We investigate the properties of the most distant quasars ULASJ134208.10+092838.61 ( z = 7.54 ) and ULASJ112001.48+064124.3 ( z = 7.08 ) studying their Optical-UV emission that shows clear evidence of the presence of an accretion disk .
We model such emission applying the relativistic disk models KERRBB and SLIMBH for which we have derived some analytical approximations to describe the observed emission as a function of the black hole mass , accretion rate , spin and the viewing angle .
We found that : 1 ] our black hole mass estimates are compatible with the ones found using the virial argument but with a smaller uncertainty ; 2 ] assuming that the virial argument is a reliable method to have a BH mass measurement ( with no systematic uncertainties involved ) , we found an upper limit for the BH spin of the two sources , ruling out the canonical maximum value ; 3 ] our Eddington ratio estimates are smaller then those found by Bañados et al .
( 4 ) and Mortlock et al .
( 35 ) by a factor \sim 2 .
Using our results , we explore the parameter space ( efficiency , accretion rate ) to describe the possible evolution of the black hole assuming a \sim 10 ^ { 2 - 4 } M _ { \odot } seed : if the black hole in these sources formed at redshift z = 10 - 20 , we found that the accretion has to proceed at the Eddington rate with a radiative efficiency \eta \sim 0.1 in order to reach the observed masses in less than \sim 0.7 Gyr .