On the Accretion Rates and Radiative Efficiencies of the Highest-redshift Quasars

We estimate the accretion rates onto the supermassive black holes that power 20 of the highest-redshift quasars, at z≳ 5.8, including the quasar with the highest redshift known to date—ULAS J1120 at z = 7.09. The analysis is based on the observed (rest-frame) optical luminosities and reliable “virial” estimates of the BH masses of the quasars, and utilizes scaling relations derived from thin accretion disk theory. The mass accretion rates through the postulated disks cover a wide range, {\dot{M}}_{disk}≃ 4{--}190 {M}_⊙ {{yr}}^-1, with most of the objects (80%) having {\dot{M}}_{disk}≃ 10{--}65 {M}_⊙ {{yr}}^-1, confirming the Eddington-limited nature of the accretion flows. By combining our estimates of {\dot{M}}_{disk} with conservative, lower limits on the bolometric luminosities of the quasars, we investigate which alternative values of η best account for all the available data. We find that the vast majority of quasars (∼85%) can be explained with radiative efficiencies in the range η ≃ 0.03{--}0.3, with a median value close to the commonly assumed η = 0.1. Within this range, we obtain conservative estimates of η ≳ 0.14 for ULAS J1120 and SDSS J0100 (at z = 6.3), and of ≳ 0.19 for SDSS J1148 (at z=6.41; assuming their BH masses are accurate). The implied accretion timescales are generally in the range {t}_{acc}\equiv {M}_{BH}/{\dot{M}}_{BH}≃ 0.1{--}1 {Gyr}, suggesting that most quasars could have had ∼ 1{--}10 mass e-foldings since BH seed formation. Our analysis therefore demonstrates that the available luminosities and masses for the highest-redshift quasars can be explained self-consistently within the thin, radiatively efficient accretion disk paradigm. Episodes of radiatively inefficient, “super-critical” accretion may have occurred at significantly earlier epochs (I.e., z≳ 10).