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 greater than or similar to 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, (M)over dot(disk) similar or equal to 4-190 M(circle dot)yr(-1), with most of the objects (80%) having (M)over dot(disk) similar or equal to 10-65 M(circle dot)yr(-1), confirming the Eddington-limited nature of the accretion flows. By combining our estimates of (M)over dot(disk) with conservative, lower limits on the bolometric luminosities of the quasars, we investigate which alternative values of eta best account for all the available data. We find that the vast majority of quasars (similar to 85%) can be explained with radiative efficiencies in the range eta similar or equal to 0.03-0.3, with a median value close to the commonly assumed eta = 0.1. Within this range, we obtain conservative estimates of eta greater than or similar to 0.14 for ULAS J1120 and SDSS J0100 (at z = 6.3), and of greater than or similar to 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) equivalent to M-BH /(M)over dot(BH) similar or equal to 0.1-1 Gyr, suggesting that most quasars could have had similar to 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 greater than or similar to 10).