Constraints on accretion disk size in the massive type 1 quasar PG
  2308+098 from optical continuum reverberation lags
  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 $T \propto R_{\rm disk}^{-3/4}$ and an X-ray/far-ultraviolet
reprocessing picture, a constraint on the radius of the accretion disk
responsible for the rest-frame 2500 \AA\ disk continuum emission was derived as
$R_{\rm disk} = 9.46^{+0.29}_{-3.12}$ light-days. The derived disk size is
slightly (1.2-1.8 times) larger than the theoretical disk size of $R_{\rm disk}
= 5.46$ light-days predicted from the black hole mass ($M_{\rm BH}$) 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 $M_{\rm BH}$ dependence of
$R_{\rm disk}$ 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.
