Based on a new large, homogeneous photometric database of 35 Galactic globular clusters (GGCs), a set of distance and reddening independent relative age indicators has been measured. The observed D(V-I)_2.5 and D(V)(HB-TO) vs. metallicity relations have been compared with the relations predicted by two recent updated libraries of isochrones. Using these models and two independent methods, we have found that self-consistent relative ages can be estimated for our GGC sample. Based on the relative age vs. metallicity distribution, we conclude that: (a) there is no evidence of an age spread for clusters with [Fe/H]<-1.2, all the clusters of our sample in this range being old and coeval; (b) for the intermediate metallicity group (-1.2<=[Fe/H]<-0.9) there is a clear evidence of age dispersion, with clusters up to ~25% younger than the older members; and (c) the clusters within the metal rich group ([Fe/H]>=-0.9) seem to be coeval within the uncertainties (except Pal12), but younger (~17%) than the bulk of the Galactic globulars. The latter result is totally model dependent. From the distribution of the GGC ages with the Galactocentric distance, we can present a possible scenario for the Milky Way formation: The GC formation process started at the same zero age throughout the halo, at least out to ~20 kpc from the Galactic center. According to the present stellar evolution models, the metal-rich globulars are formed at a later time (~ 17% lower age). And finally, significantly younger halo GGCs are found at any R(GC)>8 kpc. For these, a possible scenario associated with mergers of dwarf galaxies to the Milky Way is suggested.
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