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

Supermassive black hole (SMBH) binaries are expected in a ΛCDM cosmology given that most (if not all) massive galaxies contain a massive black hole (BH) 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 Mg II broad emission lines of 0.36 < z < 2 quasars with multiple observations in the Sloan Digital Sky Survey. For ~10⁹ M _⊙ BHs in SMBH binaries, we are sensitive to velocity drifts for binary separations of ~0.1 pc with orbital periods of ~100 yr. We find seven candidate sub-parsec-scale binaries with velocity shifts >3.4σ ~ 280 km s^-1, where σ is our systematic error. Comparing the detectability of SMBH binaries with the number of candidates (N <= 7), we can rule out that most 10⁹ M _⊙ BHs exist in ~0.03-0.2 pc scale binaries, in a scenario where binaries stall at sub-parsec scales for a Hubble time. We further constrain that <=16% (one-third) of quasars host SMBH binaries after considering gas-assisted sub-parsec 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., Baryon Oscillation Spectroscopic Survey, 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.