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Astron. Astrophys. 333, 505-523 (1998)

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5. Conclusions

After considering the various pros and cons of the traditional "vertical" and "horizontal" methods for age determination of Galactic globular clusters (based on [FORMULA]   and [FORMULA]   vs age calibrations, respectively), we have defined a new global procedure able to yield homogeneously their relative ages.

To this aim we have defined and used a new observable, [FORMULA]  , namely the difference in magnitude between an arbitrary point on the upper main sequence (MS) and the horizontal branch (HB). Following VBS, we have adopted as reference [FORMULA] -the V magnitude of the MS-ridge that is 0.05 mag redder than the MS Turn-off (TO). The observational error associated to [FORMULA]   is substantially smaller than that to [FORMULA]  .

This method shares with other differential techniques the advantage of being strictly independent of distance and reddening and with the "vertical" [FORMULA]  -technique (Iben & Faulkner, 1968) the intrinsic advantage of being based on theoretical luminosities rather than on theoretical temperatures, which are extremely sensitive to the uncertainties in the treatment of convection and radiative opacity at low temperatures.

We have also shown that the [FORMULA]   vs age calibration obtained by using the available theoretical models and different sets of transformations from the theoretical to the observational plane has a quite low dependence on metallicity. Moreover, the estimates of the relative age so obtained are also sufficiently invariant (to within [FORMULA] Gyr) with varying adopted models and transformations.

Since for clusters where the horizontal part of the HB is not populated (e.g. M13, NGC 6752, NGC 6397, 47 Tuc, etc.) the uncertainty in the estimate of the HB luminosity - [FORMULA] - directly propagates into the estimate of [FORMULA]  , the so-called "horizontal" [FORMULA]  -method (VBS, Sarajedini and Demarque 1990 -SD) based on color differences remains the most reliable technique to estimate relative cluster ages. However, to reduce the impact of the still high uncertainties in the models, it requires a proper empirical calibration.

We have used the differential ages obtained via the "vertical" [FORMULA]   parameter for a selected sample of clusters (11, with high quality CMDs, well populated HBs, trustworthy calibrations) to perform an empirical calibration of the "horizontal" observable [FORMULA]   in terms of [Fe/H]  and age.

A direct comparison with the corresponding calibration determined from the theoretical models reveals the existence of a clear-cut discrepancy with almost any kind of models plus trasformations. Such a disagreement, in general increasing with increasing the cluster metallicity, calls into question the model scaling with metallicity in the observational planes.

Based on the global sample of considered clusters, we have so obtained, within an homegeneous procedure, relative ages for 33 Galactic globulars having different metallicity, HB-morphologies, and Galactocentric distances. These new estimates have also been compared with previous latest determinations (CDS96, and Richer et al.  1996), and the detected differences have been schematically discussed.

Finally, though the available sample is still insufficient to draw any firm conclusion (as both additional data for other clusters and improvements in the calibrations are urged), we have also briefly discussed the distribution of the cluster ages with varying metallicity and Galactocentric distance. In summary, (a) there is no direct indication for any evident age-metallicity relationship (see Fig.  19); (b) there is some spread in age (still partially compatible with the errors), and the largest dispersion is found for intermediate metal-poor clusters (signature of the so-called second parameter effect?); (c) older clusters populate both the inner and outer regions of the Milky Way (quite independent of metallicity), while the younger globulars are present just in the outer regions, but the sample is too poor to yield statistically significant evidences. If further data would confirm this preliminary results, a natural conclusion is that the Galaxy collapsed with different timescales, very rapidly in the inner zones, and on a much longer period outside. Moreover, accretion phenomena and mergers of small fragments could have taken place at a significant level.

We put forward severe warnings against the uncritical assumption of a given global relative age-scale for globulars with the formal uncertainties derived by propagating observational errors since we have shown that the undeterminacies and the unconsistencies associated with the same clock (i.e. models + transformations) on which they are based can be significantly more important than any crude measurement error.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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