Major mergers of haloes, the growth of massive black holes and the evolving luminosity function of quasars

We construct a physically motivated analytical model for the quasar luminosity function, based on the joint star formation and feeding of massive black holes suggested by the observed correlation between the black hole mass and the stellar mass of the hosting spheroids. The parallel growth of massive black holes and host galaxies is assumed to be triggered by major mergers of haloes. The halo major merger rate is computed within the framework of the extended Press-Schechter model. The evolution of black holes on cosmological time-scales is achieved by the integration of the governing set of differential equations, established from a few reasonable assumptions that account for the distinct (Eddington-limited or supply-limited) accretion regimes. Finally, the typical light curves of the reactivated quasars are obtained under the assumption that, in such accretion episodes, the fall of matter on to the black hole is achieved in a self-regulated stationary way. The predicted quasar luminosity function is compared with the luminosity functions of the 2dF quasi-stellar object sample and other, higher-redshift data. We find good agreement in all cases, except for z < 1 where the basic assumption of our model is likely to break down.