A note on periodicity of long-term variations of optical continuum in
  active galactic nuclei
  Graham et al. found a sample of active galactic nuclei (AGNs) and quasars
from the Catalina Real-time Transient Survey (CRTS) that have long-term
periodic variations in optical continuum, the nature of the periodicity remains
uncertain. We investigate the periodic variability characteristics of the
sample by testing the relations of the observed variability periods with AGN
optical luminosity, black hole mass and accretion rates, and find no
significant correlations. We also test the observed periods in several
different aspects related to accretion disks surrounding single black holes,
such as the Keplerian rotational periods of 5100~\AA\ photon-emission regions
and self-gravity dominated regions and the precessing period of warped disks.
These tests shed new lights on understanding AGN variability in general. Under
the assumption that the periodic behavior is associated with SMBHB systems in
particular, we compare the separations ($\mathscr{D}_{\bullet}$) against
characteristic radii of broad-line regions ($R_{\rm BLR}$) of the binaries and
find $\mathscr{D}_{\bullet}$$\approx$ 0.05 $R_{\rm BLR}$. This interestingly
implies that these binaries have only circumbinary BLRs.
