## 7. Concluding remarks and outlook
Another equivalent way to interpret Eq. (41) is obtained by
introducing the instead of the spectral thickness. Then so that the radiative quantities such as the flux
or the radiative force for moving
media can - in the deterministic case - completely be described
In order to elucidate the connection to the static diffusion, we
consider the very special case that the mean extinction coefficient
does This result resembles the usual static Rosseland mean except that
now for the moving medium the mean extinction coefficient
over the interval In conclusion, we have derived this paper general expressions for the radiative flux and acceleration in arbitrarily shaped, optically very thick, and differentially moving media far from the surfaces. These expressions are basically rather simple but the integrals involved can be evaluated analytically only in very special cases. In addition, the dependencies on the input parameters are not immediately evident. We therefore have presented here only numerical results of the monochromatic flux for a single Lorentzian spectral line on a continuum which show that there is in fact a quite intricate interplay of the parameters. We have restricted the discussion of our examples on monochromatic quantities in order investigate the relative importance of the line core and the near and far wings. In astronomical applications strictly monochromatic radiative
quantities are only rarely of interest, they more or less serve as the
basis for calculating the more important In Paper II we show that in the limits of small and large
velocity gradients much more insight can be gained. In particular, it
is demonstrated that for
Rosseland's result for the static case is regained. In addition, for
isolated narrow Lorentzian lines on a flat continuum the wavelength
integrals can be obtained analytically. When there are many
overlapping lines, convenient expressions can be obtained for large
velocity gradients, whereas for small © European Southern Observatory (ESO) 2000 Online publication: July 7, 2000 |