Quasar evolution and the growth of black holes.

We present an attempt to relate the observed evolution of quasars to physical models of active galactic nuclei (AGN). Specifically, we suppose that a newly formed galaxy quickly grows or acquires a black hole which accretes at a rate that is ultimately limited by radiation pressure to a value close to the Eddington limit. Thereafter, black holes are presumed to accrete only intermittently at an average rate that is a universal function of black hole mass and time. We use simple limiting prescriptions for the AGN luminosity function to infer this function and to derive the current mass distribution of relict black holes in the nuclei of nearby galaxies. We deduce that the mean accretion rate <M> scales as M^-1.5^ t^-6.7^ and, for our most conservative model, that the number of relict black holes per decade declines only as M^-0.4^ for black hole masses in the range 3 X 10^7^<~M<~3 X 10^9^ M_sun_. If it is further supposed that all sufficiently massive galaxies pass through a quasar phase, with asymptotic black hole mass a monotonic function of the galaxy mass, then it is possible to compare the space density of galaxies with estimated central masses to that of distant quasars. Although there are too few galaxies with estimated central masses to draw any firm conclusions from this comparison, the very rough agreement that we find suggests that such a comparison could be useful in the future when more central masses are measured. Interpretations of other types of AGN are briefly discussed.