Growth of intermediate mass black holes by tidal disruption events in the first star clusters

We study the stellar dynamics of the first star clusters after intermediate-mass black holes (IMBHs) are formed via runaway stellar collisions. We use the outputs of cosmological simulations of Sakurai et al. (2017) to follow the star cluster evolution in a live dark matter (DM) halo. Mass segregation within a cluster promotes massive stars to be captured by the central IMBH occasionally, causing tidal disruption events (TDEs). We find that the TDE rate scales with the IMBH mass as $\dot{N}_{\rm TDE} \sim 0.3\,{\rm Myr}^{-1}(M_{\rm IMBH}/1000\,{\rm M}_\odot)^2$. The DM component affects the star cluster evolution by stripping stars from the outer part. When the DM density within the cluster increases, the velocity dispersion of the stars increases, and then the TDE rate decreases. By the TDEs, the central IMBHs grow to as massive as $700-2500\,{\rm M}_\odot$ in 15 million years. The IMBHs are possible seeds for the formation of supermassive BHs observed at $z \gtrsim 6-7$, if a large amount of gas is supplied through galaxy mergers and/or large-scale gas accretion, or they might remain as IMBHs from the early epochs to the present-day Universe.