In the late phases of stellar evolution, evolutionary tracks of stars with different masses come together along the Hayashi line in the HR diagram. The theoretical HR diagram (log L, log Teff) is accordingly partially degenerate in the domain of late-type giants and supergiants, with respect to the third parameter, the stellar mass M. The stellar radius, R, being determined by log L and log Teff, the mass determines the surface gravity log g at the radius R. These parameters enable us to transform a point in the theoretical HR diagram to the corresponding point in the empirical HR diagram MV, (R-I) or spectral type. This transformation is conventionally carried out within the framework of the plane-parallel approximation in stellar atmospheres, and the parameters for the abscissa of the empirical HR diagram are dependant upon Teffand log g alone, irrespective of the mass itself. In this case, the parameter M indirectly affects the observable quantities through log g, but the effects of a variation by Δlog g=±0.5, corresponding to Δlog M=±0.5, are almost insignificant (cf. Tsuji 1976). The transformation between the theoretical and the empirical HR diagram is, therefore, almost one-to-one, within the framework of the plane-parallel approximation. Late-type giants and supergiants, however, have moderately extended atmospheres in general (cf. Schmid-Burgk and Scholz 1975), and their photometric colors and spectra are expected to be influenced by the sphericity of the atmospheric structure. Consequently, in comparing empirical HR diagrams with theoretical ones, it is important to know how atmospheric sphericity affects the transformation in the degenerate domains of the theoretical diagram.
Diffusion in CP Stars: The Quest for Accuracy
