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Astron. Astrophys. 335, 929-942 (1998)

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6. Comparison with other clusters.

As largely debated in recent literature, the direct comparison of the CMDs of clusters with similar metallicity is the safest way to deal with many fundamental problems, e.g. possible age differences among clusters with similar metallicity.

In this respect let us first address a methodological warning. As a matter of fact, in the literature, many discussions on the argument are based on the evaluation of selected values, like the turn-off luminosity or the HB luminosity level. However, one knows that similar parameters do depend on difficult evaluations and sometimes on subjective estimates, thus containing more or less relevant errors. On the other hand, the observational CMD is the only real experimental data set one is dealing with. To substantiate this warning, let us only recall one evidence: the group of very metal poor galactic globulars has been described as having indistinguishable CMDs (see e.g. Richer, Fahlman & Vandenberg 1988, Vandenberg, Bolte & Stetson 1990). In spite of such a direct evidence, there are compilations scattered in the literature (see. e.g. Chaboyer & Kim 1995) for which these clusters should have a spread in the differences between the HB and TO luminosity, and thus different ages. According to such an evidence and in order to avoid unnecessary (and dangerous) approximations, the analysis presented below will be always based on the comparison of the original CMDs, even if in this paper we will be forced to use ridge lines for the sake of typographical clarity.

According to theoretical predictions, in old clusters with similar heavy elements abundances MS, RGB and HB should have the same color-magnitude location, with TO location marking differences in age, if any. In the case of M 80, the natural candidates for such a comparison are NGC 1904, NGC 5272 (M 3), NGC 5897, NGC 6205 (M 13), NGC 6218 (M12), and NGC 7492, clusters which have the same [Fe/H] within [FORMULA] dex.

Fig. 6 displays a comparison of the CMD of M 80 with the CMDs for some of these clusters, i.e. M 3 (Ferraro et al. 1997), M 13 (Paltrinieri et al. 1997), NGC 7492 (Buonanno et al. 1987). They show a reasonable good agreement at least as far as the location of the luminous RGB and HB stars is concerned. On the other hand, Fig. 7 shows the comparison of the CMDs for another set of clusters: M 80 (this paper), NGC 1904 (Ferraro et al. 1992a), M12 (Brocato et al. 1996), NGC 5897 (Ferraro et al. 1992b). Even a quick inspection of Fig. 7, discloses serious problems. Assuming a common magnitude for their HBs, the overlap of the their RGBs produces a discrepancy in the blue HB distribution (upper panel). On the other hand, one finds that all the HBs can be nicely overlapped, provided that a significant difference in the RGBs is accepted, with M12 branch appearing sensitively redder than that of M 80 (lower panel). In Fig. 8 we show a direct comparison of our M 80 CMD with the fiducial sequence of M12, i.e the two clusters which represent the extremes in the previous comparison.

[FIGURE] Fig. 6. Comparison of the fiducial lines of M 80, M 3, M 13, and NGC 7492.

[FIGURE] Fig. 7. Comparison of the fiducial lines of M 80 with M12, NGC 1904, and NGC 5897. The fiducial lines have been normalized at the TO (upper panel and at the HB-TD (lower panel ).

[FIGURE] Fig. 8. Comparison of the fiducial lines of M12 with the observed CMD of M 80. Two different normalizations are shown in the two panels. None gives a satisfactory overlap.

Let us try to discuss a little bit in detail the possible origin of this discrepancy. Many causes can be responsible for the detected differences, e.g. calibration errors, age, and metallicity differences. In the following we will analyse some of them:

[FORMULA] calibration errors

The most natural explanation for such an occurrence is that something was wrong in the color calibration, either in our or in the data taken from the literature. The errors in the photometric calibration might produce a spread in the relative position of the different branches in the CMD, though a spread of 0.1 magnitudes in a range of 0.6-0.9 magnitudes in (B-V) would imply an error of [FORMULA] in the slopes of the calibration curves from the instrumental to the standard magnitudes, quite unlikely in the CCD era but not unusual if photometric sequences based on photographic data have been used as `calibrators'.

In this respect the case of M 3 is emblematic: the new photometric calibration recently published by Ferraro et al. 1997, based on Landolt (1992) standard stars has been found to show large systematic differences (at a level of [FORMULA] mag) with respect to the previous photometry by Buonanno et al. (1994) based on the original calibration by Sandage (1970). The same result has been found in M 13 by Paltrinieri et al. (1997). In the latter paper the authors emphasize that the photometry calibrated on photographic sequences may be affected by strong color terms. In some cases (as in M 13) the color differences have been found to be strongly dependent on the magnitude, with effects on the morphology of the main branches in the CMD. As a matter of fact, there is no large sample of observationally (same telescope, filters, calibrations, adopted standard stars etc) homogeneous CMDs representing the galactic globular cluster system. This may play a role in comparing CMDs of different clusters.

