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A possible physical connection between helium-rich stellar populations of massive globular clusters and the UV upturn of galactic spheroids

We discuss a possible physical connection between helium-rich (Y > 0.35) stellar populations of massive globular clusters (GCs) and the ultraviolet (UV) upturn of galactic spheroids by using analytical and numerical models. In our model, all stars are initially formed as bound or unbound star clusters (SCs) formed from giant molecular clouds (GMCs) and the SCs can finally become GCs, open clusters, and field stars depending on physical properties of their host GMCs. An essential ingredient of the model is that helium-rich stars are formed almost purely from gas ejected from massive asymptotic giant branch (AGB) stars. The helium-rich star formation is assumed to occur within massive SCs if the masses of the progenitor GMCs are larger than a threshold mass (M_thres). These massive SCs can finally become either massive GCs or helium-rich field stars depending on whether they are disintegrated or not. Using this model, we show that if the initial mass functions (IMFs) in galactic spheroids are mildly top-heavy, then the mass fractions of helium-rich main-sequence stars (F_He) can be as large as ~ 0.1 for M_thres=10^7 M_sun. F_He is found to depend on IMFs and M_thres such that it can be larger for shallower IMFs and smaller M_thres. The inner regions of galactic spheroids show larger F_He in almost all models. Based on these results, we suggest that if the UV upturn of elliptical galaxies is due to the larger fractions of helium-rich stars, then the origin can be closely associated with top-heavy IMFs in the galaxies.