Fe vs Balmer Lines

As in the previous Section, we first focus on plots between Fe and Balmer lines, because these indices are mostly sensitive to age and [Fe/H] (see discussion in Section 4.3.2). We first consider the case of 47 Tuc. In all the panels in Figures 22a through 22c the models predict the correct [Fe/H] of the cluster to within $\pm$ 0.05 dex. The spectroscopic age for this cluster according to the models is $\sim$ 14 Gyr, which is older by $\sim$ 2-3 Gyr than the age based on analysis of the cluster CMD using the $\alpha$-enhanced Padova isochrones (Paper II). Roughly half of this mismatch is due to our adoption of solar-scaled isochrones in the current calculation. The rest of the discrepancy is due to an effect pointed out in Paper II, where it was shown that it is motivated by a mismatch between the observed luminosity function of the cluster and theoretical predictions, which underestimate the number of giant stars brighter than the horizontal branch (HB), relative to main sequence stars. While it is not clear whether this mismatch between data and theory in the luminosity function space is restricted to 47 Tuc and a few other clusters (e.g., Langer, Bolte & Sandquist 2000) Zoccali & Piotto (2000) found an apparent trend according to which models seem to under-predict the relative number of giants in more metal-rich clusters. Zoccali & Piotto point out that uncertainties in the bolometric corrections for metal-rich cool giants might be responsible for the mismatch, but to our knowledge this hypothesis has not yet been tested. Clearly, more work is needed to clarify this matter.

The case of M 5 is very interesting. The Balmer lines in this cluster's spectrum are too strong for its age. In Figures 22a through 22c, the spectroscopic age of M 5 according to the models is somewhere between 4 and 6 Gyr (probably even a little younger, if the [Fe/H]=-1.3 models were based on $\alpha$-enhanced isochrones). This is in stark contrast with the known CMD-based age of the cluster ($\sim$ 11 Gyr). This effect has been pointed out before (Freitas Pacheco & Barbuy 1995, Lee, Yoon & Lee 2000, Maraston & Thomas 2000, Schiavon et al. 2004b) and is due to the influence of blue HB stars which are not accounted for by the theoretical isochrones adopted in our models. These old and bright A-F-type stars have very strong Balmer lines which can mimic a young turnoff if not properly accounted for by the models. Schiavon et al. (2004b) studied this problem and devised a method to disentangle this degeneracy between age and HB-morphology, which explores the differential sensitivity of $H\delta$ and $H\beta$ to the influence of blue HB stars.

The theoretical isochrones adopted in our models do not produce blue HB stars in the metallicity range considered here. The morphology of the HB is chiefly dictated by mass loss along the giant branch phase, a phenomenon for which a deterministic theory is still lacking. As a result, models for the mass loss along the giant branch rely on empirical calibrations of mass-loss rates as a function of stellar parameters, thus having limited predictive power. Therefore, we adopt a more conservative path and just correct the observations of M 5 for the effect of blue HB stars, on the basis of a high-quality CMD for the cluster (see details in Schiavon et al. 2004b). In this way we can at least check whether our models predict correctly the cluster properties in the absence of blue HB stars. The arrows attached to the data for M 5 indicate how the line indices change when the contribution from blue HB stars is removed. These arrows were computed by Schiavon et al. (2004b), from a combination of the color-magnitude diagram of M 5 (from Piotto et al. 2002) and the fitting functions presented here. For details, see Schiavon et al. (2004b). In all panels of Figures 22a-c we can see that the age predicted by the models for the HB-free version of M 5 is $\sim$ 10 Gyr and [Fe/H] $\sim$ -1.3, in outstanding agreement with the values listed in Table 25. Given the uncertainties involved in the model calibrations at the low metallicity end and in the correction for the effects of blue HB stars, we consider this a very satisfactory result.