3 The globular cluster test

As quoted in the introduction of this paper let us verify if and how the adopted theoretical scenario is able to pass the test of actual stellar clusters. To this purpose, we choose the two globulars M 30 (Piotto 2000) and 47 Tuc (Gilliland et al. 1998) representing two extreme metallicities spanned by galactic globulars. The best fitting requires a colour-temperature relation and one finds in the literature several relations which mainly differ in predicting the colour of cool stars (Yale; Lejeune et al. 1997). However, one knows that the theoretical temperature of cool stars is actually a free parameter governed by the assumptions about the mixing length, which can be tuned in such a way that the combination of theoretical temperatures with the adopted colour-temperature relation does reproduce the observed colours of cool stars and, in the present case, the colour of globular cluster Red Giant branches. We found that the combination of the adopted theoretical scenario with Yale transformation naturally account for the CM location of RGB. Such an agreement only means that Yale atmospheres are the most suitable ones to push the theoretical RG branches with our choice about the mixing length in the right place of the CM diagram: adopting different colour-temperature relations would only require a corresponding variation in the assumed mixing length value, without affecting the final predictions.

Figure 4 shows that adopted theoretical scenario with $\eta =0.4$ is satisfactorily reproducing the CM diagram of both test clusters with reasonable assumptions about the cluster reddenings and distance moduli, i.e., within the currently accepted uncertainties on these values (see, e.g., Reed et al. 1988; Harris 1999; Sandquist et al. 1999).

Figure 4: The best fit of HST CMD of M 30 (left Panel) and 47 Tuc (right panel) with the adopted theoretical isochrones

One may notice that the best fits predict for M 30 and 47 Tuc an age of 14 and 12 Gyr, respectively. As we will discuss in the following, one cannot attribute too much weight to this absolute determination of the ages, because of systematic uncertainties. However, it appears of obvious relevance that a similar difference in ages, with 47 Tuc younger by a couple of Gyr than M 30, has been earlier suggested by Vandenberg et al. (1990) and supported by the recent investigation by Salaris & Weiss (1998).

As for absolute age determinations, the problem has been largely debated in the current literature and the situation is far from being firmly assessed. Several theoretical investigations have found that new "improved" physic inputs affect stellar models in the direction of decreasing the predicted ages (see for example Chaboyer & Kim 1995; VandenBerg et al. 1996; Cassisi et al. 1998, 1999). However, in the meantime evidences have been discussed raising serious doubts about the adequacy of such new input physics (Pols et al. 1998; Caputo et al. 1999; Castellani et al. 2000). Taking also into account that the possible (if not probable) efficiency of element sedimentation in globular cluster stars can further reduce the predicted ages (Chaboyer 1995; Castellani et al. 1997; Cassisi et al. 1998) one should regard the ages given by the adopted theoretical scenario as a reasonable upper limit for the cluster ages, real ages being possibly smaller by something of the order of 2 Gyr. However, one could be much more confident in the differential behaviour, which appears scarcely affected by the systematic uncertainties we are dealing with.