In order to study the basic radiative mechanisms in the extended envelopes of evolved stars (e.g. Long Period Variables), we determine the spectrum emerging from a very optically thick Non-LTE hydrogen layer surrounding a core of high temperature (see figure 1). Such a model was first proposed by Sobolev (1960) and Menzel (1946). It is consistent with the fact that LPVs are likely evolving toward planetary nebulae. The main parameters of the model are the temperature of the illuminating star (Tr), the dilution factor (ω) and the Lyman continuum optical depth of the envelope (τ1c). We examine their influence upon the emerging intensities in the lines and in the continua.

The model could explain some observations related to evolved stars and especially the presence of emission features in an otherwise cold environment. Furthermore atmospheric pulsation phenomena produce large variations in the emerging spectra: reddening, emission/absorption transition of the hydrogen lines, profile deformations…