StarBench: The D-type expansion of an HII region

TL;DR

StarBench systematically compares various numerical codes simulating the D-type expansion of HII regions, revealing deviations from classical models and proposing a new semi-empirical formula for improved code validation.

Contribution

This study introduces a benchmark dataset and a semi-empirical expansion law for HII regions, enhancing validation and calibration of star-formation simulation codes.

Findings

All codes agree well but deviate from classical solutions.

A new semi-empirical formula matches high-resolution simulations within 2%.

The study provides a validated dataset for code calibration.

Abstract

StarBench is a project focused on benchmarking and validating different star-formation and stellar feedback codes. In this first StarBench paper we perform a comparison study of the D-type expansion of an HII region. The aim of this work is to understand the differences observed between the twelve participating numerical codes against the various analytical expressions examining the D-type phase of HII region expansion. To do this, we propose two well-defined tests which are tackled by 1D and 3D grid- and SPH- based codes. The first test examines the `early phase' D-type scenario during which the mechanical pressure driving the expansion is significantly larger than the thermal pressure of the neutral medium. The second test examines the `late phase' D-type scenario during which the system relaxes to pressure equilibrium with the external medium. Although they are mutually in excellent agreement, all twelve participating codes follow a modified expansion law that deviates significantly from the classical Spitzer solution in both scenarios. We present a semi-empirical formula combining the two different solutions appropriate to both early and late phases that agrees with high-resolution simulations to $\lesssim2\%$. This formula provides a much better benchmark solution for code validation than the Spitzer solution. The present comparison has validated the participating codes and through this project we provide a dataset for calibrating the treatment of ionizing radiation hydrodynamics codes.