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X. Chen, E.A. Spiegel (Astronomy Department, Columbia University)
We extend Thomas' (1930) development of the solution of the equation of radiative transfer to include terms of third order in photon mean free path. The sum of the calculated higher order terms is then replaced by a Padé approximant (or rational approximation; see Baker, 1975), to provide an improved closure approximation for the radiative stress tensor, as has been done for the kinetic theory of gases by Rosenau (1993) and Slemrod (1997), and for the radiative heat equation in a grey medium (Unno and Spiegel, 1966). The results are uniformly valid in mean free path and so work well for both the optically thick and thin limits. Using simple examples, we contrast the results obtained for the transmission of shear stresses with those found with the conventional form for the radiative viscosity. These illustrate how the usual form of viscous tensor fails for transparent media and is rectified by the resummation procedure. Similarly, we exhibit the formula obtained for the radiative bulk viscosity and use it to extend the calculation of the cosmological entropy to cases with long photon mean free paths.
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