Numerical methods comparison for protostellar collapse calculations

TL;DR

This study compares AMR and SPH numerical methods for simulating protostellar collapse, establishing resolution criteria for accurate core formation modeling, which supports future low-mass star formation simulations.

Contribution

It provides a thorough comparison of AMR and SPH methods with resolution guidelines for simulating prestellar core collapse.

Findings

Both methods converge with sufficient resolution.

Resolution per Jeans mass is critical for accuracy.

Guidelines improve future simulation reliability.

Abstract

The development of parallel supercomputers allows today the detailed study of the collapse and the fragmentation of prestellar cores with increasingly accurate numerical simulations. Thanks to the advances in sub-millimeter observations, a wide range of observed initial conditions enable us to study the different modes of low-mass star formation. The challenge for the simulations is to reproduce the observational results. Two main numerical methods, namely AMR and SPH, are widely used to simulate the collapse and the fragmentation of prestellar cores. We compare here thoroughly these two methods with numerical resolution requirements deduced from previous studies. Our physical model is as simple as possible, and consists of an isothermal sphere rotating around the z-axis. We first study the conservation of angular momentum as a function of the resolution. Then, we explore a wide range of simulation parameters to study the fragmentation of prestellar cores. There seems to be a convergence between the two methods, provided resolution in each case is sufficient. Resolution criteria adapted to our physical cases, in terms of resolution per Jeans mass, for an accurate description of the formation of protostellar cores are deduced from the present study. This convergence is encouraging for future work in simulations of low-mass star formation, providing the aforementioned criteria are fulfilled.