Tracing the growth of the supermassive black holes with halo mergers

The formation mechanism of supermassive black holes (SMBHs) at the center of galaxies remains an open fundamental question. Black holes (BHs) are believed to grow by accretion of gas or by merging with other BHs. Motivated by the observation of luminous quasar around redshift z ~ 7 with SMBH mass up to 109 solar mass, we follow the growth of the early assembly of SMBHs that trace the hierarchical evolution of dark matter halos derived from large cosmological simulations. The initial masses of BH seeds in the first halos were set up according to the BH mass - halo mass relation. We assume that mergers of host galaxies cause loss of angular momentum of gas and trigger episodes of gas accretion onto BHs for available durations and at the end of each episode of accretion, BHs merge immediately. We trace the evolution of BH masses for various scenarios for central gas properties in halos. We estimate the BH to halo mass ratio and BH mass function at each redshift.