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

P Marchand,G Chabrier,K Tomida,B Commerçon

doi:10.1051/0004-6361/201936215

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.

Highlights

In Marchand et al (2018), we presented the numerical implementation of the Hall effect in the AMR code RAMSES (Teyssier 2002), aimed for application in protostellar collapse simulations
The Hall effect modifies the size of the disk by up to 50% in this setup, resulting in a factor 2 between the models with parallel and antiparallel magnetic fields
In the simulations with initial rotation, the angular momentum excess due to the Hall effect is a minor factor with respect to the total angular momentum, but our results show that conservation is still not perfect, independently of the Hall effect

Summary

Introduction

In Marchand et al (2018) (hereafter, Paper I), we presented the numerical implementation of the Hall effect in the AMR code RAMSES (Teyssier 2002), aimed for application in protostellar collapse simulations. While the implementation successfully passes several tests, showing the second-order convergence in space, the gas angular momentum is not conserved in star formation simulations. Shortly after the formation of the first Larson core, a large amount of rotation is generated in the first core and violates the conservation of the total angular momentum, which is a purely numerical issue. This problem arises in every simulation with the Hall effect, severely limiting the validity of our results. As well as in Paper I, we only consider the angular momentum of the fluid, not the magnetic field component, because there is no transfer between both in our framework

Methods

Results

Conclusion