Constraining sub-parsec binary supermassive black holes in quasars with multi-epoch spectroscopy – III. Candidates from continued radial velocity tests

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 (Hβ and Hα 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 ∼5–15 yr in the quasars’ rest frames. Cross-correlation analysis of the broad Hβ calibrated against [O III] λ5007 suggests that five of the 12 quasars remain valid as BSBH candidates. They show broad Hβ RV curves that are consistent with binary orbital motion without significant changes in the broad-line profiles. Their broad Hα (or Mg II) lines display RV shifts that are either consistent with or smaller than those seen in broad Hβ. The RV shifts can be explained by an ∼0.05–0.1 pc BSBH with an orbital period of ∼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 13 ± 5 per cent 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.