We discuss a possible physical connection between helium-rich ( Y \geq 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 \sim 0.1 for M _ { thres } = 10 ^ { 7 } { M } _ { \odot } . 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 .