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 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-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 offset broad H-beta lines from the SDSS DR7 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 H-beta lines with a rest-frame baseline of a few years to
nearly a decade. Using cross-correlation analysis, we detect significant (99%
confidence) radial accelerations in the broad H-beta lines in 24 of the 50
objects. 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 H-alpha 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.
[Abridged]
