Towards a working model for the abundance variations within Globular   Clusters stars
  A popular self--enrichment scenario for the formation of globular clusters assumes that the abundance anomalies shown by the stars in many clusters are due to a second stage of star formation occurring from the matter lost by the winds of massive asymptotic giant branch (AGB) stars. Until today, the modellizations of the AGB evolution by several different groups failed, for different reasons, to account for the patterns of chemical anomalies. Here we show that our own modelling can provide a consistent picture if we constrain the three main parameters which regulate AGB evolution: 1) adopting a high efficiency convection model; 2) adopting rates of mass loss with a high dependence on the stellar luminosity; 3) assuming a very small overshooting below the formal convective regions during the thermal pulse (TP) phase. The first assumption is needed to obtain an efficient oxygen depletion in the AGB envelopes, and the second one is needed to lose the whole stellar envelope within few thermal pulses, so that the sum of CNO elements does not increase too much, consistently with the observations. The third assumption is needed to fully understand the sodium production. We also show that the Mg - Al anticorrelation is explained adopting the higher limit of the NACRE rates for proton captures by Mg25 and Mg26, and the models are consistent with the recently discovered F-Al correlation. Problems remain to fully explain the observed Mg isotopes ratios. 
Paolo Ventura and Francesca D'Antona