Maximum helium content of multiple populations in the globular cluster NGC 6752

Context. 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. But the nature of the "polluters" remains elusive. Different types of stars have been proposed to account for the observed chemical patterns of multiple populations. Among other things, these differ by the amount of helium they spread in the surrounding medium.Aims. 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. This check is important to discriminate between the different polluter scenarios. We focus on the specific case of NGC 6752.Methods. 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 the different scenarios, including the extreme case of the fast-rotating massive star (FRMS) scenario. We use the same abundances in isochrones and atmosphere models to ensure consistency. 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. In particular, we select nonpolluted and very He-rich stars from the so-called chromosome map.Results. We re-determine the maximum helium mass fraction Y in NGC 6752, and find a value consistent with published results. 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. This result still holds even in synthetic clusters that contain less He-rich stars than predicted by the FRMS scenario. 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.Conclusions. We show that in NGC 6752 it is unlikely that stars more He-rich than the current observational limit of about 0.3 (in mass fraction) are present.