible angular momentum violation in disk formation context.

Abstract

We present here a minor modification of our numerical implementation of the Hall effect for the 2D Riemann solver used in Constrained Transport schemes, as described in Marchand et al. (2018). In the previous work, the tests showed that the angular momentum was not conserved during protostellar collapse simulations, with significant impact. By removing the whistler waves speed from the characteristic speeds of non-magnetic variables in the 1D Riemann solver, we are able to improve the angular momentum conservation in our test-case by one order of magnitude, while keeping the second-order numerical convergence of the scheme. We also reproduce the simulations of Tsukamoto et al. (2015) with consistent resistivities, the three non-ideal MHD effects and initial rotation, and agree with their results. In this case, the violation of angular momentum conservation is negligible in regard to the total angular momentum and the angular momentum of the disk.