tokens: F336W, F438W) = 0.0 and Δ(F275W−F814W) = 0.0 in the chromosome maps. The results are plotted in the two panels of Fig. 2 . We display on the horizontal axis the different chemical compositions investigated. The vertical axis displays the indices ΔC(F275W, F336W, F438W) and Δ(F275W−F814W) for all our synthetic populations. The results are quite clear. The index Δ(F275W−F814W) is affected essentially only by variations in Y; instead, the ΔC(F275W, F336W, F438W) index is in comparison weakly sensitive to Y, but is mainly affected by variations in N (e.g. Piotto et al. 2015). The range of Δ(F275W−F814W) values for P1 stars observed in several clusters like M 3 and NGC 2808 discussed here is therefore due to a range of Y abundances. This is however not found in other clusters, for example NGC 288. The extended P1 sequences in the chromosome maps also display a tilt towards increasing ΔC(F275W, F336W, F438W) for decreasing Δ(F275W−F814W) (e.g. Milone et al. 2017 ). Based on Fig. 2 , this can possibly be explained by a narrow range of N amongst P1 stars. We conclude that the spread in P1 stars indicates that a relatively wide spread of Y is present within this population, possibly accompanied by a narrow range in N. Fig. 2. Expected chromosome map indices of RGB stars with P1 chemical composition (squares), P1 with He enhanced by ΔY = 0.05 (triangles up), P1 with He enhanced by ΔY = 0.15 (triangles down), P2 extreme (crossed squares), P2 extreme with ΔY = 0.05 (stars), and P2 moderate with ΔY = 0.05 (crossed circle); see text for details. In summary, P1 stars are defined by their location on the chromosome maps, which is consistent with the position of stars with homogeneous and field-like [O/Fe] and [Na/Fe] measurements in the clusters like M 4 and NGC 2808 investigated here. These P1 stars are often called first-generation stars in the literature, according to the proposed cluster self-enrichment scenarios. We have shown here that P1 stars in clusters with extended P1 in their chromosome maps, such as NGC 2808 and M 3, show a spread of initial Y and a small range of N. In other cases, like NGC 288 with a non-extended P1 in the chromosome map, the Y and N abundances are also homogeneous, like O and Na. The former behaviour is entirely unexpected in the context of all scenarios for the origin of MPs. 3.2. Distribution of the subpopulations along the RGB An independent test for He-abundance variations among P1 stars is to look at the optical colour distributions of each of the identified subpopulations. Bolometric corrections in optical filters are negligibly affected when moving from typical P1 to P2 metal distributions (e.g. Sbordone et al. 2011 ), but an increase in Y shifts the RGB towards bluer colours because isochrones with enhanced He have hotter T eff values. For each cluster, we first identified different RGB subpop-ulations from the chromosome maps in Fig. 1 . The mean values of the ΔC(F275W, F336W, F438W) and Δ(F275W−F814W)
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