  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.
