The fraction of second generation stars in Globular Clusters from the analysis of the Horizontal Branch

Most Globular Clusters (GC) show chemical inhomogeneities in the composition of their stars, apparently due to a second stellar generation (SG) in which the forming gas is enriched by hot-CNO cycled material processed in stars belonging to a first stellar generation (FG). We propose to use the horizontal branch (HB) to infer which is today the relative number fraction of ''normal" and anomalous stars in clusters. We assume that the anomalies also include enhanced helium abundance. Helium variations have been recognized to be able to explain several puzzling peculiarities (gaps, RR Lyr periods and period distribution, ratio of blue to red stars, blue tails) in HBs. We extend the analysis to as many clusters as possible. We show that, with few exceptions, 50% or more of the stars belong to the SG. In other cases, where one would think of a simple stellar population, we suggest that the stars might all belong to the SG. We fit the optical and UV data of NGC2808, including a reproduction of the main sequence splittings and an exam of the problem of "blue hook" stars. We also show a detailed fit of the totally blue HB of M13, one among the clusters that are possibly fully made up by SG stars. We conclude that the formation of the SG is a crucial event in the life of GCs. A high fraction of SG stars can be achieved only if the initial cluster was much more massive than the present one and most of the FG low mass stars have been lost. As shown by D'Ercole et al., the mass loss due to type II supernovae of the FG may be the process responsible for triggering the expansion of the cluster, the stripping of its outer layers and the loss of most of the FG low-mass stars.