The diffusion of radiation in moving media II. Limits for large and small velocity gradients for deterministic lines

The general formulae for radiative quantities in the diffusion limit for a differentially moving 3D medium which have been derived in Paper I of this series, are evaluated for the limiting cases of very large and very small velocity gradients |w|. The extinction coefficient is specified by the continuum and the contribution of spectral lines which is formulated deterministically. For large w all radiative quantities can conveniently be calculated in terms of the spectral thickness, i.e. of the wavelength-integrated extinction coefficient, which can be well approximated by a piecewise linear function. For small w the radiative quantities are developed to the second order in w. The coefficients are essentially determined by the first two wavelength derivatives of the mean free path of the photons, i.e. of the reciprocal extinction coefficient. Since these depend on temperature, density and chemical composition only, they can be precalculated resulting in convenient expressions for hydrodynamic calculations. Examples are given for selected extinction coefficients such as a power-law continuum, a spectral edge, a single narrow line, and many, isolated as well as overlapping lines. In the non-overlapping case the lines contribute only in second order of w and the motions always lead to a decrease of the total flux whereas the radiative acceleration is unaffected. On the other hand, the effect of overlapping lines can only be determined by a detailed calculation for any specific extinction distribution. Furthermore, it is shown that the flux vector has components perpendicular to the temperature gradient if the latter is not parallel to the velocity vector.