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

¹ Department of Earth and Space Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
e-mail: pierre.marchand.astr@gmail.com
² Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
³ CRAL, Ecole normale supérieure de Lyon, UMR CNRS 5574, Université Claude Bernard Lyon 1, France
⁴ School of Physics, University of Exeter, Exeter EX4 4QL, UK

Received: 1 July 2019
Accepted: 19 September 2019

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 a former paper. 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 were 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 a previous study with consistent resistivities, the three non-ideal magnetohydrodynamic 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.