  Supermassive black hole binaries (SMBHs) are expected to result from galaxy
mergers, and thus are natural byproducts (and probes) of hierarchical structure
formation in the Universe. They are also the primary expected source of
low-frequency gravitational wave emission. We search for binary BHs using
time-variable velocity shifts in broad Mg II emission lines of quasars with
multi-epoch observations. First, we inspect velocity shifts of the binary SMBH
candidates identified in Ju et al. (2013), using SDSS spectra with an
additional epoch of data that lengthens the typical baseline to ~10 yr. We find
variations in the line-of-sight velocity shifts over 10 years that are
comparable to the shifts observed over 1-2 years, ruling out the binary model
for the bulk of our candidates. We then analyze 1438 objects with 8 yr median
time baselines, from which we would expect to see velocity shifts >1000 km/s
from sub-pc binaries. We find only one object with an outlying velocity of 448
km/s, indicating, based on our modeling, that ~< 1 per cent (the value varies
with different assumptions) of SMBHs that are active as quasars reside in
binaries with ~0.1 pc separations. Binaries either sweep through these small
separations rapidly or stall at larger radii.
