Distances, Ages, and Epoch of Formation of Globular Clusters

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Abstract
We review the results on distances and absolute ages of Galactic globular clusters (GCs) obtained after the release of the Hipparcos catalog. Several methods aimed at the definition of the Population II local distance scale are discussed, and their results compared, exploiting new results for RR Lyraes in the Large Magellanic Cloud (LMC). We find that the so-called short distance and long distance scales may be reconciled whether or not a consistent reddening scale is adopted for Cepheids and RR Lyrae variables in the LMC. Emphasis is given in the paper to the discussion of distances and ages of GCs derived using Hipparcos parallaxes of local subdwarfs. We find that the selection criteria adopted to choose the local subdwarfs, as well as the size of the corrections applied to existing systematic biases, are the main culprit for the differences found among the various independent studies that first used Hipparcos parallaxes and the subdwarf fitting technique. We also caution that the absolute age of M92 (usually considered one of the oldest clusters) still remains uncertain due to the lack of subdwarfs of comparable metallicity with accurate parallaxes. Distances and ages for the nine clusters discussed in a previous paper by Gratton et al. are rederived using an enlarged sample of local subdwarfs, which includes about 90% of the metal-poor dwarfs with accurate parallaxes (Δπ/π ≤ 0.12) in the whole Hipparcos catalog. On average, our revised distance moduli are decreased by 0.04 mag with respect to Gratton et al. The corresponding age of the GCs is t = 11.5 ± 2.6 Gyr, where the error bars refer to the 95% confidence range. The relation between the zero-age horizontal branch (ZAHB) absolute magnitude and metallicity for the nine program clusters turns out to be MV(ZAHB) = (0.18 ± 0.09)([Fe/H] + 1.5) + (0.53 ± 0.12) Thanks to Hipparcos the major contribution to the total error budget associated with the subdwarf fitting technique has been moved from parallaxes to photometric calibrations, reddening, and metallicity scale. This total uncertainty still amounts to about ±0.12 mag. We then compare the corresponding (true) LMC distance modulus μLMC = 18.64 ± 0.12 mag with other existing determinations. We conclude that at present the best estimate for the distance of the LMC is μLMC = 18.54 ± 0.03 ± 0.06, suggesting that distances from the subdwarf fitting method are ~1 σ too long. Consequently, our best estimate for the age of the GCs is revised to Age = 12.9 ± 2.9 Gyr (95% confidence range). The best relation between ZAHB absolute magnitude and metallicity is MV(ZAHB) = (0.18 ± 0.09)( + 1.5) + (0.63 ± 0.07). Finally, we compare the ages of the GCs with the cosmic star formation rate recently determined by studies of the Hubble Deep Field (HDF), exploiting the determinations of ΩM = 0.3 and ΩΛ = 0.7 provided by Type Ia supernovae surveys. We find that the epoch of formation of the GCs (at z ~ 3) matches well the maximum of the star formation rate for elliptical galaxies in the HDF as determined by Franceschini et al.