The Quasar Accretion Disk Size - Black Hole Mass Relation

TL;DR

This study uses gravitational lensing microlensing to empirically establish a relation between quasar accretion disk size and black hole mass, supporting thin disk theory but indicating lower radiative efficiency and larger disk sizes than simple models predict.

Contribution

It provides the first observational scaling relation between quasar disk size and black hole mass using microlensing data, highlighting discrepancies with standard thin disk models.

Findings

Disk size scales with black hole mass as R ~ M_BH^{0.54}

Observed disk sizes are about three times larger than predictions from simple thin disk models

Black holes radiate with lower efficiency than previously assumed.

Abstract

We use the microlensing variability observed for nine gravitationally lensed quasars to show that the accretion disk size at 2500 Angstroms is related to the black hole mass by log(R_2500/cm) = (15.6+-0.2) + (0.54+-0.28)log(M_BH/10^9M_sun). This scaling is consistent with the expectation from thin disk theory (R ~ M_BH^(2/3)), but it implies that black holes radiate with relatively low efficiency, log(eta) = -1.29+-0.44 + log(L/L_E) where eta=L/(Mdot c^2). These sizes are also larger, by a factor of ~3, than the size needed to produce the observed 0.8 micron quasar flux by thermal radiation from a thin disk with the same T ~ R^(-3/4) temperature profile. More sophisticated disk models are clearly required, particularly as our continuing observations improve the precision of the measurements and yield estimates of the scaling with wavelength and accretion rate.