Demographics of z ∼ 6 quasars in the black hole mass–luminosity plane

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 of them also have virial BH masses estimated from near-IR spectroscopy. We use forward modelling of parametrized intrinsic distributions of BH masses and Eddington ratios, and account for the sample flux limits and measurement uncertainties of the BH masses and luminosities. We find significant differences between the intrinsic and observed distributions of the quantities due to measurement uncertainties and sample flux limits. There is also marginal evidence that the virial BH masses are susceptible to a positive luminosity-dependent bias (BH mass is overestimated when luminosity is above the average), and that the mean Eddington ratio increases with BH mass. Our models provide reliable constraints on the z ∼ 6 BH mass function at M_BH > 10^8.5 M, with a median 1σ uncertainty of ∼0.5 dex in abundance. The intrinsic Eddington ratio distribution of M_BH > 10^8.5 M quasars can be approximated by a mass-dependent Schechter model, with a broad peak around log (L_bol/L_Edd) ∼ −0.9. We also find that, at 4.5 ≾ z ≾ 6, the number densities of more massive BHs tend to decline more rapidly with increasing redshift, contrary to the trend at 2.5 ≾ z ≾ 4.5 reported previously.