The Demographics of Broad-Line Quasars in the Mass-Luminosity Plane. I.
  Testing FWHM-Based Virial Black Hole Masses
  We jointly constrain the luminosity function (LF) and black hole mass
function (BHMF) of broad-line quasars with forward Bayesian modeling in the
quasar mass-luminosity plane, based on a homogeneous sample of ~ 58,000 SDSS
DR7 quasars at z ~ 0.3-5. We take into account the selection effect of the
sample flux limit; more importantly, we deal with the statistical scatter
between true BH masses and FWHM-based single-epoch virial mass estimates, as
well as potential luminosity-dependent biases of these mass estimates. The LF
is tightly constrained in the regime sampled by SDSS, and makes reasonable
predictions when extrapolated to ~ 3 magnitudes fainter. Downsizing is seen in
the model LF. On the other hand, we find it difficult to constrain the BHMF to
within a factor of a few at z>~0.7 (with MgII and CIV-based virial BH masses).
This is mainly driven by the unknown luminosity-dependent bias of these mass
estimators and its degeneracy with other model parameters, and secondly driven
by the fact that SDSS quasars only sample the tip of the active BH population
at high redshift. Nevertheless, the most likely models favor a positive
luminosity-dependent bias for MgII and possibly for CIV, such that at fixed
true BH mass, objects with higher-than-average luminosities have over-estimated
FWHM-based virial masses. There is tentative evidence that downsizing also
manifests itself in the active BHMF, and the BH mass density in broad-line
quasars contributes an insignificant amount to the total BH mass density at all
times. Within our model uncertainties, we do not find a strong BH mass
dependence of the mean Eddington ratio; but there is evidence that the mean
Eddington ratio (at fixed BH mass) increases with redshift.
