# The time step constraint in radiation hydrodynamics

## TL;DR

This paper investigates the radiative time step constraint in explicit radiation hydrodynamics simulations, revealing it is governed by combined optically thick and thin contributions, and discusses potential mitigation strategies.

## Contribution

It identifies the combined effect of optically thick and thin contributions on the radiative time step constraint and empirically determines their weighting in simulations, offering insights for improved modeling.

## Key findings

- The radiative time step constraint is governed by the sum of optically thick and thin contributions.
- In convective accretion disc simulations, the Deardorff term dominates enthalpy flux.
- Mitigation strategies for the radiative time step problem are discussed.

## Abstract

Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the Pencil Code, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations.