We estimate the initial He content in about 30% of the Galactic globular clusters (GGCs) from new star counts we have performed on the recently published HST snapshot database of Colour Magnitude Diagrams (Piotto et al. 2002). More in detail, we use the so-called $R$-parameter and estimate the He content from a calibration based on a recently updated set of stellar models. We performed an accurate statistical analysis in order to assess whether GGCs show a statistically significant spread in their initial He abundances, and whether there is a correlation with the metallicity. We do not find any significant dependence of the He abundance on the GC metallicity; this provides an important constraint for models of Galaxy formation and evolution. Apart from GGCs with the bluest HB morphology, the observed spread in the individual He abundances is statistically compatible with the individual errors. This means that either there is no intrinsic He spread among the GGCs, or that this is masked by the errors. In the latter case we have estimated a firm 1$sigma$ upper limit of 0.019 to the possible intrinsic spread. In case of the GGCs with the bluest HB morphology we detect a significant spread towards higher abundances inconsistent with the individual errors. In the hypothesis that the intrinsic dispersion on the individual He abundances is zero, taking into account the errors on the individual R-parameter estimates, as well as the uncertainties on the GGC [M/H] scale and theoretical calibration, we have determined an initial He abundance Y(GGC)=0.250pm0.006 a value in perfect agreement with current estimates based on CMB radiation analyses and cosmological nucleosynthesis computations.
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