FROST-CLUSTERS – III. Metallicity-dependent intermediate-mass black hole formation by runaway collisions in dense star clusters

ABSTRACT We explore the formation of intermediate-mass black holes (IMBHs), potential seeds for supermassive black holes (SMBHs), via runaway stellar collisions for a wide range of star cluster (surface) densities ($4\times 10^3 \lesssim \Sigma _\mathrm{h} \lesssim 4\times 10^6 \, \mathrm{M_\odot \, pc^{-2}}$) and metallicities $(0.01 \lesssim Z \lesssim 1.0 \, \mathrm{Z_\odot })$. Our sample of isolated (>1400) and hierarchical (30) simulations of young, massive star clusters with up to $N=1.8\times 10^6$ stars includes collisional stellar dynamics, stellar evolution, and post-Newtonian equations of motion for black holes using the bifrost code. High stellar wind rates suppress IMBH formation at high metallicities ($Z \gtrsim 0.2 \, \mathrm{Z_\odot }$), and low collision rates prevent their formation at low densities ($\Sigma _\mathrm{h}\lesssim 3\times 10^4 \, \mathrm{M_\odot \, pc^{-2}}$). The assumptions about stellar wind loss rates strongly affect the maximum final IMBH masses ($M_\bullet \sim 6000 \, \mathrm{M_\odot }$ versus $M_\bullet \sim 25\,000 \, \mathrm{M_\odot }$). The total stellar mass loss from collisions and collisionally boosted winds before $t=3$ Myr can together reach up to 5–10 per cent of the final cluster mass. We present fitting formulae for IMBH masses as a function of host star cluster $\Sigma _\mathrm{h}$ and Z which can be used to seed SMBHs in high-resolution cosmological hydrodynamical simulations and in semi-analytic models for galaxy formation. Our results favour IMBH formation in dense low-metallicity environments similar to $z\sim 10$ JWST (James Webb Space Telescope) proto-globular clusters. IMBH formation is suppressed in the high-metallicity and low-density conditions of the local Universe.