Impact of the Hall effect in star formation and the issue of angular momentum conservation

TL;DR

This paper implements the Hall effect in magnetohydrodynamics simulations to study its influence on star formation, revealing challenges in angular momentum conservation and the impact on core collapse dynamics.

Contribution

It introduces a second-order convergent scheme for the Hall term in RAMSES and investigates its effects on star formation and angular momentum regulation.

Findings

Hall effect influences core rotation direction

Counter-rotating envelopes form during collapse

Angular momentum is not conserved in simulations

Abstract

We present an implementation of the Hall term in the non-ideal magnetohydrodynamics equations into the adaptive-mesh-refinement code RAMSES to study its impact on star formation. Recent works show that the Hall effect heavily influences the regulation of the angular momentum in collapsing dense cores, strengthening or weakening the magnetic braking. Our method consists of a modification of the two-dimensional constrained transport scheme. Our scheme shows convergence of second-order in space and the frequency of the propagation of whistler waves is accurate. We confirm previous results, namely that during the collapse, the Hall effect generates a rotation of the fluid with a direction in the mid-plane that depends on the sign of the Hall resistivity, while counter-rotating envelopes develop on each side of the mid-plane. However, we find that the predictability of our numerical results is severely limited. The angular momentum is not conserved in any of our dense core-collapse simulations with the Hall effect: a large amount of angular momentum is generated within the first Larson core, a few hundred years after its formation, without compensation by the surrounding gas. This issue is not mentioned in previous studies and may be correlated to the formation of the accretion shock on the Larson core. We expect that this numerical effect could be a serious issue in star formation simulations.