The formation of globular clusters with top-heavy initial mass functions

Fukushima, Hajime,   & Yajima, Hidenobu

Abstract

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 (Σ_thr) 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 M_cl = 10⁶ M_⊙becausetheemissivityofionizingphotonsperstellarmassincreasesasγ decreases. For γ < 1.5, Σ_thr saturates with ~ 2000 M_⊙pc^-2thatisquiterareandobservedonlyinlocalstarburstgalaxiesduetoe.g.mergerprocesses.Thus,wesuggestthatformationsitesoflow- metallicityGCscouldbelimitedonlyintheveryhigh-surfacedensityregions.WealsofindthatΣ_thr can be modelled by a power-law function with the cloud mass (M_cl) and the emissivity of ionizing photons (s_*) as ∝ M_cl^-1∕5s_*^2∕5. Based on the relation between the power-law slope of IMF and Σ_thr, future observations with e.g. the JWST can allow us to constrain the IMF of GCs.