A general abundance problem for all self-enrichment scenarios for the origin of multiple populations in globular clusters

A number of stellar sources have been advocated as the origin of the enriched material required to explain the abundance anomalies seen in ancient globular clusters (GCs). Most studies to date have compared the yields from potential sources asymptotic giant branch stars (AGBs), fast rotating massive stars (FRMS), high-mass interacting binaries (IBs), and very massive stars (VMS) with observations of specific elements that are observed to vary from star-to-star in GCs, focusing on extreme GCs such as NGC 2808, which display large He variations. However, a consistency check between the results of fitting extreme cases with the requirements of more typical clusters, has rarely been done. Such a check is particularly timely given the constraints on He abundances in GCs now available. Here, we show that all of the popular enrichment sources fail to reproduce the observed trends in GCs, focusing primarily on Na, O and He. In particular, we show that any model that can fit clusters like NGC 2808, will necessarily fail (by construction) to fit more typical clusters like 47 Tuc or NGC 288. All sources severely overproduce He for most clusters. Additionally, given the large differences in He spreads between clusters, but similar spreads observed in Na–O, only sources with large degrees of stochasticity in the resulting yields will be able to fit the observations. We conclude that no enrichment source put forward so far (AGBs, FRMS, IBs, VMS – or combinations thereof) is consistent with the observations of GCs. Finally, the observed trends of increasing N/Fe and He spread with increasing cluster mass cannot be resolved within a self-enrichment framework, without further exacerbating the mass-budget problem.