Formation of Multiple Populations in Globular Clusters: constraints on the dilution by pristine gas

Abstract: The star-to-star differences in the abundance of light elements observed in the globular clusters (GCs) can be explained assuming that a second generation (SG) of stars form in the gas ejected by the asymptotic giant branch (AGB) stars belonging to a first stellar generation. However, while Na and O appear to be anticorrelated in the cluster stars, from the stellar models they turn out to be correlated into the AGB ejecta. In order to reconcile the stellar theory with the observational findings, all the GC models invoke an early dilution of AGB ejecta with pristine gas occurring during the SG formation. Despite a vast consensus about the occurrence of such dilution, the physical process behind it is still unknown. In the present paper we set some general constraints on the pristine gas dynamics and on the possible amount of pristine gas involved in the SG formation, making use of a one zone chemical model. We find that such a dilution is a necessary ingredient in the SG star formation to explain the observed abundance patterns. We confirm the conclusion of our previous works showing that clusters must have been initially much more massive. We also show that models assuming that clusters had an initial mass similar to their current one, and adopting a large fraction of pristine gas to form SG stars, fail to reproduce the observed Na-O anticorrelation and are not viable. We finally show that the dilution event should be restricted in time, rather than extended for the all duration of the SG formation.