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Astron. Astrophys. 354, 150-156 (2000)

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3. Theoretical uncertainties in predicted luminosity

Making reference to the set of models presented in C99, in this section we will explore the influence on central He burning models of several assumptions concerning these structures, namely, i) the efficiency of core overshooting mechanisms, and, ii) the effect of mass loss. In this way we aim to reach a clear insight on the "solidity" of the result one is dealing with in the literature.

Fig. 3 (upper panel) shows the effect on the model luminosity of selected choices about the efficiency of core overshooting when the original stellar mass is varied between 1 and 3 [FORMULA], while the lower panel in the same figure adopts the G98 representation to show the run of the same models in the HR diagram. Labels in these figure give the adopted amount of extramixing (in unity of the local pressure scale height) around the convective cores. In passing, note that comparison between this figure and Fig. 1 gives the already known evidence that the RGB phase transition shifts to lower masses as the metallicity decreases.

[FIGURE] Fig. 3. Upper panel: The luminosity of He burning models with Z=0.006 and Y=0.23 as a function of the stellar mass and for the various labeled assumptions about the efficiency of core overshooting ([FORMULA]ov), see text. Lower panel: the run of the same models but in the HR diagram.

As already known, one finds that overshooting decreases the mass of the RGB-pt (although it then occurs at a larger age) and, correspondingly, that the maximum luminosity reached by the models before the transition decreases. However, one finds that for moderate amounts of overshooting such a decrease is rather small and, in any case, models with masses of the order of 1.2 [FORMULA] or lower are little affected by such a mechanism. In addition the minimum luminosity attained at the RGB-pt varies by only [FORMULA]logL/[FORMULA] between a standard model and a model with [FORMULA]=0.25.

Thus the differences in the assumptions about the efficiency of overshooting can hardly be at the origin of the differences in Fig. 2 and, in turn, they cannot be used to reconcile Pols et al. (1998) or C99 computations with M67 or Hipparcos constraints.

The effect of mass loss deserves a bit more discussion. Here we will assume that mass loss occurs in the advanced phase of H shell burning, so that the internal structure of the He burning star is not affected by such an occurrence, which only decreases the amount of envelope surrounding the central He core. Under this assumption, the effect of mass loss on He burning models can be easily computed by simply decreasing the envelope of the constant-mass model. Fig. 4 maps the effect in the HR diagram of different amount of mass loss from the selected models. The behavior depicted by data in this figure can be easily understood as follows:

[FIGURE] Fig. 4. The HR diagram location of He burning structures under different assumptions about the amount of mass loss in the pre He burning phase. Open circles give the location of models without mass loss with the labeled values of the stellar masses. The shift in the HR diagram expected by decreasing the total mass by step of 0.1 [FORMULA] is shown for the four labeled values of the original mass. Dashed line gives the expected distribution for models having lost 10% of their original mass.

i) As long as models develop strong electron degeneracy (i.e., for masses lower or of the order of 1.5 [FORMULA]) the mass of the He core at the He ignition is the result of RGB evolution. As a consequence it is largely independent of the evolving mass and, in addition, it is little affected by mass loss (see, e.g., the discussion in Castellani & Castellani 1993), thus He burning models with mass-losing progenitors behave like models without mass loss but starting their evolution with the actual mass of the He burning model. In this case the evolutionary behavior with mass loss can be easily predicted in terms of canonical models without mass loss.

ii) For larger stellar masses the He core at the He ignition is largely connected to the extension of the convective cores in the previous MS structures. As a consequence, the mass of the He core in He burning structures is now a sensitive function of the original stellar mass, whereas it keeps being little affected by mass loss, which mainly occurs in the post MS phases. In such case theoretical expectations for the luminosity abandon the location of canonical models, as shown in Fig. 4.

As an example, Fig. 4 gives theoretical predictions assuming for all stars a common mass loss of 10%.

This is intended to be a useful illustration of the effect we get assuming reasonable mass loss along the RGB. However, one should keep in mind that the real situation may well be more complicate. Assuming the Reimers (1975) mass-loss rates, for instance, one finds that stars of higher mass lose less mass along the RGB. This is so because they have lower RGB-tip luminosities, evolve at higher effective temperatures, and have a shorter RGB lifetime. In this case, stars more massive than about 1.5 [FORMULA] would lose negligible amounts of mass on the RGB, contrarily to the lowest-mass ones (see Fig. 6 in Girardi 1999). In the context of the present discussion, this means that mass-loss is expected to be less effective exactly in the mass range in which it would more affect the luminosity of the He-burning models, i.e. in the left part of Fig. 4.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000