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_⊙ by performing three-dimensional radiative-hydrodynamic simulations. Considering the uncertainty of the initial mass function (IMF) of stars formed in low-metallicity and high-density clouds, we investigate the impacts of the IMF on the cloud condition for the GC formation with the range of the power-law index of IMF as γ = 1-2.35. We find that the threshold surface density (Σ_thr) for the GC formation increases from 800 M_⊙ pc^-2 at γ = 2.35 to 1600 M_⊙ pc^-2 at γ = 1.5 in the cases of clouds with M_cl = 10⁶ M_⊙ because the emissivity of ionizing photons per stellar mass increases as γ decreases. For γ < 1.5, Σ_thr saturates with ~2000 M_⊙ pc^-2 that is quite rare and observed only in local starburst galaxies due to e.g. merger processes. Thus, we suggest that formation sites of low-metallicity GCs could be limited only in the very high-surface density regions. We also find that Σ_thr can be modelled by a power-law function with the cloud mass (M_cl) and the emissivity of ionizing photons (s_*) as $\propto M_{\rm cl}^{-1/5} s_{*}^{2/5}$. 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.