THE QUASAR ACCRETION DISK SIZE-BLACK HOLE MASS RELATION

We use the microlensing variability observed for 11 gravitationally lensed quasars to show that the accretion disk size at a rest-frame wavelength of 2500 angstrom is related to the black hole mass by log(R-2500/cm) = (15.78 +/- 0.12) + (0.80 +/- 0.17) log(M-BH/10(9) M-circle dot). This scaling is consistent with the expectation from thin-disk theory (R proportional to M-BH(2/3) ), but when interpreted in terms of the standard thin-disk model (T proportional to R-3/4), it implies that black holes radiate with very low efficiency, log(eta) = -1.77 +/- 0.29 + log(L/L-E), where eta = L/((M) over dotc(2)). Only by making the maximum reasonable shifts in the average inclination, Eddington factors, and black hole masses can we raise the efficiency estimate to be marginally consistent with typical efficiency estimates (eta approximate to 10%). With one exception, these sizes are larger by a factor of similar to 4 than the size needed to produce the observed 0.8 mu m quasar flux by thermal radiation from a thin disk with the same T proportional to R-3/4 temperature profile. While scattering a significant fraction of the disk emission on large scales or including a large fraction of contaminating line emission can reduce the size discrepancy, resolving it also appears to require that accretion disks have flatter temperature/surface brightness profiles.