Diffusion-limit asymptotics of the transport equation, the P1/3 equations, and two flux-limited diffusion theories

We compare the asymptotic accuracy of one variant of P-1 theory and two variants of grey diffusion theory in the equilibrium diffusion limit. All of these variants were developed to yield the correct radiation propagation speed in the optically thin streaming limit while presumably retaining full accuracy in the equilibrium diffusion limit. Accuracy in the equilibrium diffusion limit has traditionally meant reproducing the exact transfer asymptotics to leading (zeroth) order. We show that the exact asymptotics must be reproduced to first order to yield full accuracy in the equilibrium diffusion limit. The P-1 variant and one of the grey diffusion variants that we analyze yield first-order accuracy while the other grey diffusion variant yields only zeroth-order accuracy. Published by Elsevier Science Ltd. All rights reserved.