Turbulent radiative diffusion and turbulent Newtonian cooling

TL;DR

This paper investigates how turbulence affects radiative cooling in stellar atmospheres, revealing that turbulence modifies decay rates of temperature perturbations and can be described by an enhanced Newtonian cooling model, with implications for thermal equilibration times.

Contribution

It introduces a detailed analysis of turbulent radiative decay rates across regimes, showing that turbulence can be modeled by an enhanced Newtonian cooling process, which is a novel insight.

Findings

Decay rates increase with wavenumber, but less steeply than passive scalar diffusion.

Turbulent decay in optically thin regimes follows a square root dependence on wavenumber.

Cooling times are comparable to turbulent turnover times, affecting thermal equilibrium.

Abstract

Radiation transport plays important roles in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent decay is well described by an enhanced Newtonian cooling process in the optically thin limit, which is found to show a weak increase proportional to the square root of the wavenumber. In the optically thick limit, the increase in turbulent decay is somewhat steeper for wavenumbers below the energy-carrying wavenumber of the turbulence, but levels off toward larger wavenumbers. In the presence of turbulence, the typical cooling time is comparable to the turbulent turnover time. We observe that the temperature takes a long time to reach equilibrium in both the optically thin and thick cases, but in the former, the temperature retains smaller scale structures for longer.