Formation of resonance doublet profiles in rapidly expanding envelopes

Abstract

Generalization of the escape probability method introduced by Sobolev allows us to study the transfer of spectral line radiation for a resonance doublet in rapidly expanding envelopes. For the cases of outward-accelerating (or equivalently inward-decelerating) and outward-decelerating (or equivalently inward-accelerating) envelopes we derive, in the frame of a three-level atom model, the expressions for the spectral radiation fieldsJ 12 andJ 13, for the resulting radiative force FRE exerted per atom and for the resonance doublet profileE(X)/C c; we take into account the complex radiative coupling, in both resonance transitions 1⇌2 and 1⇌3, between distant parts of the atmosphere. For various physical and geometrical conditions prevailing in the expanding media, we illustrate and discuss the behaviours of those quantities as well as their dependence on the parameters of the model. Namely, we deduce criteria under which resonance doublet profiles formed in outward-accelerating and/or outward-decelerating envelopes would appear to be resolved into double P Cygni profiles. We also stress the importance of treating a resonance doublet as being formed by two distinct resonance transitions when evaluating the resulting radiative force FRE acting on an atom. It is indeed shown that if we use a two-level atom model to represent a resonance doublet-i.e., assigning to it an oscillator strength equal to the sum of the oscillator strengths of both resonance transitions-the amplitude of the resulting radiative force can be underestimated by factors reaching 100% and more in the regions of the expanding envelope which are optically thick to the spectral line radiation. In this context, it would be essential to revise the previous models of radiation-driven winds developed for early-type stars in which the lines belonging to any multiplet were treated as a single line.