Supermassive Black Holes in the Hierarchical Universe: A General
  Framework and Observational Tests
  (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 (L_bol>~10^46 erg
s^-1) to low luminosity AGNs (L_bol<~ 10^45 erg s^-1), in good agreement with
observations.
