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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 supermassiveblack holes (BSBHs). We identified a sample of 16 BSBH candidates based ontwo-epoch spectroscopy among 52 quasars with significant RV shifts over a fewrest-frame years. The candidates showed consistent velocity shiftsindependently measured from two broad lines (H$\beta$ and H$\alpha$ or Mg${\rm\,II}$) without significant changes in the broad-line profiles. Here in thethird paper of the series, we present further third- and fourth-epochspectroscopy for 12 of the 16 candidates for continued RV tests, spanning$\sim$5--15 yr in the quasars' rest frames. Cross-correlation analysis of thebroad H$\beta$ calibrated against [O${\rm\,III}]\,\lambda 5007$ suggests that 5of the 12 quasars remain valid as BSBH candidates. They show broad H$\beta$ RVcurves that are consistent with binary orbital motion without significantchanges 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 thoseseen in broad H$\beta$. The RV shifts can be explained by a $\sim$0.05--0.1 pcBSBH with an orbital period of $\sim$40--130 yr, assuming a mass ratio of0.5--2 and a circular orbit. However, the parameters are not well constrainedgiven the few epochs that sample only a small portion of the hypothesizedbinary orbital cycle. The apparent occurrence rate of sub-pc BSBHs is$\lesssim$13$\pm$5% among all SDSS quasars, with no significant difference inthe subsets with and without single-epoch broad line velocity offsets.Dedicated long-term spectroscopic monitoring is still needed to further confirmor reject these BSBH candidates.

monthly notices of the royal astronomical society

Constraining Sub-Parsec Binary Supermassive Black Holes in Quasars with  Multi-Epoch Spectroscopy. III. Candidates from Continued Radial Velocity  Tests