Accretion disk instabilities, cold dark matter models, and their role in quasar evolution

We have developed a consistent analytical model to describe the observed ev olution of the quasar luminosity function. Our model combines black hole ma ss 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 o ccurring in the accretion disks. Quasar evolution and cold dark matter (CDM ) models are mutually constraining; therefore, our model gives an estimatio n of the exponent, n, of the power spectrum, P(k), which is found to be -1. 8 less than or equal to n less than or equal to -1.6. We were able to rejec t a generally assumed hypothesis of a constant ratio between dark matter ha lo and black hole mass, since the observed data could not be fitted under t his assumption. We found that the relation between the dark matter halos an d black hole masses is better described by This model provides a reasonable fit to the observed quasar luminosity function at M-BH = M-DMH(0.668). red shifts higher than similar to2.0. We suggest that the disagreement at lower redshift is due to mergers. Based on the agreement at high redshift, we es timated the merger rate at lower redshift, and argue that this rate should depend on the redshift, as (1+z)(3).