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

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.

💡 Research Summary

The paper addresses the long‑standing problem of reproducing the observed Na–O anticorrelation in globular cluster (GC) stars within the framework of the asymptotic giant branch (AGB) self‑enrichment scenario. Spectroscopic surveys have shown that second‑generation (SG) stars in GCs display a clear Na‑O anticorrelation, while theoretical AGB yields predict a positive correlation between Na and O in the ejecta. Consequently, every viable GC formation model must invoke dilution of the AGB ejecta with pristine (i.e., unprocessed) gas. The authors set out to quantify the amount of pristine gas required, the timing of its accretion, and the implications for the initial mass of the first generation (FG) of stars.

Using a simple one‑zone chemical evolution model, they follow the composition of the intra‑cluster medium (ICM) from the onset of SG formation (≈32 Myr after the birth of the FG) to a fiducial end time of 100 Myr. The FG is assumed to follow a Kroupa initial mass function, and the total mass of AGB ejecta retained by the cluster is taken to be ~5 % of the FG mass (M_ej ≈ 0.05 M_FG). If one assumes that the present‑day mass of the FG is comparable to its initial mass, then to produce a SG population comparable in size to the FG one must accrete a pristine gas mass M_pr ≈ M_FG. This yields a dilution factor M_ej/M_pr ≈ 0.05, far too low to generate the observed spread in Na and O. The model therefore predicts that FG and SG stars would occupy essentially the same locus in the