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 \arcsec - 16 \arcsec , ii ) common proper motion pairs with 5 \arcsec - 30 \arcsec 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 .
Both samples yield similar relations , with the largest systematic difference of 0.25 mag for F0 to M5 stars , and a root-mean-square scatter of 0.13 mag .
A similar level of agreement is obtained with photometric parallax relations recently proposed by Jurić et al .
( 35 ) .
The measurements show a root-mean-square scatter of \sim 0.30 mag around the best fit M _ { r } ( r - i ) relation , and a mildly non-Gaussian distribution .
We attribute this scatter to metallicity effects and additional unresolved multiplicity of wide binary components .
Aided by the derived photometric parallax relation , we construct a series of high-quality catalogs of candidate main-sequence binary stars .
These range from a sample of \sim 17 , 000 candidates with the probability of each pair to be a physical binary ( the “ efficiency ” ) of \sim 65 \% , to a volume-limited sample of \sim 1 , 800 candidates with an efficiency of \sim 90 \% .
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 Öpik distribution , f ( a ) \propto 1 / a , for a < a _ { break } , where a _ { break } increases roughly linearly with the height Z above the Galactic plane ( a _ { break } \propto 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 .