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

TL;DR

This study analyzes the demographics of z ~ 6 quasars, revealing intrinsic black hole mass functions and Eddington ratio distributions, and how these properties evolve with redshift and luminosity, using a sample of over 100 quasars.

Contribution

It introduces a forward modeling approach to constrain the intrinsic black hole mass and Eddington ratio distributions at z ~ 6, accounting for measurement uncertainties and selection effects.

Findings

Intrinsic BH mass function constrained for M_BH > 10^8.5 M_Sun.

Eddington ratio distribution peaks around log(L_bol/L_Edd) ~ -0.9.

Number densities of massive BHs decline more rapidly at higher redshifts.

Abstract

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 modeling of parameterized 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 black hole mass function at M_BH > 10^8.5 M_Sun, with a median 1-sigma uncertainty of ~0.5 dex in abundance. The intrinsic Eddington ratio distribution of M_BH > 10^8.5 M_Sun 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.