Milne-Eddington Solutions for Relativistic Plane-Parallel Flows

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Radiative transfer in a relativistic plane-parallel flow, e.g., an accretion-disk wind, has been examined using a fully special-relativistic treatment. Under the assumption of a constant flow speed, for a relativistically moving atmosphere, we analytically obtained generalized Milne–Eddington solutions of radiative moment equations: the radiation energy density, the radiative flux, and the radiation pressure. In the static limit these solutions reduce to the traditional Milne–Eddington ones for a plane-parallel static atmosphere, whereas the source function nearly becomes constant as the flow speed increases. Using the analytical solutions, we analytically integrated the relativistic transfer equation to obtain the specific intensity. This specific intensity also reduces to the Milne–Eddington case in the static limit, while the emergent intensity is strongly enhanced toward the flow direction due to Doppler and aberration effects as the flow speed increases (relativistic peaking).

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