The diffusion of radiation in moving media

In this paper we present analytical expressions for the radiative flux, the effective extinction coefficient, and the radiative acceleration deep inside a differentially moving, very optically thick medium with many spectral lines. It is shown that the line contribution is essentially given by the characteristic function of wavelength averages of the extinction coefficient. It can be calculated either by means of the generalized opacity distribution function or by means of a Poisson point process model. Several examples are given to demonstrate the basic consequences of line densities, widths, and strengths, as well as velocity gradients on the diffusive flux. We demonstrate that for Poisson distributed lines the diffusive flux decreases with increasing absolute values of the velocity gradient (i.e. that the flux has a maximum for static media), and that such lines have hardly a direct influence on the radiative acceleration.