2001ApJ...547...90H

We have developed a consistent analytical model to describe the observed evolution of the quasar luminosity function. Our model combines black hole mass distributions based on the Press-Schechter theory of structure formation in the universe with quasar luminosity functions resulting from a physics-based emission model that takes into account the time-dependent phenomena occurring in the accretion disks. Quasar evolution and cold dark matter (CDM) models are mutually constraining; therefore, our model gives an estimation of the exponent, n, of the power spectrum, P(k), which is found to be -1.8≤n≤-1.6. We were able to reject a generally assumed hypothesis of a constant ratio between dark matter halo and black hole mass, since the observed data could not be fitted under this assumption. We found that the relation between the dark matter halos and black hole masses is better described by M_BH=M^0.668_DMH. This model provides a reasonable fit to the observed quasar luminosity function at redshifts higher than ∼2.0. We suggest that the disagreement at lower redshift is due to mergers. Based on the agreement at high redshift, we estimated the merger rate at lower redshift, and argue that this rate should depend on the redshift, as (1+z)³.