A simple black hole model of quasar abundance and evolution in the infinitely long cosmic-string scheme

The formation and evolution of quasars are investigated in relation to the infinitely long cosmic-string scheme. Using the mass function of high-density sites of cold dark matter in the cosmic-string model a simple black hole model for the evolution of quasar abundance and luminosity function is developed by assuming an appropriate gas accretion rate into the central black holes. To compare with the observations, we apply statistical methods, assuming a Gaussian distribution, to the formation epoch of quasar host galaxies z(G), to the mass fraction F of host-galaxy-fueling central black holes, and to the radiative efficiency epsilon, respectively. There is a time lag between the formation of host galaxies and the birth of high-redshift quasars. The simulated results with reasonable parameter values are in good agreement with the observed evolution of quasar abundance and luminosity function. It is necessary to have enough nonlinear regions for host galaxies at around z similar or equal to 7 to adequately reproduce the observations.