A simple model for the evolution of super-massive black holes and the   quasar population
  An empirically motivated model is presented for accretion-dominated growth of the super massive black holes (SMBH) in galaxies, and the implications are studied for the evolution of the quasar population in the universe. We investigate the core aspects of the quasar population, including space density evolution, evolution of the characteristic luminosity, plausible minimum masses of quasars, the mass function of SMBH and their formation epoch distribution. Our model suggests that the characteristic luminosity in the quasar luminosity function arises primarily as a consequence of a characteristic mass scale above which there is a systematic separation between the black hole and the halo merging rates. At lower mass scales, black hole merging closely tracks the merging of dark halos. When combined with a declining efficiency of black hole formation with redshift, the model can reproduce the quasar luminosity function over a wide range of redshifts. The observed space density evolution of quasars is well described by formation rates of SMBH above $\sim 10^8 M_\odot$. The inferred mass density of SMBH agrees with that found independently from estimates of the SMBH mass function derived empirically from the quasar luminosity function. 
Asim Mahmood, Julien E. G. Devriendt and Joseph Silk