Candidate Disk Wide Binaries in the Sloan Digital Sky Survey

Using SDSS Data Release 6, we construct two independent samples of candidate stellar wide binaries selected as i) pairs of unresolved sources with angular separation in the range 3'' - 16'', ii) common proper motion pairs with 5'' - 30'' angular separation, and make them publicly available. These samples are dominated by disk stars, and we use them to constrain the shape of the main-sequence photometric parallax relation M_r(r-i) and to study the properties of wide binary systems. We estimate M_r(r-i) by searching for a relation that minimizes the difference between distance moduli of primary and secondary components of wide binary candidates. We model M_r(r-i) by a fourth degree polynomial and determine the coefficients using Markov Chain Monte Carlo fitting, independently for each sample. Aided by the derived photometric parallax relation, we construct a series of high-quality catalogs of candidate main-sequence binary stars. Using these catalogs, we study the distribution of semi-major axes of wide binaries, a, in the 2,000 < a < 47,000 AU range. We find the observations to be well described by the Opik distribution, f(a)~1/a, for a<a_{break}, where a_{break} increases roughly linearly with the height Z above the Galactic plane (a_{break}~12,300 Z[kpc]^0.7 AU). The number of wide binary systems with 100 AU < a < a_{break}, as a fraction of the total number of stars, decreases from 0.9% at Z=0.5 kpc to 0.5% at Z=3 kpc. The probability for a star to be in a wide binary system is independent of its color. Given this color, the companions of red components seem to be drawn randomly from the stellar luminosity function, while blue components have a larger blue-to-red companion ratio than expected from luminosity function.