Two years ’ worth of u - , g - , r - , i - , and z -band optical light curves were obtained for the massive type 1 quasar PG 2308+098 at z = 0.433 using the 1.05-m Kiso Schmidt telescope/Kiso Wide Field Camera , and inter-band time lags of the light curves were measured .
Wavelength-dependent continuum reverberation lag signals of several tens of days relative to the u -band were detected at g - , r - , i - , and z -bands , where the longer wavelength bands showed larger lags .
From the wavelength-dependent lags , and assuming the standard disk temperature radial profile T \propto R _ { disk } ^ { -3 / 4 } and an X-ray/far-ultraviolet reprocessing picture , a constraint on the radius of the accretion disk responsible for the rest-frame 2500 Å disk continuum emission was derived as R _ { disk } = 9.46 ^ { +0.29 } _ { -3.12 } light-days .
The derived disk size is slightly ( 1.2 - 1.8 times ) larger than the theoretical disk size of R _ { disk } = 5.46 light-days predicted from the black hole mass ( M _ { BH } ) and Eddington ratio estimates of PG 2308+098 .
This result is roughly in accordance with previous studies of lower mass active galactic nuclei ( AGNs ) , where measured disk sizes have been found to be larger than the standard disk model predictions by a factor of \sim 3 ; however , the disk size discrepancy is more modest in PG 2308+098 .
By compiling literature values of the disk size constraints from continuum reverberation and gravitational microlensing observations for AGNs/quasars , we show that the M _ { BH } dependence of R _ { disk } is weaker than that expected from the standard disk model .
These observations suggest that the standard Shakura-Sunyaev accretion disk theory has limitations in describing AGN/quasar accretion disks .