A&A Supplement series, Vol. 129, April II 1998, 267-279
Received February 27; accepted September 22, 1997
S. Cassisi 
, 
, V. Castellani , 
,
S. Degl'Innocenti , 
, and A. Weiss 
Send offprint request: V. Castellani, Dipartimento di Fisica Università
di Pisa, piazza Torricelli 2, 56126 Pisa, Italy, vittorio@astrte.te.astro.it
Osservatorio Astronomico di Collurania, via Mentore Maggini I-64100 Teramo, Italy
Dipartimento di Fisica, Universitá de L'Aquila, via
Vetoio, 67010 L'Aquila, Italy
Dipartimento di Fisica dell'Universitá di Pisa, piazza Torricelli 2,
I-56126 Pisa, Italy
Istituto Nazionale di Fisica Nucleare,
Sezione di Ferrara, via Paradiso 12, I-44100 Ferrara, Italy
Max Plank Institut for Astrophysics, Karl Schwarzschild
strasse 1, D-85470 Garching b. Munchen, Germany
In the first part of this paper we revisit the history of theoretical predictions for HB luminosities in old Population II stellar clusters, starting from the results of "old" evolutionary computations to introduce in various steps all the available "new" physics. We discuss the influence of physical ingredients on selected evolutionary parameters, finally presenting models which incorporate all the most recent updating of the relevant physics. The evolutionary behavior of such models is extensively investigated for selected choices about the cluster metallicity, discussing theoretical predictions concerning both cluster isochrones and the calibration of the parameter R in terms of the original amount of He in stellar matter. One finds that the "new" physics has a relevant influence on both these parameters, moving cluster ages into a much better agreement with current cosmological evaluations. This scenario is implemented by a further set of stellar models where element diffusion is taken into account. The comparison between theoretical scenarios with or without diffusion is presented and discussed. A discussion of current observational constraints in the light of the updated theory closes the paper.
keywords: stars: evolution; general; fundamental parameters; horizontal-branch
Since galaxies were born in an already expanding Universe, the age of the Universe appears as a safe upper limit for the age of any star and any stellar cluster. The fact that several determinations of globular cluster ages yielded values larger than the age of the Universe as based on current evaluations of the Hubble constant (see, e.g., Van den Bergh 1994; Tanvir et al. 1995) has stimulated a renewed interest in the theory of globular cluster Pop. II stars. At the same time, significant improvements in the input physics needed for stellar evolution have been made, such that noticeable changes of the theoretical results could be expected. These improvements initially were motivated by the results of helioseismology, which opened a new window into the interior of the Sun, allowing an extremely accurate determination of the solar structure. The efforts undertaken resulted in a new generation of opacity data (Rogers & Iglesias 1992; Seaton et al.\ 1994; Iglesias & Rogers 1996) and equations of state (Mihalas et al. 1990; Rogers et al.\ 1996), which led to a much better prediction of solar oscillations and also resolved many long-standing problems in our understanding of pulsating stars. In addition, helioseismology required particle diffusion to be taken into account in solar models (see Bahcall et al. 1995 and references therein).
The new opacities and equation of state, along with improvements in low-temperature opacities (e.g. Alexander & Ferguson 1994), nuclear cross-sections and neutrino emission rates, have now been applied to low-mass metal-poor stars in order to investigate the above-mentioned age problem. Several investigations (Chaboyer & Kim 1995; Mazzitelli et al. 1995: MDC; VandenBerg et al. 1996; D'Antona et al. 1997; Salaris et al. 1997: Paper I) have already shown that updated models predict lower cluster ages, thus decreasing the size of the discrepancy, if not resolving it. The new physics still needs to be applied to more massive and more metal-rich stars, although some of it, e.g. opacities, already are in use (Bono et al. 1997a,b) However, the full consequences of all improvements have not yet been evaluated. As an example we mention the evolution and pulsations of Cepheid stars.
In the present paper we are concerned with Pop. II stars only. We have a twofold purpose. Firstly, we present stellar models appropriate for globular cluster studies that include all of the improvements listed above. These models cover the complete relevant mass and metallicity range, and include all evolutionary stages from the zero-age main sequence until the end of the helium-burning phase on the horizontal branch. Our calculations therefore provide the most up-to-date set of stellar models applicable to all problems of globular cluster dating. In particular, we show for the first time how particle diffusion influences the evolution of low-mass stars until the end of the horizontal-branch phase.
Secondly, we demonstrate how each of the various steps in improving the input physics influences the models. This is important because of the variety of calculations available in the literature that include some but not all of the new physics. In order to compare these results, it is necessary to be able to translate the differences in physical assumptions into differences in stellar properties. In the first part of this paper we will approach this problem, starting from a suitable set of "old'' evolutionary computations and introducing, step by step, the available "new'' physics in order to make clear the influence of the new assumptions on selected evolutionary parameters. At the end of Sect. 2, we will finally present our best models which will incorporate the most recent improvements in the relevant physics. However, these models will still be calculated ignoring element diffusion.
In Sect. 3 evolutionary predictions for these best models are investigated for selected choices of the cluster metallicity, presenting theoretical predictions for cluster isochrones. This is repeated in Sect. 4 for a set of stellar models where element diffusion is properly taken into account. The comparison between theoretical scenarios with and without diffusion is presented and discussed. Section 5 deals with a discussion of the influence on the R-parameter and the consequences for the inferred original amount of helium in stellar matter. The theoretical uncertainties on R are critically discussed and final conclusion given.
