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We study the demographics of z ~ 6 broad-line quasars in the black hole (BH)mass-luminosity plane using a sample of more than 100 quasars at 5.7 < z < 6.5.These quasars have well quantified selection functions and nearly one third ofthem also have virial BH masses estimated from near-IR spectroscopy. We useforward modeling of parameterized intrinsic distributions of BH masses andEddington ratios, and account for the sample flux limits and measurementuncertainties of the BH masses and luminosities. We find significantdifferences between the intrinsic and observed distributions of the quantitiesdue to measurement uncertainties and sample flux limits. There is also marginalevidence that the virial BH masses are susceptible to a positiveluminosity-dependent bias (BH mass is overestimated when luminosity is abovethe average), and that the mean Eddington ratio increases with BH mass. Ourmodels provide reliable constraints on the z ~ 6 black hole mass function atM_BH > 10^8.5 M_Sun, with a median 1-sigma uncertainty of ~0.5 dex inabundance. The intrinsic Eddington ratio distribution of M_BH > 10^8.5 M_Sunquasars can be approximated by a mass-dependent Schechter model, with a broadpeak around log(L_bol/L_Edd}) ~ -0.9. We also find that, at 4.5 < z < 6, thenumber densities of more massive BHs tend to decline more rapidly withincreasing redshift, contrary to the trend at 2.5 < z < 4.5 reportedpreviously.

Demographics of z ~ 6 Quasars in the Black Hole Mass-Luminosity Plane