Comparison with Cluster Data

A fundamental test to which every stellar population synthesis model must be submitted is the comparison to Galactic clusters. If the models cannot reproduce the data for these well-known resolved systems, using the right set of input parameters, their application to galaxy evolution can be rightly called into question. It is not surprising, therefore, that there is a vast literature dedicated to such comparisons (e.g., Rose 1994, Bruzual et al. 1997, Schiavon & Barbuy 1999, Gibson et al. 1999, Vazdekis et al. 2001, Schiavon et al. (2002a,b), Maraston et al. 2003, Schiavon et al. 2004b, Proctor et al. 2004, Schiavon et al. (2004a,b), Lee & Worthey 2005, Lilly & Fritze-v. Alvensleben 2006, and references therein). In this section, we show that our models match the data of four well-known Galactic clusters to high accuracy. Our discussion is focussed on a few well known representative clusters for which very high quality CMD data and abundance analyses of cluster members are available in the literature. The absorption line indices for our globular clusters of choice were measured in the very high S/N integrated spectra collected by Schiavon et al. (2005) and, in the case of M 67, they were taken from Paper III and converted to our system of equivalent widths (but see Section 5.1). While essentially all results presented here are valid for the entire sample of 40 globular clusters observed by Schiavon et al. (2005), we defer an in-depth discussion of the whole sample to a forthcoming paper.

The clusters examined here are M 5 (=NGC 5904), 47 Tuc (=NGC 104), NGC 6528, and M 67 (=NGC 2682). Relevant data for these clusters are summarized in Table 25. Ages come from analyses of CMD data by Salaris & Weiss (2002, M 5), Paper II (47 Tuc), Ortolani et al. (2001, NGC 6528), and Paper III (M 67). The iron abundance for M 67 comes from the compilation in Paper III. Abundances for M 5 come from Cohen, Briley & Stetson (2002, [C/Fe] and [N/Fe]) and Ramírez & Cohen (2003, other ratios). Carbon and nitrogen abundances for 47 Tuc stars come from Briley et al. (2004), while for other elements abundances come from Carretta et al. (2004) and Alves-Brito et al. (2005). Oxygen abundances in 47 Tuc dwarfs come from Carretta et al. (2005). Abundances for NGC 6528 are averages of the determinations by Carretta et al. (2001), Zoccali et al. (2004), and Origlia, Valenti & Rich (2005) (but see discussion below and in Section 5.3). Regarding the abundances of carbon and nitrogen, we note that stars in M 5 and 47 Tuc (and perhaps in all globular clusters) are known to present a bimodal distribution of the abundances of these elements (e.g., Dickens, Bell & Gustafsson 1979, Norris & Freeman 1979, Smith, Bell & Hesser 1989, Cannon et al. 1998, Cohen et al. 2002, Briley et al. 2004, Carretta et al. 2005, Lee 2005, Smith & Briley 2006). For these elements, we list the extremes of the range of values spanned by cluster main sequence stars. Unfortunately, no such study is available for the C and N abundances of main sequence stars in NGC 6528. Origlia, Valenti & Rich (2005) determined carbon abundances in four bright NGC 6528 giants, reporting [C/Fe]=-0.4. This value probably reflects the workings of internal mixing, and we choose not to consider it. For M 67, the abundance ratios were taken from the compilation in Paper III, except for oxygen, calcium and titanium, which were taken from Tautvaisiene et al. (2000) and Shetrone & Sandquist (2000). Finally, because different groups disagree as to the metal abundances of NGC 6528 (Carretta et al. 2001, Barbuy et al. 2004, Zoccali et al. 2004), abundances by these two different groups are listed for this cluster. This issue is further discussed in Section 5.3.

Comparison of the data on elemental abundances shown in Tables 6 and 25 suggests that the overall abundance pattern of the cluster stars is mostly quite similar (to within 0.1 dex) to that of our library stars with the same [Fe/H]. In fact, in the case of M 67 there is an almost perfect match between cluster and field star abundance patterns. For the globular clusters, though, there are a few important exceptions that need to be kept in mind. The relative abundances of carbon and nitrogen in globular-cluster stars deviate strongly from those of field stars. The main consequence is that, in integrated light, globular clusters tend to show strongly enhanced CN lines and slightly weaker CH lines when compared to models based on spectra of field stars (see Paper I for a detailed discussion). This should mainly affect the comparison of our model predictions to data on the CN$_1$, CN$_2$, G4300, and C$_2$4668 indices but can also disturb other indices whose passband and/or pseudo-continua contain lines due to these molecules (for instance, Ca4227, see below, or the $H\gamma$ indices). Another important difference is the one between the abundance pattern of NGC 6528 and that of library stars of near-solar metallicity. This bulge cluster has higher [O/Fe] by $\sim$ 0.1 dex and [Ca/Fe] (potentially) lower by $\sim$ 0.4 than field stars of the same metallicity. Its relative magnesium abundance seems to be slightly higher as well. These few exceptions aside, it is fair to say that the abundance patterns of the clusters and the field stars employed in our model construction are a relatively good match. Therefore, we first compare our base-model predictions with cluster data without performing any correction to bring the models into the cluster abundance pattern (except in the case of M 67, for which such comparisons were discussed in Paper III and will not be repeated here). Confrontation between cluster data and models tuned to the clusters abundance patterns are discussed in Sections 5.2.3 and 5.3.