Flux-limited diffusion in a scattering medium

We present a diffusion equation (FDT) with a coefficient that reduces to the appropriate limiting form in the streaming and near thermodynamic limits for a moving fluid in which the dominant source of opacity is Thomson scattering. This expression, derived from the general diffusion theory of Levermore & Pomraning and Pomraning, is fully flux-limited, and is useful for the radiative-hydrodynamical simulation of scattering media such as accretion-disk coronae. We compare our results to those obtained with the corresponding equations for an absorptive medium, and we show that the flux can differ by a large factor (≫ 1) between the two, depending on the temperature profile within the atmosphere. A direct comparison of our equations with exact solutions of the transfer equation suggests that FDT for a scattering medium is accurate to better than ≲ 17% over the range of optical depths 0 ≲τ ≲ 3.