The formation of globular clusters with top-heavy initial mass functions
We study the formation of globular clusters (GCs) in massive compact clouds with the low metallicity of Z = 10-3 Z⊙byperformingthree-dimensionalradiative- hydrodynamicsimulations.Consideringtheuncertaintyoftheinitialmassfunction(IMF)ofstarsformedinlow- metallicityandhigh-densityclouds,weinvestigatetheimpactsoftheIMFonthecloudconditionfortheGCformationwiththerangeofthepower- lawindexofIMFasγ = 1-2.35. We find that the threshold surface density (Σthr) for the GC formation increases from 800 M⊙pc^-2atγ = 2.35 to 1600 M⊙pc^-2atγ = 1.5 in the cases of clouds with Mcl = 106 M⊙becausetheemissivityofionizingphotonsperstellarmassincreasesasγ decreases. For γ < 1.5, Σthr saturates with ~ 2000 M⊙pc^-2thatisquiterareandobservedonlyinlocalstarburstgalaxiesduetoe.g.mergerprocesses.Thus,wesuggestthatformationsitesoflow- metallicityGCscouldbelimitedonlyintheveryhigh-surfacedensityregions.WealsofindthatΣthr can be modelled by a power-law function with the cloud mass (Mcl) and the emissivity of ionizing photons (s*) as ∝ Mcl-1∕5s*2∕5. Based on the relation between the power-law slope of IMF and Σthr, future observations with e.g. the JWST can allow us to constrain the IMF of GCs.