Radiative transfer in spherical dust shells using a generalized two-stream Eddington approximation

Application of a generalized two-stream Eddington approximation to the problem of radiative transfer in extended, spherically symmetric dust shells is presented. It is assumed that the radiation field can be characterized by the mean intensity, the flux, and a positionally dependent direction cosine specifying the division into two solid-angle ranges. The direction cosine is not specified a priori and is a function of the geometry, opacity, and emissivity in the dust shell. A multiple-grain-size multiple-temperature-distribution dust shell is postulated in which isotropic and anisotropic scattering as well as absorption and thermal reemission are allowed. A program has been developed that solves for the multiple temperature distributions by applying the constraint of radiative equilibrium to each grain size, and then calculates emergent fluxes. Results of one such calculation are presented for a model dust shell having a maximum optical depth (approximately 41) in the visible, clearly showing large optical extinction and a moderate infrared excess.