A Large Systematic Search for Close Supermassive Binary and Rapidly
  Recoiling Black Holes - III. Radial Velocity Variations
  We have been spectroscopically monitoring 88 quasars selected to have broad
H$\beta$ emission lines offset from their systemic redshift by thousands of km
s$^{-1}$. By analogy with single-lined spectroscopic binary stars, we consider
these quasars to be candidates for hosting supermassive black hole binaries
(SBHBs). In this work we present new radial velocity measurements, typically
3-4 per object over a time period of up to 12 years in the observer's frame. In
29/88 of the SBHB candidates no variability of the shape of the broad H$\beta$
profile is observed, which allows us to make reliable measurements of radial
velocity changes. Among these, we identify three objects that have displayed
systematic and monotonic velocity changes by several hundred km s$^{-1}$ and
are prime targets for further monitoring. Because the periods of the
hypothetical binaries are expected to be long, we cannot hope to observe many
orbital cycles during our lifetimes. Instead, we seek to evaluate the
credentials of the SBHB candidates by attempting to rule out the SBHB
hypothesis. In this spirit, we present a method for placing a lower limit on
the period, and thus the mass, of the SBHBs under the assumption that the
velocity changes we observe are due to orbital motion. Given the duration of
our monitoring campaign and the uncertainties in the radial velocities, we were
able to place a lower limit on the total mass in the range
$4.7\times10^4-3.8\times10^8$ $M_{\scriptscriptstyle \odot}$, which does not
yet allow us to rule out the SBHB hypothesis for any candidates.
