Radiative transfer in circumstellar dust shells

An iterative numerical procedure is developed to calculate the radiation field as a function of position, direction, and wavelength within a spherically symmetric circumstellar dust shell. The dust shell is assumed to consist of gray, isotropically scattering dust particles in thermal equilibrium with the radiation field and to be characterized by seven parameters: radius of the central star, inner radius of the shell, outer radius of the shell, total optical depth of the shell, an index which specifies the density distribution, albedo of the dust particles, and temperature of the central star. When the shell is close to the star, the angular distribution of the stellar component of the radiation field is determined by direct integration along lines of sight to the stellar surface, and the back-warming effect of the shell is included in the calculations to determine the net stellar flux. Using this procedure, the temperature distributions and radiation fields within several model dust shells are determined and used to calculate for each shell the spectral-energy and spatial-energy distributions of the radiation emitted at 11 wavelengths from 0.4 to 20 microns. For shells of moderate optical depth, it is found that the radiation field is quite anisotropic, especially at shorter wavelengths, and that the shape of the spectral-energy distribution is strongly dependent on all seven model parameters. The Eddington factor as a function of wavelength and optical depth is calculated for each model.