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Quasars whose broad emission lines show temporal, bulk radial velocity (RV) shifts have been proposed as candidate sub-parsec (sub-pc), binary supermassive black holes (BSBHs). We identified a sample of 16 BSBH candidates based on two-epoch spectroscopy among 52 quasars with significant RV shifts over a few rest-frame years. The candidates showed consistent velocity shifts independently measured from two broad lines (H$beta$ and H$alpha$ or Mg${rm ,II}$) without significant changes in the broad-line profiles. Here in the third paper of the series, we present further third- and fourth-epoch spectroscopy for 12 of the 16 candidates for continued RV tests, spanning $sim$5--15 yr in the quasars rest frames. Cross-correlation analysis of the broad H$beta$ calibrated against [O${rm,III}],lambda 5007$ suggests that 5 of the 12 quasars remain valid as BSBH candidates. They show broad H$beta$ RV curves that are consistent with binary orbital motion without significant changes in the broad line profiles. Their broad H$alpha$ (or Mg${rm ,II}$) lines display RV shifts that are either consistent with or smaller than those seen in broad H$beta$. The RV shifts can be explained by a $sim$0.05--0.1 pc BSBH with an orbital period of $sim$40--130 yr, assuming a mass ratio of 0.5--2 and a circular orbit. However, the parameters are not well constrained given the few epochs that sample only a small portion of the hypothesized binary orbital cycle. The apparent occurrence rate of sub-pc BSBHs is $lesssim$13$pm$5% among all SDSS quasars, with no significant difference in the subsets with and without single-epoch broad line velocity offsets. Dedicated long-term spectroscopic monitoring is still needed to further confirm or reject these BSBH candidates.
We present a method for comparing the H$beta$ emission-line profiles of observed supermassive black hole (SBHB) candidates and models of sub-parsec SBHBs in circumbinary disks. Using the approach based on principal component analysis we infer the val
We present analysis of Chandra X-ray observations of seven quasars that were identified as candidate sub-parsec binary supermassive black hole (SMBH) systems in the Catalina Real-Time Transient Survey (CRTS) based on apparent periodicity in their opt
Elusive supermassive black hole binaries (SMBHBs) are thought to be the penultimate stage of galaxy mergers, preceding a final coalescence phase. SMBHBs are sources of continuous gravitational waves, possibly detectable by pulsar timing arrays; the i
We have been spectroscopically monitoring 88 quasars selected to have broad H$beta$ emission lines offset from their systemic redshift by thousands of km s$^{-1}$. By analogy with single-lined spectroscopic binary stars, we consider these quasars to
Broad absorption line (BAL) quasars probe the high velocity gas ejected by luminous accreting black holes. BAL variability timescales place constraints on the size, location, and dynamics of the emitting and absorbing gas near the supermassive black