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

Hajime Fukushima; Hidenobu Yajima

doi:10.1093/mnras/stad1956

paper

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

arXiv:2303.12405 · doi:10.1093/mnras/stad1956

Abstract

We study the formation of globular clusters in massive compact clouds with the low-metallicity of $Z = 1 0^{- 3} Z_{⊙}$ 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 $γ = 1 - 2.35$ . We find that the threshold surface density ( $Σ_{thr}$ ) for the GC formation increases from $800 M_{⊙} p c^{- 2}$ at $γ = 2.35$ to $1600 M_{⊙} p c^{- 2}$ at $γ = 1.5$ in the cases of clouds with $M_{cl} = 1 0^{6} M_{⊙}$ because the emissivity of ionizing photons per stellar mass increases as $γ$ decreases. For $γ < 1.5$ , $Σ_{thr}$ saturates with $\sim 2000 M_{⊙} p c^{- 2}$ 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 $Σ_{thr}$ can be modelled by a power-law function with the cloud mass ( $M_{cl}$ ) and the emissivity of ionizing photons ( $s_{*}$ ) as $\propto M_{cl}^{- 1/5} s_{*}^{2/5}$ . Based on the relation between the power-law slope of IMF and $Σ_{thr}$ , future observations with e.g., the James Webb Space Telescope can allow us to constrain the IMF of GCs.

arXiv comment9 pages, 6 figures, accepted for publication in MNRAS

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