Formation of P Cygni line profiles in relativistically expanding atmospheres

The probabilistic approach of Surdej (1979) is followed to generalize the Sobolev (1958) formalism to the case of special relativity, in order to interpret accurately the P Cygni line profiles observed in the spectrum of broad absorption-line quasars and supernovae. The expressions of the source function and of the line profile are derived, and it is shown that the relativistic P Cygni line profiles are significantly different from those computed in the framework of the classical theory. Thus, for increasing values of the terminal wind velocity, the red emission wing becomes definitely narrower than the blue one, while the line center emission increases. This is no longer symmetrical in accordance with the relativistic expression of the Doppler effect.