2002ApJ...566L..17M

Following the discovery of a black hole (BH) with a mass of 10³-10⁶ M_☉ in the starburst galaxy M82, we study the formation of such a BH via successive merging of stellar-mass BHs within a star cluster. The merging has a runaway characteristic. This is because massive BHs sink into the cluster core and have a high number density and because the merging probability is higher for more massive BHs. We use the Smoluchowski equation to study analytically the evolution of the BH mass distribution. Under favorable conditions, which are expected for some star clusters in starburst galaxies, the timescale of the runaway merging is on the order of at most 10⁷ yr. This is short enough to account for the presence of a BH heavier than 10³ M_☉ in an ongoing starburst region.