We present high-quality fluid dynamical simulations of isothermal gas flows in a rotating barred potential. We show that a large quantity of gas is driven right into the nucleus of a model galaxy when the potential lacks a central mass concentration, but the inflow stalls at a nuclear ring in comparison simulations that include a central massive object. The radius of the nuclear gas ring increases linearly with the mass of the central object. We argue that bars drive gas right into the nucleus in the early stages of disk galaxy formation, where a nuclear star cluster and perhaps a massive black hole could be created. The process is self-limiting, however, because inflow stalls at a nuclear ring once the mass of gas and stars in the nucleus exceeds ~1% of the disk mass, which shuts off rapid growth of the black hole. We briefly discuss the relevance of these results to the seeding of massive black holes in galaxies, the merger model for quasar evolution, and the existence of massive black holes in disk galaxies that lack a significant classical bulge.
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