Constraints on Black Hole Growth, Quasar Lifetimes, and Eddington Ratio Distributions From the SDSS Broad-Line Quasar Black Hole Mass Function

We present an estimate of the black hole mass function of broad-line quasars (BLQSOs) that self-consistently corrects for incompleteness and the statistical uncertainty in the mass estimates, based on a sample of 9886 quasars at 1 1 it is highly incomplete at M BH 150 ± 15 Myr for black holes at z = 1 with a mass of M BH = 109 M sun, and we constrain the maximum mass of a black hole in a BLQSO to be ~3 × 1010 M sun. Our estimated distribution of BLQSO Eddington ratios peaks at L/L Edd ~ 0.05 and has a dispersion of ~0.4 dex, implying that most BLQSOs are not radiating at or near the Eddington limit; however, the location of the peak is subject to considerable uncertainty. The steep increase in number density of BLQSOs toward lower Eddington ratios is expected if the BLQSO accretion rate monotonically decays with time. Furthermore, our estimated lifetime and Eddington ratio distributions imply that the majority of the most massive black holes spend a significant amount of time growing in an earlier obscured phase, a conclusion which is independent of the unknown obscured fraction. These results are consistent with models for self-regulated black hole growth, at least for massive systems at z > 1, where the BLQSO phase occurs at the end of a fueling event when black hole feedback unbinds the accreting gas, halting the accretion flow.