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, dM_disk/dt~4-190 Msol/yr, with most of the
objects (80\%) having dM_disk/dt~10-65 Msol/yr, confirming the
Eddington-limited nature of the accretion flows. By combining our estimates of
dM_disk/dt 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 (~85\%) can
be explained with radiative efficiencies in the range \eta~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>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 =
M_BH / dM_BH/dt ~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 or above).
