The stellar correlation function from SDSS A statistical search for wide binary stars

We study the statistical properties of the wide binary population in the Galaxy field with projected separations larger than 200 AU by constructing the stellar angular two-point correlation function (2PCF) from a homogeneous sample of nearly 670 000 main sequence stars. The selected stars lie within a rectangular region around the Northern Galactic Pole and have apparent r-band magnitudes between 15 and 20.5 mag and spectral classes later than G5 (g-r > 0.5 mag). The data were taken from the Sixth Data Release of the Sloan Digital Sky Survey. We model the 2PCF by means of the Wasserman-Weinberg technique including several assumptions on the distribution of the binaries' orbital parameters, luminosity function, and density distribution in the Galaxy. In particular, we assume that the semi-major axis distribution is described by a single powerlaw. The free model parameters - the local wide binary number density n(WB) and the power-law index lambda of the semi-major axis distribution - are inferred simultaneously by least-square fitting. We find the separation distribution to follow Opik's law (lambda = 1) up to the Galactic tidal limit, without any break and a local density of 5 wide binaries per 1000 pc(3) with both components having spectral type later than G5. This implies that about 10% of all stars in the solar neighbourhood are members of such a late-type wide binary system. With a relative statistical (2 sigma) error of about 10%, our findings are in general agreement with previous studies of wide binaries. The data suggest that about 800 very wide pairs with projected separations larger than 0.1 pc exist in our sample, whereas none are found beyond 0.8 pc. Modern large-scale surveys make the 2PCF method a viable tool for studying wide binary stars and a true complement to common proper motion studies. The method is, however, seriously limited by the noise from optical pairs and the (over) simplifying assumptions made to model the selection effects and to interpret the measured clustering signal.