Constraints on black hole duty cycles and the black hole-halo relation from SDSS quasar clustering

TL;DR

This study uses SDSS quasar clustering data to constrain the relationship between quasar luminosity, host halo mass, and black hole duty cycle, revealing different behaviors at various redshifts and luminosities.

Contribution

It provides new constraints on the duty cycle and scatter in the luminosity-halo mass relation using clustering data at intermediate redshifts.

Findings

Clustering bias shows little change between faint and bright quasars at z=1.45.

Models with small scatter and low duty cycle fit the data well.

High-luminosity quasars at z~4 suggest near-unity duty cycle and minimal scatter.

Abstract

We use Shen et al.'s (2009) measurements of luminosity-dependent clustering in the SDSS Data Release 5 Quasar Catalog, at redshifts 0.4 < z < 2.5, to constrain the relation between quasar luminosity and host halo mass and to infer the duty cycle f_opt, the fraction of black holes that shine as optically luminous quasars at a given time. We assume a monotonic mean relation between quasar luminosity and host halo mass, with log-normal scatter \Sigma. For specified f_opt and \Sigma, matching the observed quasar space density determines the normalization of the luminosity-halo mass relation, from which we predict the clustering bias. The data show no change of bias between the faint and bright halves of the quasar sample but a modest increase in bias for the brightest 10%. At the mean redshift z=1.45 of the sample, the data can be well described either by models with small intrinsic scatter (\Sigma=0.1 dex) and a duty cycle f_opt=6*10^(-4) or by models with much larger duty cycles and larger values of the scatter. "Continuity equation" models of the black hole mass population imply f_opt > 2*10^(-3) in this range of masses and redshifts, and the combination of this constraint with the clustering measurements implies scatter \Sigma > 0.4 dex. These findings contrast with those inferred from the much stronger clustering of high-luminosity quasars at z~4, which require minimal scatter between luminosity and halo mass and duty cycles close to one.