Supermassive black holes in the hierarchical universe: A general framework and observational tests

We present a simple framework for the growth and evolution of supermassive black holes (SMBHs) in the hierarchical structure formation paradigm, adopting the general idea that quasar activity is triggered in major mergers. In our model, black hole accretion is triggered during major mergers (mass ratio ≳0.3) of host dark matter halos. The successive evolution of quasar luminosities follows a universal light-curve (LC) form during which the growth of the SMBH is modeled self-consistently: an initial exponential growth at a 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 LC 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. At z < 0.5, our model underestimates the LF at L _bol < 10⁴⁵ erg s ^-1, allowing room for the active galactic nuclei (AGNs) activity triggered by secular processes instead of major mergers. At z > 4.5, in order to reproduce the observed quasar abundance, the typical quasar hosts must shift to lower mass halos, and/or minor mergers can also trigger quasar activity. 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 lognormal, which broadens and shifts to lower mean values from high luminosity quasars (L _bol ≳ 10⁴⁶ erg s^-1) to low-luminosity AGNs (L _bol ≲ 10⁴⁵ erg s^-1), in good agreement with observations. The model predicts that the vast majority of ≳10 ^8.5 M SMBHs were already in place by z = 1, and ≲50% of them were in place by z = 2; but the less massive (≲10⁷ M) SMBHs were assembled more recently, likely more through secular processes than by major mergers - in accordance with the downsizing picture of SMBH assembly since the peak of bright quasar activity around z 2-3.