8 The age of NGC 6528

Armed with the cleanest colour-magnitude diagram so far for the globular cluster NGC 6528 we are in a position to address its age using both stellar isochrones as well as in relation to other well studied metal-rich globular clusters.

8.1 The metallicity of NGC 6528

Since age and metallicity are degenerate in colour-magnitude diagrams it is important to have a good estimate of the metallicity if we want to use stellar isochrones to find the absolute age of the cluster. In Table 1, we summarize the current metallicity and iron abundance estimates for NGC 6528 available in the literature.

Due to the faintness of metal-rich globular clusters detailed stellar abundance studies of individual stars in these clusters have been few. The results of the first such study was reported in Barbuy (1999) who obtained spectra of one, very cool ( $T_{\rm eff} =3600$K) giant star in NGC 6528 and derived a [Fe/H] of -0.6 dex, [Ca/Fe] = 0.0 dex and [Ti/Fe] = +0.6 dex.

Using the HIRES spectrograph on KECK Carretta et al. (2001) and Cohen et al. (1999), in two accompanying papers, derive iron abundances as well as abundances for a large number of other elements for four stars in NGC 6528 and five stars in NGC 6553. Carretta et al. (2001) found that all four stars in NGC 6528 show very similar [Fe/H] ( +0.05, +0.08, + 0.09, +0.04 dex respectively) thus their final [Fe/H] estimate for the whole cluster appears very robust. The accompanying study of NGC 6553 and the discussion of the [Fe/H] for NGC 6553 appear to indicate that a total error in [Fe/H] on the order of 0.1 dex appear a reasonable estimate (see detailed discussions in Carretta et al. 2001).

Figure 15: Final colour-magnitude diagram based on the data from WF2 and WF3 corrected for differential reddening. Cuts in $\sqrt {\mu _{l}^2+ \mu _{b}^2}$ as in Fig. 7.

Figure 16: Comparison of our final colour-magnitude diagram with the ridge line derived for NGC 6553 by Zoccali et al. (2001). Their ridge line is showed as a set of connected $\times$ symbols. Both the mains-sequence, red giant branch as well as the horizontal branch coincide well. The ridge line of NGC 6553 was moved +0.4 mag in $V_{\rm 555}$ and -0.18 in $V_{\rm 555}-I_{\rm 814}$.

Figure 17: Colour-magnitude diagram with fiducial points indicated by large open circles. The horizontal branch stars are indicated by $\times$ and the AGB stars with $\bullet$. Note that no points are defined for the lower part of the red giant branch, see text for a discussion of this. Cuts in $\sqrt {\mu _{l}^2+ \mu _{b}^2}$ as in previous plots.

See also their detailed discussion of the problems with analysis of cold giants. It appears that the disagreement between the two studies could be due to different temperature scales having been used. Since the Carretta et al. (2001) study is the larger one and also guided by their discussion on the temperature and errors from other sources we here give higher weight to that study for determination of stellar abundances in NGC 6528. However, further independent studies of the stellar abundances in this cluster should be undertaken to solve this issue.

Further Carretta et al. (2001) found that the $\alpha$-elements Si and Ca in NGC 6528 show large excesses compared to the solar values, while Ti and Mg appear to be solar. This type of abundance pattern is reminiscent of that observed for stars in the Galactic bulge (McWilliam & Rich 1994) and might be indicative of a rapid chemical enrichment process prior to the formation of the stars observed. The exact interpretation of these data is, however, pending.

In Carretta et al. (2001) the cluster membership for the four stars studied was ascertained by observing only horizontal branch stars. The stellar spectra were also used to derive radial velocities for the program stars and their velocities further confirmed the cluster membership for the four targets.

Having assessed the currently available abundance information for NGC 6528 we find it safe to assume that the cluster is probably as metal-rich as the sun and is enhanced, at least in some, $\alpha-$elements.

8.2 Comparison with NGC 6553

In Fig. 16 we compare the ridge line for NGC 6553 found by Zoccali et al. (2001) with our colour-magnitude diagram. To fit the colour-magnitude diagram for NGC 6528 with the ridge line of NGC 6553 we need to move the ridge line from Zoccali et al. (2001) by 0.4 in $V_{\rm 555}$ and -0.18 in $V_{\rm 555}-I_{\rm 814}$. If the two clusters have the same metallicity (as indicated by the recent detailed abundance analyses) this nice fit indicates that their ages are very close too. We thus find that NGC 6553 has been more reddened than NGC 6528, i.e. the negative shift applied in $V_{\rm 555}-I_{\rm 814}$. Using Table 12 in Holtzman et al. (1995b) we find that shift in $V_{\rm 555}-I_{\rm 814}$ corresponds to a shift in $V_{\rm 555}$ of -0.46. Thus NGC 6553 appears to be marginally closer to us that NGC 6528. However, it should be remembered that both in Zoccali et al. (2001) and in this work the colour-magnitude diagrams have been corrected for differential reddening so the interpretation of such shifts is less clear in terms of distance modulus. The $\Delta E(B-V)$, as measured here, between the two clusters is $\sim$0.15, using Table 12 in Holtzman et al. (1995b).

