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, focussing 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, focussing
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 over-produce 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.
