Massive black hole assembly in nuclear star clusters

Nuclear star clusters, which fragment into metal-poor stars in situ at the centers of protogalaxies, provide ideal environments for the formation of intermediate-mass black holes with masses ${10}^3-{10}^6{M}_{\odot }$. We utilize the semianalytic model implemented in Rapster, a public rapid cluster evolution code. We implement simple recipes for stellar collisions and gas accretion/expulsion into the code and identify the regimes where each channel contributes to the dynamical formation of intermediate-mass black holes via repeated mergers of stellar black hole seeds. We find that intermediate-mass black hole formation in gas-rich environments is almost inevitable if the initial mean density of the nuclear cluster is $>{10}^8{M}_{\odot }{\mathrm{p}\mathrm{c}}^{-3}$. A million solar mass black hole can form within 100~Myr in the heaviest ($>{10}^7{M}_{\odot }$) and most compact ($<0.5\mathrm{p}\mathrm{c}$) nuclear clusters. We demonstrate that by today these resemble the observed range of nuclear clusters in dwarf galaxies and that there are potential gravitational-wave signatures of the massive black hole formation process.