Finding binary star fractions in any distribution.

Candidate visual binary systems are often found by identifying two stars that are closer together than would be expected by chance. However, in regions with non-trivial density distributions, the 'random' distances between stars varies because of the background distribution, as well as the presence of binaries. We show that when no binaries are present, the distribution of the ratios of the distances to the nearest and tenth nearest neighbours, d 1/ d 10, is always well approximated by a Gaussian with mean 0.2–0.3 and variance 0.16–0.19 for any underlying density distribution. The introduction of binaries causes some (or all) nearest neighbours to become closer than expected by random chance, introducing a component to the distribution where d 1/ d 10 is much lower than expected. We show how a simple single or double Gaussian fit to the distribution of d 1/ d 10 can be used to find the binary fraction in any underlying density distribution quickly and simply. [ABSTRACT FROM AUTHOR]