6. Conclusions and outlook
The expressions derived in this paper show that inside of an optically very thick, differentially moving medium the total flux and the total radiative acceleration in the limits of large and small velocity gradients w are given on the one hand by simple functions of w and on the other by expressions that depend on the plasma properties only and that therefore can be precalculated without any knowledge of the velocity field. For large w, essentially, a wavelength average of the extinction coefficient enters. For the more important case of small w, the free mean path is of primary importance as in the static case, i.e. regions of low opacity contribute most. This is in contrast to optically thin or partially thick configurations such as e.g. stellar winds. The Doppler shifts lead to derivatives, and since these enter the flux and radiative acceleration in a highly non-linear way, predictions even of the signs of the effects (as e.g. the change of the flux with velocity) are uncertain without the knowledge of specific details. We have therefore concentrated the analysis in this paper on very simple spectral features and investigated a few more complicated systems only numerically.
An alternative to this approach - which in addition provides a way for understanding systems comprising many spectral lines - is to represent the line positions, strengths, and shapes by a statistical model and then solve the corresponding stochastic equations. This will be done for a Poisson point process in a subsequent paper.
© European Southern Observatory (ESO) 2000
Online publication: July 7, 2000