The diffusion of radiation in moving media I. Basic assumptions and formulae

The 3D radiative transfer equation for differentially moving media is derived upon the assumption that the motions are sufficiently slow. Its solution is then applied to the limiting case of large optical depths, i.e. to the diffusion approximation. Although the effective extinction for static 1D media has been derived by Rosseland already in 1924, it is for the first time in this Paper that for moving 3D media with many spectral lines general expressions for radiative quantities are derived in a rigorous way. Given are simple to use monochromatic as well as wavelength-integrated expressions for the flux and the radiative acceleration, and a generalized version of the Rosseland mean opacity. The essential effects of the motions upon the radiative flux are discussed for the simple case of a single spectral line on a continuum.