Supermassive Black Holes in the Hierarchical Universe: A General Framework and Observational Tests
Abstract
(Abridged) We present a simple framework for the growth and evolution of supermassive black holes (SMBHs) in the hierarchical structure formation paradigm. In our model, black hole accretion is triggered during major mergers (mass ratio>~0.3) between host dark matter halos. The successive evolution of quasar luminosities follows a universal light curve form: an initial exponential growth at constant Eddington ratio of order unity until it reaches the peak luminosity, followed by a power-law decay. Assuming that the peak luminosity correlates with the post-merger halo mass, we convolve the light curve with the triggering rate of quasar activity to predict the quasar luminosity function (LF). Our model reproduces the observed LF at 0.5<z<4.5 for the full luminosity ranges probed by current optical and X-ray surveys. Our model reproduces both the observed redshift evolution and luminosity dependence of the linear bias of quasar/AGN clustering. Due to the scatter between instantaneous luminosity and halo mass, quasar/AGN clustering weakly depends on luminosity at low to intermediate luminosities; but the linear bias rises rapidly with luminosity at the high luminosity end and at high redshift. In our model, the Eddington ratio distribution is roughly log-normal, which broadens and shifts to lower mean values from high luminosity quasars (Lbol>~1046 erg s-1) to low luminosity AGNs (Lbol<~ 1045 erg s-1), in good agreement with observations.