Search for Supermassive Black Hole Binaries in the Sloan Digital Sky Survey Spectroscopic Sample

Supermassive black hole (SMBH) binaries are expected in a Lambda CDM cosmology given that most (if not all) massive galaxies contain a massive black hole at their center. So far, however, direct evidence for such binaries has been elusive. We use cross-correlation to search for temporal velocity shifts in the MgII broad emission lines of 0.36 < z < 2 quasars with multiple observations in the Sloan Digital Sky Survey. For ~ 10^9 Msun BHs in SMBH binaries, we are sensitive to velocity drifts for binary separations of ~ 0.1 pc with orbital periods of ~100 years. We find seven candidate sub-pc--scale binaries with velocity shifts > 3.4 sigma ~ 280 km/s, where sigma is our systematic error. Comparing the detectability of SMBH binaries with the number of candidates (N < 7), we can rule out that most 10^9 Msun BHs exist in ~ 0.03-0.2 pc scale binaries, in a scenario where binaries stall at sub-pc scales for a Hubble time. We further constrain that < one-third of quasars host SMBH binaries after considering gas-assisted sub-pc evolution of SMBH binaries, although this result is very sensitive to the assumed size of the broad line region. We estimate the detectability of SMBH binaries with ongoing or next-generation surveys (e.g., BOSS, Subaru Prime Focus Spectrograph), taking into account the evolution of the sub-parsec binary in circumbinary gas disks. These future observations will provide longer time baselines for searches similar to ours and may in turn constrain the evolutionary scenarios of SMBH binaries.