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 { 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 { 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 { 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 .