Distances and ages of NGC 6397, NGC 6752 and 47 Tuc

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Abstract
Distances and absolute ages for the globular clusters NGC6397, NGC6752, and 47 Tuc are obtained using Main Sequence Fitting. Accurate reddenings and metal abundances (errors of 0.005 mag and 0.04 dex) are obtained by comparing B-V, b-y colours and UVES spectra for clusters TO-stars and subgiants with similar data for Hipparcos subdwarfs, using a reddening free temperature indicator (Halpha). Errors in distances and ages are 0.07 mag and 1 Gyr. NGC6397 and NGC6752 have ages of 13.5\pm 1.1 and 13.4\pm 1.1 Gyr, while 47 Tuc is probably about 2.6 Gyr younger, in agreement with results obtained by techniques sensitive to relative ages. Considering possible systematic errors, the age of the oldest globular clusters is 13.4\pm 0.8\pm 0.6 Gyr (random and systematic errors). This age is fully compatible with WMAP results, and indicates that the oldest Galactic globular clusters formed within the first 1.7 Gyr after the Big Bang, corresponding to a redshift of z\geq 2.5, in a standard LambdaCDM model. The epoch of formation of the (inner halo) globular clusters lasted about 2.6 Gyr, ending at a time corresponding to a redshift of z\geq 1.3. Once combined with values of Ho given by WMAP and by the HST Key Project, our age estimate provides a robust upper limit at 95% level of confidence of Omega_M<0.57, indicating the need for a vacuum energy independent of results from type Ia SNe and clusters of galaxies. Using cluster distances, we derive a value of M_V(HB)=(0.22\pm 0.05)([Fe/H]+1.5)+(0.56\pm 0.07) for the zero point of the relation between the horizontal branch absolute magnitude and metallicity. When combined with the apparent average luminosity of the RR Lyrae stars in the LMC by Clementini et al. (2003), this zero point provides a new estimate of the distance modulus to the LMC: (m-M)o=18.50\pm 0.09.

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