Contribution to spectral line formation in moving stellar envelopes - Radiation field and statistical equilibrium equations

The escape probability method introduced by Sobolev (1947) is used to derive the mean intensity of the radiation field at any point of an envelope which expands spherically with a positive or negative radial-velocity gradient. When considering outward-decelerating envelopes, an additional contribution to the mean intensity of the radiation field must be taken into account when compared with the results obtained by Castor (1970) in the case of outward-accelerating envelopes. A general discussion of the net radiative rates which populate the levels of an atom relates the problem of spectral-line formation in a moving medium to the one in a transparent atmosphere at rest. Namely, it is shown that dilution effects are expected to play an important role in envelopes where very large velocity gradients occur.