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.