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Intermediate-mass black hole incubators. Gas accretion onto stellar black hole clusters in galactic central molecular zones

The stellar dynamical evolution of massive star clusters formed during starburst periods leads to the segregation of $\gtrsim10^4 M_\odot$ stellar-mass black hole sub-clusters in their centres. In gas-rich environments, such as galactic central molecular zones, these black hole clusters are likely to accrete large amounts of the gas from their surroundings, which in turn affects their internal dynamics. In this Letter we estimated the corresponding accretion rate onto the black hole cluster and its radiative feedback. We assessed whether such an accretion flow can lead to the collapse of the black hole cluster into an intermediate-mass black hole. The estimates were obtained analytically, considering the astrophysical conditions and star formation history reported for the central molecular zone of our Galaxy. We find that a stellar black hole cluster with mass $\gtrsim10^4 M_\odot$ located in the twisted ring of molecular clouds with radius $\approx100$ pc that is observed in the central molecular zone of our Galaxy can accrete about the same mass in gas on a timescale of a few million years. We suggest that this is sufficient for its subsequent collapse into an intermediate-mass black hole. Based on an estimate of the dynamical friction inspiral time, we further argue that the locations of the intermediate-mass black hole candidates recently observed in the central molecular zone are compatible with their formation therein during the last starburst period reported to have occurred $\approx1$ Gyr ago.