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

Abstract

We study the formation of globular clusters in massive compact clouds with the low-metallicity of $Z=10^{-3}{Z}_{\odot }$ by performing three-dimensional radiative-hydrodynamics 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 $\gamma =1-2.35$. We find that the threshold surface density (${\Sigma }_{\mathrm{thr}}$) for the GC formation increases from $800M_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$ at $\gamma =2.35$ to $1600M_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$ at $\gamma =1.5$ in the cases of clouds with $M_{\mathrm{cl}}=10^6{M}_{\odot }$ because the emissivity of ionizing photons per stellar mass increases as $\gamma$ decreases. For $\gamma <1.5$, ${\Sigma }_{\mathrm{thr}}$ saturates with $\sim 2000M_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$ 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 ${\Sigma }_{\mathrm{thr}}$ can be modelled by a power-law function with the cloud mass ($M_{\mathrm{cl}}$) and the emissivity of ionizing photons ($s_{\ast }$) as $\propto M_{\mathrm{cl}}^{-1/5}{s}_{\ast }^{2/5}$. Based on the relation between the power-law slope of IMF and ${\Sigma }_{\mathrm{thr}}$, future observations with e.g., the James Webb Space Telescope can allow us to constrain the IMF of GCs.

9 pages, 6 figures, accepted for publication in MNRAS

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