Context. Globular clusters host multiple populations of long-lived low-mass stars whose origin remains an open question. Several scenarios have been proposed to explain the associated photometric and spectroscopic peculiarities. They differ, for instance, in the maximum helium enrichment they predict for stars of the second population, which these stars can inherit at birth as the result of the internal pollution of the cluster by different types of stars of the first population. Aims. We present the distribution of helium-rich stars in present-day globular clusters as it is expected in the original framework of the fast-rotating massive stars scenario (FRMS) as first-population polluters. We focus on NGC 6752. Methods. We completed a grid of 330 stellar evolution models for globular cluster low-mass stars computed with different initial chemical compositions corresponding to the predictions of the original FRMS scenario for [Fe/H] = −1.75. Starting from the initial helium-sodium relation that allows reproducing the currently observed distribution of sodium in NGC 6752, we deduce the helium distribution expected in that cluster at ages equal to 9 and 13 Gyr. We distinguish the stars that are moderately enriched in helium from those that are very helium-rich (initial helium mass fraction below and above 0.4, respectively), and compare the predictions of the FRMS framework with other scenarios for globular cluster enrichment. Results. The effect of helium enrichment on the stellar lifetime and evolution reduces the total number of very helium-rich stars that remain in the cluster at 9 and 13 Gyr to only 12% and 10%, respectively, from an initial fraction of 21%. Within this age range, most of the stars still burn their hydrogen in their core, which widens the MS band significantly in effective temperature. The fraction of very helium-rich stars drops in the more advanced evolution phases, where the associated spread in effective temperature strongly decreases. These stars even disappear from the horizontal branch and the asymptotic giant branch at 13 Gyr. Conclusions. The helium constraint is no suitable criterion for clearly distinguishing between the scenarios for GC self-enrichment because only few very helium-rich stars are predicted in the investigated framework and because it is difficult to derive the helium content of GC stars observationally. However, the helium constraint indicates some difficulties of the original FRMS scenario that require the exploration of alternatives.

In our HST photometric survey, we have been searching for multiple stellar populations (MPs) in Magellanic Clouds (MCs) massive star clusters which span a significant range of ages (∼ 1.5 − 11 Gyr). In the previous papers of the series, we have shown that the age of the cluster represents one of the key factors in shaping the origin of the chemical anomalies. Here we present the analysis of four additional clusters in the MCs, namely Lindsay 38, Lindsay 113, NGC 2121 and NGC 2155, for which we recently obtained new UV HST observations. These clusters are more massive than ∼ 10 4 M and have ages between ∼ 2.5 − 6 Gyr, i.e. located in a previously unexplored region of the cluster age/mass diagram. We found chemical anomalies, in the form of N spreads, in three out of four clusters in the sample, namely in NGC 2121, NGC 2155 and Lindsay 113. By combining data from our survey and HST photometry for 3 additional clusters in the Milky Way (namely 47 Tuc, M15 and NGC 2419), we show that the extent of the MPs in the form of N spread is a strong function of age, with older clusters having larger N spreads with respect to the younger ones. Hence, we confirm that cluster age plays a significant role in the onset of MPs.

Context. Our understanding of the formation and early evolution of globular clusters (GCs) has been totally overthrown with the discovery of the peculiar chemical properties of their long-lived host stars. Aims. As a consequence, the interpretation of the observed color-magnitude diagrams and of the properties of the GC stellar populations requires the use of stellar models computed with relevant chemical compositions.Methods. We present a grid of 224 stellar evolution models for low-mass stars with initial masses between 0.3 and 1.0 M and initial helium mass fraction between 0.248 and 0.8 computed for [Fe/H] = -1.75 with the stellar evolution code STAREVOL. This grid is made available to the community. Results. We explore the implications of the assumed initial chemical distribution for the main properties of the stellar models: evolution paths in the Hertzsprung-Russel diagram (HRD), duration and characteristics of the main evolutionary phases, and the chemical nature of the white dwarf remnants. We also provide the ranges in initial stellar mass and helium content of the stars that populate the different regions of the HRD at the ages of 10 and 13.4 Gyr, which are typical for Galactic GCs.

Context. Globular clusters host multiple stellar populations showing different sodium enrichments. These various populations can be observed along the main sequence, red giant and horizontal branch phases. Recently it was shown, however, that at least in the globular cluster NGC 6752, no sodium-rich stars are observed along the early asymptotic giant branch (AGB), posing an apparent problem for stellar evolution. Aims. We present an explanation for this lack of sodium-rich stars in this region of the colour-magnitude diagram. Methods. We computed models for low-mass stars following the prediction of the so-called fast rotating massive stars model for the initial composition of second-generation stars. We studied the impact of different initial helium contents on the stellar lifetimes and the evolutionary path in the Hertzsprung-Russell diagram. Results. We propose that the lack of sodium-rich stars along the early-AGB arises because sodium-rich stars were born with a high initial helium abundance, as predicted by the fast rotating massive stars scenario. Helium-rich stars have much shorter lifetimes for a given initial mass than stars with a normal helium abundance, and above a cutoff initial helium abundance that slightly depends on the mass-loss rate on the RGB they do not go through the AGB phase and evolve directly into a white dwarf stage. Within the fast rotating massive stars framework we obtained a cutoff in [Na/Fe] between the second-generation models evolving into the AGB phase and those skipping that phase between 0.18 and 0.4 dex, depending on the mass loss rate used during the red giant phase. In view of the uncertainties in abundance determinations, the cutoff obtained by the present model agrees well with the one inferred from recent observations of the cluster NGC 6752. Conclusions. The helium-sodium correlation needed to explain the lack of sodium-rich stars along the early-AGB of NGC 6752 corresponds to the one predicted by the fast rotating massive stars models. A crucial additional test of the model is the distribution of stars with various helium abundances among main-sequence stars. Our model predicts that two magnitudes below the turnoff a very large percentage of stars, about 82%, probably has a helium content lower than 0.275 in mass fraction, while only 5% of stars are expected to have helium abundances greater than 0.4.

Context. Several models compete to explain the abundance properties of stellar populations in globular clusters. One of the main constraints is the present-day ratio of first-and second-generation stars that are currently identified based on their sodium content. Aims. We propose an alternative interpretation of the observed sodium distribution, and suggest that stars with low sodium abundance that are counted as members of the first stellar generation could actually be second-generation stars. Methods. We compute the number ratio of second-generation stars along the Na distribution following the fast rotating massive star model using the same constraints from the well-documented case of NGC 6752 as in our previous developments. Results. We reproduce the typical percentage of low-sodium stars usually classified as first-generation stars by invoking only secondary star formation from material ejected by massive stars and mixed with original globular cluster material in proportions that account for the Li-Na anti-correlation in this cluster. Conclusions. Globular clusters could be totally devoid of first-generation low-mass stars today. This can be tested with the determination of the carbon isotopic ratio and nitrogen abundance in turn-off globular cluster stars. Consequences and related issues are briefly discussed.