Theoretical Line Profiles for Stars of P Cygni Type

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Abstract
A simple model is set up of a star enclosed by an expanding envelope. The star is emitting a continuous spectrum and the envelope scatters radiation in the neighbourhood of a resonance frequency. The profiles which result from these assumptions are of the emission-line type. In varying degrees they show violet absorption borders, central reversals and occultation of the red edge, which are characteristic features of lines in P Cygni spectra. The profiles are obtained by numerical solution of a pair of integral equations for the emissivity in the envelope and the flux of radiation from the system. The critical parameter for the appearance of central reversal is the ratio of expansion velocity to turbulent velocity in the envelope. (⁠|$\upsilon /{\upsilon }^{*}\sim 3$|⁠.) Noticeable occultation of the emission component sets in when the effective radii of envelope and star fall below the ratio |${R}_{1}/{R}_{0}\sim 1.25$|⁠. For profiles in which the net energy in the line exceeds the underlying continuous spectrum, the Zanstra recombination cycle is introduced. The computed contours show, in addition to an increase in intensity of the emission components, an enhancement of the associated central reversal. In some cases this results in obscuring the violet absorption border. The theoretically derived profiles encompass a wide range of lines, not only of P Cygni type but of some types of Be emission lines as well.

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