The Quasar Accretion Disk Size-Black Hole Mass Relation

Abstract

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 Å is related to the black hole mass by log(R ₂₅₀₀/cm) = (15.78 ± 0.12) + (0.80 ± 0.17)log(M _BH/10⁹ M _sun). This scaling is consistent with the expectation from thin-disk theory (R vprop M ^2/3 _BH), but when interpreted in terms of the standard thin-disk model (T vprop R ^-3/4), it implies that black holes radiate with very low efficiency, log(η) = -1.77 ± 0.29 + log(L/L _E), where η =L/(\dot{M}c^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 (η ≈ 10%). With one exception, these sizes are larger by a factor of ~4 than the size needed to produce the observed 0.8 μm quasar flux by thermal radiation from a thin disk with the same T vprop 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.

Based on observations obtained with the Small and Moderate Aperture Research Telescope System (SMARTS) 1.3 m, which is operated by the SMARTS Consortium, the Apache Point Observatory 3.5 m telescope, which is owned and operated by the Astrophysical Research Consortium, the WIYN Observatory which is owned and operated by the University of Wisconsin, Indiana University, Yale University, and the National Optical Astronomy Observatories (NOAO), the 6.5 m Magellan Baade telescope, which is a collaboration between the observatories of the Carnegie Institution of Washington (OCIW), University of Arizona, Harvard University, University of Michigan, and Massachusetts Institute of Technology, and observations made with the NASA/ESA Hubble Space Telescope for program HST-GO-9744 of the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.