On the maximum helium content of multiple populations in the globular
  cluster NGC6752
  Multiple populations in globular clusters are usually explained by the
formation of stars out of material with a chemical composition that is polluted
to different degrees by the ejecta of short-lived, massive stars of various
type. Among other things, these polluters differ by the amount of helium they
spread in the surrounding medium. In this study we investigate whether the
present-day photometric method used to infer the helium content of multiple
populations indeed gives the true value or underestimates it by missing very
He-rich, but rare stars. We focus on the specific case of NGC6752. We compute
atmosphere models and synthetic spectra along isochrones produced for this
cluster for a very broad range of He abundances covering the predictions of
different pollution scenarios, including the extreme case of the fast-rotating
massive star (FRMS) scenario. We calculate synthetic photometry in HST filters
best suited to study the helium content. We subsequently build synthetic
clusters with various distributions of stars. We finally determine the maximum
helium mass fraction of these synthetic clusters using a method similar to that
applied to observational data. We build toy models of clusters with various
distributions of multiple populations and ensure that we are able to recover
the input maximum Y. We then build synthetic clusters with the populations
predicted by the FRMS scenario and find that while we slightly underestimate
the maximum Y value, we are still able to detect stars much more He-rich than
the current observed maximum Y. It is easier to determine the maximum Y on main
sequence stars than on red giant branch stars, but qualitatively the results
are unaffected by the sample choice. We show that in NGC6752 it is unlikely
that stars more He-rich than the current observational limit of about 0.3 are
present.
