The demographics of broad-line quasars in the mass-luminosity plane. II. Black hole mass and eddington ratio functions

Brandon C. Kelly, Yue Shen

Research output: Contribution to journalArticlepeer-review


We employ a flexible Bayesian technique to estimate the black hole (BH) 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 Sloan Digital Sky Survey (SDSS) DR7. We find that the SDSS becomes significantly incomplete at MBH ≲ 3 × 108 M⊙ 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 BHs 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 Shen & Kelly, 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 growth times for the BHs in Type 1 quasars and find that they are 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 BHs reside in what are locally early-type galaxies, and we interpret our results within the context of models of self-regulated BH growth.

Original languageEnglish (US)
Article number45
JournalAstrophysical Journal
Issue number1
StatePublished - Feb 10 2013
Externally publishedYes


  • black hole physics
  • galaxies: active
  • quasars: general
  • surveys

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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