We estimate the accretion rates onto the supermassive black holes that power 20 of the highest-redshift quasars , at z \gtrsim 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 } \simeq 4 - 190 M _ { \odot } { yr } ^ { -1 } , with most of the objects ( 80 % ) having \dot { M } _ { disk } \simeq 10 - 65 M _ { \odot } { 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 \eta best account for all the available data .
We find that the vast majority of quasars ( \sim 85 \% ) can be explained with radiative efficiencies in the range \eta \simeq 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 \gtrsim 0.14 for ULAS J1120 and SDSS J0100 ( at z = 6.3 ) , and of \gtrsim 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 } \simeq 0.1 - 1 Gyr , suggesting that most quasars could have had \sim 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 \gtrsim 10 ) .