# Formation of Intermediate-Mass Black Holes through Runaway Collisions in the First Star Clusters

## TL;DR

This study investigates how runaway stellar collisions in early dense star clusters can lead to the formation of intermediate-mass black holes, linking early universe conditions to present-day black hole observations.

## Contribution

It demonstrates that runaway stellar collisions in first star clusters can produce IMBHs with masses up to 1900 solar masses, influenced by host halo properties.

## Key findings

- Runaway collisions occur within a few million years in most models.
- Central massive stars reach 400-1900 solar masses.
- IMBH mass to cluster mass ratios are comparable to observed black hole-bulge ratios.

## Abstract

We study the formation of massive black holes in the first star clusters. We first locate star-forming gas clouds in proto-galactic haloes of $\gtrsim \!10^7\,{\rm M}_{\odot}$ in cosmological hydrodynamics simulations and use them to generate the initial conditions for star clusters with masses of $\sim \!10^5\,{\rm M}_{\odot}$. We then perform a series of direct-tree hybrid $N$-body simulations to follow runaway stellar collisions in the dense star clusters. In all the cluster models except one, runaway collisions occur within a few million years, and the mass of the central, most massive star reaches $\sim \!400-1900\,{\rm M}_{\odot}$. Such very massive stars collapse to leave intermediate-mass black holes (IMBHs). The diversity of the final masses may be attributed to the differences in a few basic properties of the host haloes such as mass, central gas velocity dispersion, and mean gas density of the central core. Finally, we derive the IMBH mass to cluster mass ratios, and compare them with the observed black hole to bulge mass ratios in the present-day Universe.