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We study the stellar dynamics of the first star clusters afterintermediate-mass black holes (IMBHs) are formed via runaway stellarcollisions. 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 thecentral IMBH occasionally, causing tidal disruption events (TDEs). We find thatthe TDE rate scales with the IMBH mass as $\dot{N}_{\rm TDE}\sim0.3\,{\rmMyr}^{-1}(M_{\rm IMBH}/1000\,{\rm M}_{\odot})^2$. The DM component affects thestar cluster evolution by stripping stars from the outer part. When the DMdensity within the cluster increases, the velocity dispersion of the starsincreases, and then the TDE rate decreases. By the TDEs, the central IMBHs growto as massive as $700-2500\,{\rm M}_{\odot}$ in 15 million years. The IMBHs arepossible seeds for the formation of supermassive BHs observed at $z\gtrsim6-7$, if a large amount of gas is supplied through galaxy mergers and/orlarge-scale gas accretion, or they might remain as IMBHs from the early epochsto the present-day Universe.

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