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Milne-Eddington Solutions for Relativistic Plane-Parallel Flows

Radiative transfer in a relativistic plane-parallel flow, e.g., an accretion disk wind, is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed, for the relativistically moving atmosphere we analytically obtain 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 the plane-parallel static atmosphere, whereas the source function nearly becomes constant as the flow speed increases. Using the analytical solutions, we analytically integrate the relativistic transfer equation to obtain the specific intensity. This specific intensity also reduces to the Milne-Eddinton case in the static limit, while the emergent intensity is strongly enhanced toward the flow direction due to the Doppler and aberration effects as the flow speed increases (relativistic peaking).