Confronting Models with M 67 Data

In Paper III we presented a detailed comparison between our solar-scaled models and Lick indices for M 67. We showed that our models match the Balmer line indices $H\beta$, $H\gamma _F$, and $H\delta _F$ for the same age that is inferred from the fit of the cluster's color-magnitude diagram, to within $\sim$ 0.5 Gyr. Moreover, we showed that the indices $<Fe>$ (the average of indices Fe5270 and Fe5335), Mg $b$, CN$_1$, and CN$_2$ were matched for the known cluster elemental abundances to within $\pm$ 0.1 dex. Here we extend these comparisons to include the remaining indices modelled in this paper. In order to find the model that best matches the data for M 67, we applied the method described in Section 4.4 and found the following best-fitting parameters, using the Padova solar-scaled isochrones and assuming solar [O/Fe]: age $\sim$ 3.8 Gyr, [Fe/H]=-0.08, [Mg/Fe]=0.01, [C/Fe]=-0.03, [N/Fe]=+0.02, and [Ca/Fe]=-0.03. The models computed for this abundance pattern are provided in Table A in the Appendix. Inspection of Table 25 shows that these results agree with the known cluster values to within 0.3 Gyr and 0.08 dex in age and metal abundances, respectively. In Figures 18 through 21 these best-fitting models are compared with Lick indices for M 67 in a number of relevant index-index diagrams. The model ages and metallicities plotted are as follows: 1.2, 1.5, 2.5, 3.5, 7.9, and 14.1 Gyr, and [Fe/H] = -0.7, -0.4, 0.0, and +0.2. The filled squares represent data for NGC 6528, which will be discussed in Section 5.3.

Figures 18 and 19 compare data to models in metal vs. age-sensitive-index plots. For almost all indices, the data for M 67 fall within 1-$\sigma$ of our model prediction for a solar-metallicity, 3.5 Gyr-old, single stellar population. In Figures 20 and 21 the data for indices sensitive to carbon, nitrogen, magnesium, and calcium are compared with the models, using $H\beta$ as age indicator. Again, the models are a satisfactory match to the data for the correct age and metal abundances. We call attention for the very good match obtained for Ca4227, which was not discussed in Paper III. We note that in that paper we could not match the M 67 data for G4300. The match here is slightly improved, though still not entirely satisfactory. The G4300 index is matched for a model with [Fe/H]$\sim$+0.1, which is almost 0.2 dex too metal-rich compared with the value obtained from the match to the C$_2$4668 index, which is in much better agreement with the cluster known carbon abundance. This result should serve as a warning against use of the G4300 index for carbon abundance determinations in metal-rich stellar populations (see Graves & Schiavon 2006, in preparation).

In summary, the models match the age of M 67 and its abundances of iron, carbon, nitrogen, magnesium and calcium to within 1 Gyr and 0.1 dex. Most importantly, the ages according to all Balmer line indices are consistent to within 0.5 Gyr. This is a very encouraging result that ratifies the application of our models for estimation of mean ages and metal abundances of stellar systems in a very important age/metallicity regime. To some extent, this is not surprising, given that the integrated light of the cluster over most of the spectral interval involved in this study is dominated by turnoff stars which, in the case of M 67, are characterized by mid-F spectral types of solar metallicity, for which most of the physical input and calibrations underlying the models are very well established. The fact that the abundance pattern of our models for solar metallicity are a close match to that of the cluster is also very helpful. In the next sections we focus on the more challenging task of matching the data for Galactic globular clusters, which depart considerably from the regime where such favorable conditions are enjoyed.