All the recent observational data on quasars and AGNs, in combination with theoretical studies of their evolution and the accretion processes that produce both their luminosity and growth in mass, are now enabling new global studies of their history (e.g., Yu & Tremaine 2002; Yu 2003; Steed, Weinberg, & Miralda-Escudé, in preparation). The goal is to determine how an initial black hole mass function evolves into the one observed today in the local Universe by considering the continuity equation and how the the masses grow with accretion processes. The simple equation L = ( / Edd)M c2, where L is the luminosity produced by an accretion rate in Eddington units with efficiency for a black hole of mass M, tells us that if we could observationally determine L and along with black hole masses, for example, we would have enough information to model the evolution of the black holes in galaxies. Put another way, the general goal is to combine the black hole mass function, the time history of accretion, and the distribution of accretion rates and efficiencies to see if we can match the observed luminosity and mass functions for AGNs and black holes. One immediate problem at present is that we do not have a way of separately estimating and / Edd; typically people assume that is 0.1 or some range of values depending on the accretion models they adopt. Another problem is accounting properly for the number of obscured sources in flux-limited samples.
Nonetheless, there are enough existing data to permit interesting progress on the problem. For example, the combination of the black hole mass function for local galaxies and the X-ray background provide integral constraints that must be satisfied by any model. The mass function represents the end point of the accretion processes, while the X-ray background provides a measure of the integrated luminosity produced by accretion over the history of the Universe. The improved optical data on the quasar luminosity functions provide additional constraints on how and when this all occurred, because they map out the evolution of the emitted light with cosmic time. At the same time, the deep X-ray and radio surveys and related optical observations provide crucial information on the contribution of obscured sources to the accretion history of the Universe.
Yu & Tremaine (2002) find that the quasar luminosity functions and local black hole mass functions are consistent if 0.1 and the black hole mass growth occurred during the optically bright phase. The lifetime of luminous quasars would be of order 108 years. At the same time, there remain important questions about the accretion efficiency of lower luminosity quasars and AGNs and its dependence on accretion rate, for example.