NGC 6528

The bulge cluster NGC 6528 is one of the most metal-rich Galactic globular clusters, with [Fe/H] determinations ranging between -0.15 and +0.1 (Carretta et al. 2001, Zoccali et al. 2004, Origlia et al. 2005). Besides, it is known to be old ($\sim$ 11 Gyr, Ortolani et al. 1995, Feltzing & Johnson 2002). The abundance pattern of NGC 6528 is still a subject of debate, as the three recent studies mentioned above quote significantly different abundances for some very important elements (Table 25). For instance, abundance determinations in these studies differ by as much as 0.2 dex in the case of iron, 0.3 dex in the case of oxygen, magnesium, and silicon, 0.4 dex for titanium, and 0.8 dex in the case of calcium. Moreover, the carbon and nitrogen abundances of main sequence stars are unknown. These uncertainties are probably due to difficulties associated to the cluster's distance and severe reddening, which has made it so far impossible to obtain high-resolution spectra of unevolved stars, for which both the uncertainties involved in the abundance determinations and star-to-star variations are less important.

As a prelude to our effort towards matching the data on NGC 6528 with models based on the cluster abundance pattern, we show in Figures 18 through 21, the indices for NGC 6528 over-plotted on models with a nearly solar abundance pattern. The abundance pattern of these models (models 1-5 in Table 24, and Table 6) differs from that of the cluster (Table 25), so we do not expect a perfect match to the data, but the comparison might be nonetheless instructive. From these figures, it can be seen that: 1) the age of the cluster according to $H\beta$ is $\sim$ 14 Gyr, which is slightly too old, while it is a bit younger according to the $H\gamma$ and $H\delta$ indices (roughly 10 and 12 Gyr, respectively). This is not unexpected given that, while NGC 6528 stars seem to be at least slightly oxygen-enhanced, the isochrones adopted in the model computations are solar-scaled. Recall that different Balmer lines respond differently to $\alpha$-enhancement (Section 4.3) and therefore should change in different ways if we switched to $\alpha$-enhanced models. 2) The iron abundances, according to Fe4383, Fe5270, and Fe5335 range between -0.3 and -0.2 dex, in rough agreement with the lower value in Table 25; 3) relative to the models, the cluster looks too strong in the CN indices, which suggests the existence of CN-strong stars, just as in the case of 47 Tuc and M 5; 4) NGC 6528 looks mildly too strong in the Mg indices, which is consistent with its measured [Mg/Fe]; 5) as in the case of 47 Tuc and M 5, NGC 6528 is very weak in Ca4227 which, given its very strong CN indices, is hinting that the effect of CN lines on Ca4227 discussed in the case of 47 Tuc might be in operation also for NGC 6528.

Now we turn to the task of producing models that mirror the abundance pattern of NGC 6528. Ideally, we would perform an exercise similar to that of Section 5.2.3, but given the above mentioned uncertainties in the cluster elemental abundances, we have to proceed differently. Instead, we adopt the method discussed in Section 4.4 in order to search the age, metallicity, and abundance pattern that are a best match to the cluster data. We adopt solar-scaled Padova isochrones in this exercise, because they match more closely the abundance pattern of the cluster, particularly the abundance of oxygen. The $\alpha$-enhanced Padova isochrones were computed assuming [O/Fe] = +0.5, whereas the cluster, according to analyses of individual stars by Zoccali et al. and Carretta et al. has at most [O/Fe] $\sim$ +0.15. Other $\alpha$-elements, like magnesium and titanium, are roughly +0.4 dex more enhanced relative to iron in the $\alpha$-enhanced Padova isochrones, which is roughly +0.3 dex higher than measured in cluster stars. Moreover, as discussed in Section 4.3.1, Weiss et al. (2006) have shown that there is a problem with the metal-rich $\alpha$-enhanced Padova isochrones, so we refrain from adopting them in the analysis of NGC 6528. The input abundances of titanium, sodium, and silicon were taken from Zoccali et al. (2004, see Table 25).

The parameters of the best-fitting model are listed in Table 27, and it is compared with cluster data in representative index-index diagrams in Figures 25 and 26 Comparing the numbers in Tables 25 and 27, one can see that the best-fitting spectroscopic age (based on $H\beta$, according to the method described in Section 4.4) is 2-Gyr older than the CMD-based age from Feltzing & Johnson (2002). While on one hand this difference is comfortably within the errors, given the error bars in both studies ($\pm$ 2 Gyr), on the other it can be traced to Feltzing & Johnson's adoption of the $\alpha$-enhanced Padova isochrones for Z=0.04. According to Table 24, this model has [Fe/H] = 0.01 and [O/Fe] = +0.5, which are respectively $\sim$ 0.2 and 0.4 dex higher than found in this study and in spectroscopic abundance determinations of cluster stars (which mostly preceded Feltzing & Johnson's study). Accounting for both [Fe/H] and [O/Fe] differences would bring the ages in both studies into agreement.

