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

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2. Comparing theories

According to Girardi et al. (1998), the Hipparcos sample of neighboring He burning giants is largely populated by stars with masses below or in the range of the so-called Red Giant Branch phase transition (RGB-pt). Since the pioneering paper by Sweigart et al. (1990) this range of stellar masses has been the subject of several careful evolutionary investigations. As well known, as we go from stars with M[FORMULA]1 [FORMULA] to higher masses, we progressively find H-shell burning stars with a lower degree of electron degeneracy in their cores. Eventually, He is quietly ignited in the center of the structure. As a consequence, the mass of the He core at the He ignition progressively decreases, reaching a minimum at a star mass which depends on the original chemical composition. After this minimum, the He core grows again with mass, following the increasing size of the central convective core in the Main Sequence structures.

Fig. 1 gives selected quantities concerning the behavior of He burning models across the RGB-pt as computed for Z=0.02 and the two alternative assumptions Y=0.27 or 0.23. All models have been computed according to the theoretical scenario already presented in C99, which incorporates all the most recent evaluations of the input physics. As everywhere in the following, quantities given in Fig. 1 refer to the first model which, after igniting central He, has already reached the HR diagram location where it will spend the major phase of central He burning. Let us here notice that the luminosity of these He burning models is not related only to the mass of the He core. Initially this luminosity increases in spite of the decreasing He core, since the increased efficiency of the H burning shell overcomes the decreased output of He-burning reactions. However, eventually the decrease of the He core dominates and the luminosity reaches its minimum, whereas the lifetime in the central helium burning phase increases following the decrease of the efficiency of the He burning reactions. The subject of the RGB-pt has been already widely debated in the literature (see, e.g., Renzini & Buzzoni 1986, Corsi et al. 1994, Girardi & Bertelli 1998 and references therein) and here it does not deserve further comments.

[FIGURE] Fig. 1. Selected quantities depicting the behavior of stellar models across the Red Giant Transition as computed for solar metallicity (Z=0.02) and for the two choices about the amount of original helium Y=0.27 or Y=0.23. Top to bottom: i) the mass of the He core at the beginning of the major phase of central He burning, ii) the predicted luminosity of the same models and, iii) the predicted He burning lifetime.

However, Fig. 2 compares the luminosities given in Fig. 1 with similar results but by Girardi et al. (1998: G98 hereinafter). To our surprise, one finds that G98 luminosities appear systematically fainter than in C99 by about [FORMULA]log L/[FORMULA] [FORMULA] 0.1 [FORMULA] 0.15, which is far from being a negligible amount and, in turn, it appears of the right amount to solve the already quoted M67 discrepancy.

[FIGURE] Fig. 2. He clump luminosity as a function of the stellar mass for Z=0.02 and Y[FORMULA]0.27 by various authors, as labeled; "over" marks evolutions with core overshooting.

Such an evidence prompted us to investigate similar data in the literature, aiming to find the origin of such a difference. To this purpose, the same Fig. 2 shows the predictions already given in the literature on the basis of of the Frascati or Padua evolutionary codes before the last updating of the input physics. The figure gives the comforting evidence that luminosities from Castellani et al. (1992) appear in rather good agreement with similar data by Bressan et al. (1993). As we will further discuss in the next section, the slight underluminosity and the little difference in the RGB-pt mass of Bressan et al. models is only the expected consequence of their adoption of a moderate core overshooting scenario.

The same figure shows that the updated input physics adopted in C99 has the effect of increasing the luminosity of the models with a degenerate progenitors, according to the discussion already given in Cassisi et al. (1998) and in reasonable agreement with stellar models recently presented by Pols et al. (1998). However, one also finds that the new input physics in the Padua models (Girardi & Bertelli 1998, Girardi et al. 1999) has the opposite effect, sensitively decreasing the predicted luminosities. As a whole, one finds that uncertainties on predicted luminosities can be even larger than [FORMULA]logL[FORMULA]0.1, leaving an unpalatable uncertainty in the current evolutionary scenario.

On general grounds, one expects that the quoted differences are the results of differences either in the input physics or in the assumptions about the efficiency of macroscopic mechanisms, like core overshooting, which can affect the evolution of stellar structures. To discuss this point, in the next sections we will investigate the range of variability in current theoretical predictions, as produced by the various assumptions governing the evolutionary behaviour.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000
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