Radiative Transfer with Partially Frequency Coherent Scattering

We consider a spectral line formed with a linear combination of monochromatic scattering and complete frequency redistribution. A previous theoretical and numerical investigation by Hemsch and Ferziger in 1971 and 1972 suggests that a very small percentage of complete frequency redistribution is sufficient to significantly modify a coherent scattering process. This article reexamines this result with numerical solutions of the radiative transfer equation calculated with an iterative method, introduced by Paletou and Auer in 1995 for radiative transfer with partial frequency redistribution. The partial frequency redistribution process is defined by a branching ratio b with values in [0,1], with 0 for complete frequency redistribution and 1 for monochromatic scattering. It is characterized by two dispersion functions, which are derived here by a Fourier transform of an integral equation constructed with the radiative transfer equation. The calculations are performed for a plane-parallel semi-infinite medium, with a uniform internal source of photons and a uniform single scattering albedo 1−ϵ. They show that complete frequency redistribution dominates the scattering process as soon as b becomes smaller than a critical value bcrit≃1−ϵ, given by the intersection the two dispersion functions.