Consistency between age estimates based on the various Balmer line indices has also been largely achieved. Ages according to $H\gamma _F$, (10 Gyr), $H\delta _F$ (12 Gyr), and $H\gamma _A$ (13 Gyr, not shown) agree very well with the $H\beta$-based age. The only exception is that of $H\delta _A$ (not shown), according to which the spectroscopic age of the cluster is $\sim$ 8 Gyr. We recall that no such effect was seen for more metal-poor and younger clusters in Sections 5.2 and 5.1.2. Inspection of the Korn et al. (2005) tables reveals that the elemental abundance that affects $H\delta _A$ the most strongly (after iron) is that of silicon. If we adopt the [Si/Fe] determination by Carretta et al. (2001), which is higher than that of Zoccali et al. (2004) by $\sim$ 0.3 dex, the $H\delta _A$-based age becomes 10 Gyr, which is in much better agreement with the ages based on the other Balmer lines. That might also explain why no such discrepancy was found for the other clusters, for which the abundance of silicon used as input is well constrained. While this result could be construed as favoring a [Si/Fe] value at the higher end of the wide range allowed by abundance determinations from the literature, we prefer to wait for the matter to be settled by further detailed abundance studies. We therefore conclude that the Balmer line indices are indicating consistent ages for NGC 6528, the only exception being $H\delta _A$, which indicates mildly too young ages, possibly because the index is affected by the (poorly constrained) abundance of silicon. Finally, we note that, within the uncertainties, there is a trend of slightly younger ages towards higher-order Balmer lines. We speculate that this mismatch is partially due to the adoption of theoretical isochrones whose [O/Fe] is too low. While the Girardi et al. (2000) isochrones adopted in the mild-$\alpha$ models have [O/Fe]=0, spectroscopic determinations tell us that the cluster has at least [O/Fe] $\sim$ +0.1 and might be slightly higher. As discussed in Section 4.3.1, model predictions for $H\beta$ are substantially more affected by oxygen abundances than the higher order Balmer lines. In fact, it can be seen in Figure 12 that in the old, metal-rich, regime ($\sim$ 14 Gyr, [Fe/H] $\mathrel{\copy\simgreatbox}$ 0) $H\delta _F$ is essentially unaffected by the oxygen abundance of the theoretical isochrones adopted. Therefore, adoption of theoretical isochrones with slightly higher [O/Fe] would decrease the $H\beta$-based ages and bring it into better agreement with those based on the higher order Balmer lines and analysis of the cluster CMD.

The best-fitting abundances of iron and magnesium are also in very good agreement with values from the literature, though in both cases our estimates fall at the low end of the range allowed by abundance determinations from the literature. We call attention for the remarkable consistency of the [Fe/H] estimates coming from Fe4383, Fe5270, and Fe5335 (Fe5015 is not available for NGC 6528), which agree with each other within 0.05 dex. Magnesium abundances according to Mg $b$ and Mg$_2$ differ by $\sim$ 0.2 dex, in the sense that the latter are higher. It is hard to understand the reason for this discrepancy. One possible explanation may be the existence of line opacity sources that are unaccounted in the Korn et al. (2005) sensitivity tables. A strong candidate would be the TiO molecule, which is very strong in cool giants which must be present in metal-rich systems such as NGC 6528. However, from the discussion in Section 4.2, we would expect Mg $b$ to indicate higher magnesium abundances than Mg$_2$, which is the opposite of what we are observing. While this issue certainly deserves further scrutiny, we believe that the Mg $b$-based abundance is more reliable, since this index is not affected by flux-calibration or IMF uncertainties (Sections 2.2 and 5.2.2, respectively).

The abundances of carbon and nitrogen in NGC 6528 stars were not determined in the studies summarized in Table 25, so that our estimates listed in Table 27 are a first attempt in that direction. We find that NGC 6528 follows a pattern that is similar to that 47 Tuc (Section 5.2), being slightly carbon-depleted and very strongly nitrogen-enhanced. It is reasonable to suppose that the same type of dichotomy in the abundances of carbon and nitrogen that is found in M 5, 47 Tuc, and many other clusters (e.g., Dickens et al. 1979 Norris & Freeman 1979, Smith et al. 1989, Cannon et al. 1998, Cohen et al. 2002, Briley et al. 2004, Carretta et al. 2005, Lee 2005, Smith & Briley 2006, and references therein) may also be present in NGC 6528, though this needs to be confirmed by spectroscopy of individual stars. We note that there is a slight disagreement between the carbon abundances obtained from matching the G4300 and C$_2$4668 indices, in that the latter are higher by $\sim$ 0.1 dex. While this discrepancy is minor it should be subject to further investigation in the future (Graves & Schiavon 2006, in preparation). Finally, we point out that our value for [Ca/Fe] falls within the range of abundance determinations from the literature, which is no great accomplishment, given the sizable disagreement between the estimates by the different groups. Clearly, more work is needed in this front.

We conclude that the data for NGC 6528 are very well matched for a mildly $\alpha$-enhanced abundance pattern and for an age that is in very good agreement with determinations based on analysis of the cluster color-magnitude diagram. Furthermore, we find that the cluster data are well matched for a [C/Fe]= $\sim$ -0.1 and [N/Fe] $\sim$ +0.5, which mirrors the abundance pattern of other Galactic clusters, indicating that NGC 6528 stars are liable to present similar bimodal distributions in their carbon and nitrogen abundances. We found outstanding consistency between the ages and iron abundances determined from different indices, but small discrepancies in the cases of carbon and magnesium.

The models computed for the abundance pattern given in Table 27 are provided in Table A in the Appendix.