The Demographics of Broad Line Quasars in the Mass-Luminosity Plane II. Black Hole Mass and Eddington Ratio Functions

TL;DR

This study uses Bayesian methods to analyze the black hole mass and Eddington ratio functions of Type 1 quasars, revealing their evolution, selection effects, and implications for black hole growth and galaxy evolution.

Contribution

It introduces a Bayesian approach to estimate black hole and Eddington ratio functions from a large quasar sample, addressing selection biases and challenging the existence of a sub-Eddington boundary.

Findings

Quasars show downsizing in mass and Eddington ratio.

Maximum Eddington ratio observed is about 3.

No statistical evidence for a sub-Eddington boundary.

Abstract

We employ a flexible Bayesian technique to estimate the black hole mass and Eddington ratio functions for Type 1 (i.e., broad line) quasars from a uniformly-selected data set of ~58,000 quasars from the SDSS DR7. We find that the SDSS becomes significantly incomplete at M_{BH} < 3 x 10^8 M_{Sun} or L / L_{Edd} < 0.07, and that the number densities of Type 1 quasars continue to increase down to these limits. Both the mass and Eddington ratio functions show evidence of downsizing, with the most massive and highest Eddington ratio black holes experiencing Type 1 quasar phases first, although the Eddington ratio number densities are flat at z < 2. We estimate the maximum Eddington ratio of Type 1 quasars in the observable Universe to be L / L_{Edd} ~ 3. Consistent with our results in Paper I, we do not find statistical evidence for a so-called "sub-Eddington boundary" in the mass-luminosity plane of broad line quasars, and demonstrate that such an apparent boundary in the observed distribution can be caused by selection effect and errors in virial BH mass estimates. Based on the typical Eddington ratio in a given mass bin, we estimate typical growth times for the black holes in Type 1 quasars and find that they are typically comparable to or longer than the age of the universe, implying an earlier phase of accelerated (i.e., with higher Eddington ratios) and possibly obscured growth. The large masses probed by our sample imply that most of our black holes reside in what are locally early type galaxies, and we interpret our results within the context of models of self-regulated black hole growth.