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 /10 9 M ). This scaling is consistent with the expectation from thin-disk theory (R ∝ M 2/3 BH ), but when interpreted in terms of the standard thin-disk model (T ∝ 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/(Ṁc 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 ∝ 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.

Structure of the Accretion Disk in the Lensed Quasar Q2237+0305 From Multi-Epoch and Multi-Wavelength Narrowband Photometry

“…Gravitational microlensing (Chang & Refsdal 1979, 1984; see also Kochanek 2004 andWambsganss 2006) is the main tool used to estimate both parameters, either from time variability or through the wavelength dependence of the microlensing magnification. Microlensing studies (see e.g., Pooley et al 2007;Morgan et al 2010;Blackburne et al 2011Blackburne et al , 2014Blackburne et al , 2015Sluse et al 2011;Jiménez-Vicente et al 2012Hainline et al 2013;Mosquera et al 2013;MacLeod et al 2015) have found that the mean sizes of quasar accretion disks are roughly a factor of 2-3 greater than the predictions of the standard thin disk model. These differences are too large to be explained by contamination from the broad emission lines and the pseudo-continuum contributions, or scattering on scales larger than the accretion disk (Dai et al 2010;Morgan et al 2010).…”

“…Microlensing studies (see e.g., Pooley et al 2007;Morgan et al 2010;Blackburne et al 2011Blackburne et al , 2014Blackburne et al , 2015Sluse et al 2011;Jiménez-Vicente et al 2012Hainline et al 2013;Mosquera et al 2013;MacLeod et al 2015) have found that the mean sizes of quasar accretion disks are roughly a factor of 2-3 greater than the predictions of the standard thin disk model. These differences are too large to be explained by contamination from the broad emission lines and the pseudo-continuum contributions, or scattering on scales larger than the accretion disk (Dai et al 2010;Morgan et al 2010). Recent measurements of wavelength-dependent continuum lags in two local active galactic nuclei (AGNs) are consistent with the microlensing results (Shappee et al 2014;Edelson et al 2015;Fausnaugh et al 2016).…”

Apparent quasar disc sizes in the “bird’s nest” paradigm

“…We applied our model to single spectral band accretion disc size measurements made by Morgan et al (2010). The advantage of these data set is the existence of de-lensed fluxes that allow us to make independent mass accretion rate estimates.…”

“…The advantage of these data set is the existence of de-lensed fluxes that allow us to make independent mass accretion rate estimates. We consider the sample from Morgan et al (2010) with the data for one object (Q J0158-4325) replaced by newer data from Morgan et al (2012), following our work in Abolmasov & Shakura (2012). Mass accretion rate was estimated using monochromatic delensed fluxes from Morgan et al (2010).…”

“…We consider the sample from Morgan et al (2010) with the data for one object (Q J0158-4325) replaced by newer data from Morgan et al (2012), following our work in Abolmasov & Shakura (2012). Mass accretion rate was estimated using monochromatic delensed fluxes from Morgan et al (2010). Standard multi-colour accretion disc approximation allows us to link monochromatic flux (at observer frame λ obs = 0.79µm, which is close to the observable I-band flux) with the mass accretion rate assuming the black hole mass is known.…”