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 Sloan Digital Sky Survey (SDSS) spectroscopy of the broad H beta line. Our working model is that (1) one and only one of the two BHs in the binary is active; (2) the active BH dynamically dominates its own broad-line region (BLR) in the binary system, so that the mean velocity of the BLR reflects the mean velocity of its host BH; (3) the inactive companion BH is orbiting at a distance of a few R-BLR, where R-BLR similar to 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 rest frame. Out of similar to 700 pairs of spectra for which we have good measurements of the velocity shift between two epochs (1 sigma error similar to 40 km s(-1)), we detect 28 systems with significant velocity shifts in broad H beta, among which 7 are the best candidates for the hypothesized binaries, 4 are most likely due to broad-line variability in single BHs, and the rest are ambiguous. Continued spectroscopic observations of these candidates will easily strengthen or disprove these claims. 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 rest frame). 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. Future time-domain spectroscopic surveys of normal quasars can provide vital prior information on the structure function of stochastic velocity shifts induced by broad-line variability in single BHs. Such surveys with improved spectral quality, increased time baseline, and more epochs can greatly improve the statistical constraints of this method on the general binary population in broad-line quasars, further shrink the allowed binary parameter space, and detect true sub-parsec binaries.