The Demographics of Broad Line Quasars in the Mass-Luminosity Plane II.
  Black Hole Mass and Eddington Ratio Functions
  We employ a flexible Bayesian technique to estimate the black hole mass and
Eddington ratio functions for Type 1 (i.e., broad line) quasars from a
uniformly-selected data set of ~58,000 quasars from the SDSS DR7. We find that
the SDSS becomes significantly incomplete at M_{BH} < 3 x 10^8 M_{Sun} or L /
L_{Edd} < 0.07, and that the number densities of Type 1 quasars continue to
increase down to these limits. Both the mass and Eddington ratio functions show
evidence of downsizing, with the most massive and highest Eddington ratio black
holes experiencing Type 1 quasar phases first, although the Eddington ratio
number densities are flat at z < 2. We estimate the maximum Eddington ratio of
Type 1 quasars in the observable Universe to be L / L_{Edd} ~ 3. Consistent
with our results in Paper I, we do not find statistical evidence for a
so-called "sub-Eddington boundary" in the mass-luminosity plane of broad line
quasars, and demonstrate that such an apparent boundary in the observed
distribution can be caused by selection effect and errors in virial BH mass
estimates. Based on the typical Eddington ratio in a given mass bin, we
estimate typical growth times for the black holes in Type 1 quasars and find
that they are typically comparable to or longer than the age of the universe,
implying an earlier phase of accelerated (i.e., with higher Eddington ratios)
and possibly obscured growth. The large masses probed by our sample imply that
most of our black holes reside in what are locally early type galaxies, and we
interpret our results within the context of models of self-regulated black hole
growth.
