The second and third parameters of the Horizontal Branch in Globular Clusters

The Horizontal Branch (HB) second parameter of Globular Clusters (GCs) is a major open issue in stellar evolution. Large photometric and spectroscopic databases allow a re-examination of this issue. We derive median and extreme (90% of the distribution) colours and magnitudes of stars along the HB for about a hundred GCs. We transform these into median and extreme masses of stars on the HB taking into account evolutionary effects, and compare these masses with those expected at the tip of the Red Giant Branch to derive the total mass lost by the stars. A simple linear dependence on metallicity of this total mass lost explains well the median colours of HB stars. Adopting this mass loss law as universal, we find that age is the main second parameter. However, at least a third parameter is clearly required. The most likely candidate is the He abundance, which might be different in GCs stars belonging to the different stellar generations whose presence was previously derived from the Na-O and Mg-Al anticorrelations. Variations in the median He abundance allow explaining the extremely blue HB of some GCs; such variations are correlated with the R-parameter. Suitable He abundances allow deriving ages from the HB which are consistent with those obtained from the Main Sequence. Small corrections to these latter ages are then proposed, producing a tight age-metallicity relation for disk and bulge GCs. Star-to-star variations in the He content explain the extension of the HB. There is a strong correlation between this extension and the interquartile of the Na-O anticorrelation. The main driver for the variations in the He-content within GCs seems the total cluster mass. 47 Tuc and M3 exhibit exceptional behaviours; however, they can be accommodated in a scenario for the formation of GCs that relates their origin to cooling flows generated after very large episodes of star formation.