[FORMULA] age differences

We already mentioned that clusters with similar metallicities should have similar CMD locations for all the evolutionary phases, but the TO. To enter into details, such clusters are expected with nearly identical MSs and the RGBs only slightly moving toward the red as the cluster age increases. Quantitatively, one finds that at the luminosity of the HB the RGB becomes redder by about [FORMULA] when passing from 12 to 16 Gyr, with a further reduced dependence on age for larger ages.

Bearing in mind such a theoretical scenario, by playing with cluster reddenings and distance moduli one can produce a relative location of the TO regions in the two clusters as expected if M12 is older (by about 2-3 Gyr) than M 80. However, Fig. 8 (upper panel) shows that under these assumptions the HB locations disagree in a way not supported by any theoretical prediction.

One can perform a much more reasonable comparison by observing that the turn down of the HB luminosity at the larger temperatures (HB-TD) should be largely unaffected both by the cluster age and by the cluster metallicity. For what concerns the first statement, we note that the age affects the ZAHB sequences of a given chemical composition through variation in the mass of the He core ([FORMULA]) at the He ignition. From Sweigart & Gross (1976) results one obtains for ZAHB models in the RR Lyrae region (but the dependence on [FORMULA] is negligible): [FORMULA]. Furthermore, from Straniero & Chieffi (1991) one derives a variation of [FORMULA] in the core mass at the He flash for models of given [Fe/H]=-1.7 passing from an age of 12 Gyr to 16 Gyr. This means that only a variation of [FORMULA] is expected in this case.

[FORMULA] metallicity differences

Fig. 9 shows the theoretical prediction for the CMDs for the given labeled age but for a cluster metallicity spanning the range Z= 0.0001-0.001. As an important point, one finds that, whereas the RGB and - to a less extent - the MS depend on the metallicity, the HB-TD appears independent of such a parameter. This is the consequence of the small dependence of the HB luminosity on metallicity and of the evidence that the HB-TD is a temperature indicator, marking the effective temperature where bolometric corrections start sensitively affecting the V magnitude . On the basis of theoretical evaluations presented by Bono et al. (1995) one can add the further evidence that both the HB-TD and the RGB are fairly independent of the assumed amount of original He.

[FIGURE] Fig. 9. H-burning isochrones as in the previous figure but for a fixed age of 16 Gyr and for various values of the metallicity (lines). Theoretical ZAHBs for three choices of the metallicity from Castellani et al. 1991 (symbols).

As a whole, one derives the theoretical evidence that the HB-TD is the only observational parameter whose CMD location is expected on theoretical ground to remain reasonably fixed when varying cluster ages and/or metallicities and/or the amount of the original He. That is, the HB-TD appears an useful observational parameter to reasonably compare the CMD of different clusters. According to such an evidence, one concludes that the more meaningful comparison between M 80 and M12 should be just the one already reported in the lower panel of Fig. 8. By comparing the relative location in that figure with the theoretical predictions given in Fig. 9, one finds that the differences between the two clusters are just the ones expected if M12 is more metal rich than M 80. As an important point, Fig. 8 shows that in this case both clusters do not show a clear difference in age, differences in the turn-off distributions being expected as a consequence of the difference in metallicity.

In the following we will adopt the metallicity scale defined by Zinn (Zinn & West 1984, Zinn 1985), though a new scale has been recently proposed by Carretta & Gratton (1997). This scale has been obtained from direct measurements of the Fe lines in high resolution spectra of a sample of giants in each cluster. In general the Carretta & Gratton (1997) scale assigns higher metallicity ([FORMULA] dex) with respect to Zinn scale, but the relation between the two scales is not linear (see Carretta & Gratton 1997 for a discussion). Another important point that deserves attention in defining the metallicity of a cluster is the abundance of the so-called [FORMULA]-elements (O, Ne, Mg, Si, S, Ca). As stated by Renzini (1977), the location of the RGB in the CMD is mainly driven by the abundance of the low-ionization potential elements (mainly Mg, Si and Fe). Moreover, as noted more than 10 years ago by Geisler (1984), the observed [FORMULA] color of the RGBs of the GGCs correlates better with [FORMULA] than with [Fe/H] (cf. also Salaris & Cassisi 1996). So the [FORMULA]-elements abundance plays a fundamental role in this play.

