Determining Quasar Black Hole Mass Functions from their Broad Emission Lines: Application to the Bright Quasar Survey

TL;DR

This paper introduces a Bayesian statistical method to accurately estimate quasar black hole mass functions from broad emission line data, accounting for measurement errors and survey limits, and applies it to local quasar data.

Contribution

A novel Bayesian approach using MCMC for estimating the quasar black hole mass function from broad line data, improving bias correction and uncertainty quantification.

Findings

The local active black hole mass function follows a power-law with slope ~2 for masses > 10^8 solar masses.

Broad line quasars at z<0.5 have an average Eddington ratio of ~0.4.

The method constrains the BHMF beyond survey detection limits.

Abstract

We describe a Bayesian approach to estimating quasar black hole mass functions (BHMF) when using the broad emission lines to estimate black hole mass. We show how using the broad line mass estimates in combination with statistical techniques developed for luminosity function estimation leads to statistically biased results. We derive the likelihood function for the BHMF based on the broad line mass estimates, and derive the posterior distribution for the BHMF, given the observed data. We develop our statistical approach for a flexible model where the BHMF is modelled as a mixture of Gaussian functions. Statistical inference is performed using markov chain monte carlo (MCMC) methods. Our method has the advantage that it is able to constrain the BHMF even beyond the survey detection limits at the adopted confidence level, accounts for measurement errors and the intrinsic uncertainty in broad line mass estimates, and provides a natural way of estimating the probability distribution of any quantities derived from the BHMF. We conclude by using our method to estimate the local active BHMF using the z < 0.5 Bright Quasar Survey sources. At z = 0.2, the quasar BHMF falls off approximately as a power law with slope ~ 2 for M_{BH} > 10^8. Our analysis implies that z < 0.5 broad line quasars have a typical Eddington ratio of ~ 0.4 and a dispersion in Eddington ratio of < 0.5 dex (abridged).