Local Spherical Collapsing Box in Athena++: Numerical Implementation and Benchmark Tests

TL;DR

This paper introduces a local spherical collapsing gas cloud model in Athena++, demonstrating its implementation and testing through benchmark problems, with applications to star and planet formation studies.

Contribution

The paper presents a novel numerical implementation of a local spherical collapse model within Athena++, including benchmark tests and analysis of wave and flow behaviors.

Findings

Code conserves mass and momentum to machine precision

Wave speed and sound amplitude increase in the local frame during collapse

Model effectively captures local physics of protostellar collapse

Abstract

We implement a local model for a spherical collapsing/expanding gas cloud into the Athena++ magnetohydrodynamic code. This local model consists of a Cartesian periodic box with time-dependent geometry. We present a series of benchmark test problems, including non-linear solutions and linear perturbations of the local model, confirming the code's desired performance. During a spherical collapse, a horizontal shear flow is amplified, corresponding to angular momentum conservation of zonal flows in the global problem; wave speed and amplitude of sound waves increase in the local frame, due to the reduction in the characteristic length scale of the box, which can lead to an anisotropic effective sound speed in the local box. Our code conserves both mass and momentum to machine precision. This numerical implementation of the local model has potential applications to the study of local physics and hydrodynamic instabilities during protostellar collapse, providing a powerful framework for better understanding the earliest stages of star and planet formation.