The agreement between the NGC 6553 ridge line and our data is very good. At the brightest end the NGC 6553 ridge line appears to fall slightly below the NGC 6528 data. However, since the NGC 6553 data does not go as bright as the NGC 6528 data one should not draw any conclusions regarding the relative metallicities of the clusters from this.

This comparison does, as has also been reported in e.g. Ortolani et al. (1995), show that these two clusters have indeed very similar ages.

8.3 Age from fitting stellar isochrones

Since NGC 6528 is found to be enhanced, at least in some, $\alpha-$elements we compare our fiducial points with that of theoretical stellar isochrones from Salasnich et al. (2000) in which $\alpha$-enhancement has been included. To facilitate the comparison with the stellar isochrones we define a set of fiducial points which are shown in Fig. 17 and tabulated in Table 8.

 

 

Table 8: Fiducial points for NGC 6528.

$V_{\rm 555}-I_{\rm 814}$	$V_{\rm 555}$
1.5	21.4
1.45	21
1.42	20.6
1.4	20.2
1.68	18.8
1.71	18.3
1.75	17.75
1.8	17.35

The fiducial points are marked with large circles and trace the upper main-sequence as well as the upper part of the red giant branch. We have deliberately not defined any point for the lower red giant branch or for the sub-giant branch as we feel that these regions are less well defined and thus that any fiducial point might be misleading. We have also marked those stars that we will explicitly show in the diagrams where we fit isochrones. It is fairer to show all the AGB and horizontal branch stars rather than try to represent them with a fiducial line since then each reader is able to judge for themselves the goodness of the fit.

Examples of fits are shown in Fig. 18.

Figure 18: Fiducial points for NGC 6528 together with stellar isochrones from Salasnich et al. (2000). Isochrones are for Z= 0.019 and Z=0.040. Horizontal branch stars and AGB stars are coded as previously.

In the case of Z=0.019 we moved the isochrones by $\Delta(V_{\rm 555})=15.95$ and $\Delta(V_{\rm 555}-I_{\rm 814})=+0.63$. The turn-off is well represented by the 11 Gyr isochrone and the horizontal branch is well matched too. However, all the isochrones are brighter than the AGB. In order for Z=0.019 isochrones to fit our data on the AGB we would need to increase the distance modulus and the best fitting isochrone would then be very young, younger than 9 Gyr. The horizontal branch would not be well fitted either. Thus it appears unlikely that our data could be well fitted with $\alpha$-enhanced isochrones with Z=0.019.

For the Z=0.040 isochrones we moved them with the following amount $\Delta(V_{\rm 555})=15.95$ and $\Delta(V_{\rm 555}-I_{\rm 814})=$ +0.655. Here the AGB is much better reproduced and both turn-off and horizontal branch can be well fitted simultaneously. The 11 Gyr isochrone appears to fit best. However as this fit cannot be rigorous due to the limitations in the data the estimated error bar on this must be rather large, perhaps up to 2 Gyr.

These $\Delta{\it V}_{\rm 555}$ and $\Delta(V_{\rm 555}- I_{\rm 814})$correspond to (using Table 12 in Holtzman et al. 1995a) an E(B-V) of 0.54 and thus a distance modulus of 14.29 which corresponds to a physical distance of 7.2 kpc. The derived distance, is compatible with that found by Richtler et al. (1998) who used the magnitude of the horizontal branch to determine the distance to NGC 65628. With $m_v({\rm HB})=17.21\pm 0.05$ they found that the distance to NGC 6528 is between 6.0 and 8.9 kpc depending on the exact value for reddening and metallicity as well as the relation between magnitude for the horizontal branch and metallicity (see their Table 10). Since we have a better handle on the metallicity we are able to be more sure about the distance and reddening. Note that the reddening that we derive here is a "minimum'' reddening in the sense that we have dereddened the stars on WF3 relative to those on WF2 according to the differential reddenings found.