Wide Binaries in Tycho-{\it Gaia}: Search Method and the Distribution of Orbital Separations

We mine the Tycho-{\it Gaia} astrometric solution (TGAS) catalog for wide stellar binaries by matching positions, proper motions, and astrometric parallaxes. We separate genuine binaries from unassociated stellar pairs through a Bayesian formulation that includes correlated uncertainties in the proper motions and parallaxes. Rather than relying on assumptions about the structure of the Galaxy, we calculate Bayesian priors and likelihoods based on the nature of Keplerian orbits and the TGAS catalog itself. We calibrate our method using radial velocity measurements and obtain 6196 high-confidence candidate wide binaries with projected separations $s\lesssim1$ pc. The normalization of this distribution suggests that at least 0.6\% of TGAS stars have an associated, distant TGAS companion in a wide binary. We demonstrate that {\it Gaia}'s astrometry is precise enough that it can detect projected orbital velocities in wide binaries with orbital periods as large as 10$^6$ yr. For pairs with $s\ \lesssim\ 4\times10^4$~AU, characterization of random alignments indicate our contamination to be $\approx$5\%. For $s \lesssim 5\times10^3$~AU, our distribution is consistent with \"{O}pik's Law. At larger separations, the distribution is steeper and consistent with a power-law $P(s)\propto s^{-1.6}$; there is no evidence in our data of any bimodality in this distribution for $s \lesssim$ 1 pc. Using radial velocities, we demonstrate that at large separations, i.e., of order $s \sim$ 1 pc and beyond, any potential sample of genuine wide binaries in TGAS cannot be easily distinguished from ionized former wide binaries, moving groups, or contamination from randomly aligned stars.