It is now generally accepted that [FORMULA]-elements are overabundant with respect to iron in GGCs (e.g. Gratton 1987); on the other hand, direct measures of the [FORMULA]-element abundances have been obtained, up to now, only for an admittedly small sample of GGCs (see Table 2 by Carney 1996 and Table 1 by Salaris & Cassisi 1996). Salaris, Chieffi and Straniero (1993) have investigated the influence of the [FORMULA]-elements on the evolution of low mass stars and concluded that [FORMULA]-enhanced ishocrones are mimicked by standard scaled solar isochrones of corresponding global metallicity [FORMULA] given by:

[EQUATION]

where [FORMULA] is the enhancement factor.

In this scenario the detected differences shown in Fig. 7 could derive from similar abundances in [Fe/H], but different values of global metallicity ([FORMULA]) reflecting different abundances of the [FORMULA] elements present in different clusters.

The behavior discussed above, prompted us to compare the CMDs of M12 and M 80 with other Galactic halo clusters. We selected a sample of intermediate-low metallicity clusters for which the list with magnitudes and positions were available in electronic form. The references of the selected data base is listed in the caption of Fig. 11. To provide a quantitative description, we have approached the problem as follows. We have devised a new parameter ([FORMULA]) to measure the distance (in color) between the HB-TD and the RGB: we fixed the HB-TD at [FORMULA] and measured the RGB color at 0.5 magnitudes brighter than the HB-TD level. As the position of the HB turn down is fixed, [FORMULA] just shows the displacement of the RGB as a function of the metal content. Fig. 10 show the parameter [FORMULA] for the mean ridge line of NGC 1904 (Ferraro et al. 1992a) which has been used for reference.

[FIGURE] Fig. 10. The fiducial line of NGC 1904 used as reference; the [FORMULA] is also shown.

[FIGURE] Fig. 11. The [FORMULA] is plotted against the metallicity for 26 globular clusters. The dotted line represents the expected trend of [FORMULA] from the Straniero and Chieffi (1991) models. The objects we have used are: NGC288: (Bergbusch 1993), NGC1261 (Ferraro et al. 1993), NGC1851 (Walker 1992), NGC1904 (Ferraro et al.1992a), NGC2808 (Ferraro et al. 1990), NGC4590 (Walker 1994) IC4499: (Ferraro et al.1995), NGC 5272 (Ferraro et al. 1997) NGC 5286, NGC 6218, NGC6717, NGC6981 (Brocato et al. 1996), NGC5466 (Buonanno et al. 1984), NGC5694 (Ortolani and Gratton 1990), NGC5897 (Ferraro et al. 1992b), NGC 5904 (Sandquist et al. 1996), NGC 6093 (this paper), NGC 6205 (Paltrinieri et al. 1997), NGC6341 (Carney et al. 1992), NGC 6397 (Kaluzny et al. 1997), NGC6584 (Sarajedini and Forrester 1995), NGC 6809 (Desidera 1996), NGC7078 (Durrel and Harris 1993), NGC 7099 (Bergbush 1996), NGC7492 (Buonanno et al. 1987), Arp 2 (Buonanno et al. 1995).

Fig. 11 shows [FORMULA] as a function of the metallicity for the selected sample of clusters. The trend with the metallicity is clear, and in the direction expected from the theoretical models. The dashed line shows the expected value of [FORMULA] from Straniero and Chieffi (1991) models. The general trend of the points is the one expected from the models, though we note a large dispersion, which is particularly evident at intermediate metallicity ([FORMULA][Fe/H][FORMULA]), slightly larger than expected on the basis of the measurement errors. This dispersion can be interpreted simply as a spread in the values [FORMULA] due to measurement and calibration errors, or in terms of a real (physical) dispersion. As suggested above, the abundances of [FORMULA] elements can play an important role in increasing the dispersion in Fig. 10, for this reason the direct determination of the [FORMULA] elements for an extensive sample of GGCs is fundamental in order to shed light into this problem.

To summarize, the possibility given by modern computing technique to directly compare the CMDs presented in the literature brings to the light the evidence that over a very large range of (nominal) metallicities the difference in color between the HB-TD and the RGB in the CMDs of galactic globular clusters appears to follow the general trend predicted by the theoretical models, but with a large spread.

Such an evidence might simply be the consequence of the errors in the photometry calibration, as already quoted in the previous paragraph. But if observational errors are not the main responsible for the distribution shown in Fig. 11, the field is obviously open to discussions and investigations. We have shown that cluster ages can hardly play a role in this scenario, while it is possible that the observed distribution reflects a peculiar distribution in the global metallicity of the clusters. Direct measures of [FORMULA] elements are urged to better understand the observed behaviour.

Let us to close the paper without entering in further details, since, in our feeling, the actual priority is to test whether or not the presented scenario will survive to further investigations. If this will be the case, this will of course open a series of related questions about the history of the galactic halo.

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998
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