Stellar evolution with turbulent diffusion .II. The HR diagram of supergiant stars

We present new evolutionary models for high and intermediate mass stars in which the fully convective regions (inner cores, external envelopes and intermediate shells) are let extend into their surrounding regions of overshoot. However,in these layers instead of assuming mixing to be instantaneous and fully efficient, we treat it according to the diffusive scheme elaborated by Deng et al. (1996a). The major difference with respect to standard stellar models is that, while fully unstable regions turn out to be completely homogenized by the diffusive algorithm in use, this is not the case for the overshoot regions which undergo partial mixing and build up smooth chemical profiles. The diffusion algorithm makes use of the so-called scale length most effective for mixing expressed as l(d) = P-dif X 10(-5) l(o), where l(o) is the largest scale in the unstable region in units of the local cal pressure scale height Hp, and finally P-dif is a fine tuning parameter of the order of unity (see the text for more details). The analysis by Deng et al. (1996a) has clarified that P-dif = 0.4 leads to stellar models that are able to match a number of properties of massive and intermediate mass stars. The characterizing feature of these models is that they possess at the same time evolutionary characteristics that were separately typical of model calculated with different schemes of mixing. In other words, they share the same properties of models with standard overshoot, namely a wider main sequence band, higher luminosity, and longer lifetimes, but also perform extended loops that are the main signature of the semiconvective description of convection at the border of the core. The stellar models presented in this paper span the mass range 5 to 100 M(.) and go from the zero age main sequence to the stage of central He-exhaustion. They have been calculated assuming P-dif = 0.4 over the whole range of masses. Two sets of initial chemical compositions are considered, namely [Z=0.008 and Y=0.25] suited to the Large Magellanic Cloud (LMC) supergiant stars, and [Z=0.020 and Y=0.28] suited to the same stars in the solar vicinity. With the aid of these stellar models we analyze the HR diagram (HRD) of supergiant stars in the LMC by Fitzpatrick & Garmany (1990) and that of supergiant stars in the Milky Way by Blaha & Humphreys (1989). Particular attention is paid to the star counts across the HRD, the stars in the Hertzsprung-Russell gap and related possible widening of the main sequence band, the so-called ledge, the ratio of blue to red supergiants N-B/N-R, the location of Wolf-Rayet stars (WR), and the blue progenitor of the SN 1987A. We find that taking into account a plausible scatter in the chemical composition of the supergiant stars in the samples, the many stars in the gap and the ledge can be easily accounted for. However, problems remains as far as the number frequencies of stars among the various spectral types, the possibility that the main sequence band can extend to spectral types up to B3, and the ratio N-B/N-R. Furthermore, despite the net advantages offered by these new stellar models with diffusive mixing, the location of WR stars in the CMD encounters the same difficulties as with the classical models. We suggest that a distinct evolutionary scenario must be invoked for this type of stars (Deng et al. 1996b). Finally, the blue progenitor of SN 1987A is not matched by the models, even if clues can be found within the same evolutionary scheme for a possible way out.