A two-phase model of galaxy formation: I. The growth of galaxies and supermassive black holes

We develop a model for galaxy formation and the growth of supermassive black holes (SMBHs), based on the fact that cold dark matter haloes form their gravitational potential wells through a fast phase with rapid change in the potential, and that the high universal baryon fraction makes cooled gas in haloes self-gravitating and turbulent before it can form rotation-supported discs. Gas fragmentation produces subclouds so dense that cloud-cloud collision and drag on clouds are not significant, producing a dynamically hot system of subclouds that form stars and move ballistically to feed the central SMBH. Active galactic nucleus (AGN) and supernova feedback is effective only in the fast phase, and the cumulative effects are to regulate star formation and SMBH growth, as well as to reduce the amount of cold gas in haloes to allow the formation of globally stable discs. Using a set of halo assembly histories, we demonstrate that the model can reproduce a number of observations, including correlations among SMBH mass, stellar mass of galaxies and halo mass, the number densities of galaxies and SMBH, as well as their evolution over the cosmic time.