Constraining sub-parsec binary supermassive black holes in quasars with multi-epoch spectroscopy. II. the population with kinematically offset broad balmer emission lines

A small fraction of quasars have long been known to show bulk velocity offsets (of a few hundred to thousands of km s^-1) in the broad Balmer lines with respect to the systemic redshift of the host galaxy. Models to explain these offsets usually invoke broad-line region gas kinematics/asymmetry around single black holes (BHs), orbital motion of massive (∼sub-parsec (sub-pc)) binary black holes (BBHs), or recoil BHs, but single-epoch spectra are unable to distinguish between these scenarios. The line-of-sight (LOS) radial velocity (RV) shifts from long-term spectroscopic monitoring can be used to test the BBH hypothesis. We have selected a sample of 399 quasars with kinematically offset broad Hβ lines from the Sloan Digital Sky Survey (SDSS) Seventh Data Release quasar catalog, and have conducted second-epoch optical spectroscopy for 50 of them. Combined with the existing SDSS spectra, the new observations enable us to constrain the LOS RV shifts of broad Hβ lines with a rest-frame baseline of a few years to nearly a decade. While previous work focused on objects with extreme velocity offset (>10³ km s^-1), we explore the parameter space with smaller (a few hundred km s^-1) yet significant offsets (99.7% confidence). Using cross-correlation analysis, we detect significant (99% confidence) radial accelerations in the broad Hβ lines in 24 of the 50 objects, of ∼10-200 km s^-1 yr^-1 with a median measurement uncertainty of ∼10 km s^-1 yr^-1, implying a high fraction of variability of the broad-line velocity on multi-year timescales. We suggest that 9 of the 24 detections are sub-pc BBH candidates, which show consistent velocity shifts independently measured from a second broad line (either Hα or Mg II) without significant changes in the broad-line profiles. Combining the results on the general quasar population studied in Paper I, we find a tentative anti-correlation between the velocity offset in the first-epoch spectrum and the average acceleration between two epochs, which could be explained by orbital phase modulation when the time separation between two epochs is a non-negligible fraction of the orbital period of the motion causing the line displacement. We discuss the implications of our results for the identification of sub-pc BBH candidates in offset-line quasars and for the constraints on their frequency and orbital parameters.