The Demographics Of Broad-line Quasars In The Mass-luminosity Plane

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We jointly constrain the luminosity function (LF) and black hole mass function (BHMF) of broad-line quasars using a Bayesian approach that describes the underlying active BHMF and Eddington ratio distribution to match the observed distributions in the quasar mass-luminosity plane, based on ˜58,000 uniformly selected quasars from the SDSS DR 7 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 quasars, and makes reasonable predictions when extrapolated to ˜3 magnitudes fainter than the SDSS flux limit. 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 (when the virial mass estimator switches from Hbeta to MgII and CIV). This is mainly driven by the unknown luminosity-dependent bias of these virial 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. 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. The luminosity-dependent bias and the statistical scatter between virial and true masses, combined with the sample flux limit, change the distribution in the mass-luminosity plane significantly.

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