Constraining sub-Parsec Binary Supermassive Black Holes in Quasars with
  Multi-Epoch Spectroscopy. I. The General Quasar Population
  We perform a systematic search for sub-parsec binary supermassive black holes
(BHs) in normal broad line quasars at z<0.8, using multi-epoch SDSS
spectroscopy of the broad Hbeta line. Our working model is that: only one of
the two BHs in the binary is active, and dynamically dominates its own broad
line region (BLR); the inactive companion BH is orbiting at a distance of a few
R_BLR, where R_BLR~0.01-0.1 pc is the BLR size. We search for the expected
line-of-sight acceleration of the broad line velocity from binary orbital
motion by cross-correlating SDSS spectra from two epochs separated by up to
several years in the quasar restframe. Out of ~700 pairs of spectra for which
we have good measurements of the velocity shift between two epochs (1-sigma
error~40 km/s), we detect 28 systems with significant velocity shifts in broad
Hbeta, among which seven are the best candidates for the hypothesized binaries.
We use the distribution of the observed accelerations (mostly non-detections)
to place constraints on the abundance of such binary systems among the general
quasar population. Excess variance in the velocity shift is inferred for
observations separated by longer than 0.4 yr (quasar restframe). Attributing
all the excess to binary motion would imply that most of the quasars in this
sample must be in binaries; that the inactive BH must be on average more
massive than the active one; and that the binary separation is at most a few
times the size of the BLR. However, if this excess variance is partly or
largely due to long-term broad line variability, the requirement of a large
population of close binaries is much weakened or even disfavored for massive
companions. [Abridged]
