A Statistical Detection of Wide Binary Systems in the Ultra-Faint Dwarf
  Galaxy Reticulum II
  Binary stars can inflate the observed velocity dispersion of stars in dark
matter dominated systems such as ultra-faint dwarf galaxies (UFDs). However,
the population of binaries in UFDs is poorly constrained by observations, with
preferred binary fractions for individual galaxies ranging from a few percent
to nearly unity. Searching for wide binaries through nearest neighbor (NN)
statistics (or the two-point correlation function) has been suggested in the
literature, and we apply this method for the first time to detect wide binaries
in a UFD. By analyzing the positions of stars in Reticulum II (Ret II) from
Hubble Space Telescope images, we search for angularly resolved wide binaries
in Ret II. We find that the distribution of their NN distances shows an
enhancement at projected separations of $<1$ arcsec relative to a model
containing no binaries. We show that such an enhancement can be explained by a
wide~binary fraction of $f_b\approx0.007^{+0.008}_{-0.003}$ at separations of
more than 3000 AU. Under the assumption that the binary separation distribution
is similar to that in the Milky Way, the total binary fraction in Ret II may be
on the order of 50%. We also use the observed magnitude distribution of stars
in Ret II to constrain the initial mass function over the mass range
$0.34-0.78~M_{\odot}$, finding that a shallow power-law slope of $1.01 \le
\alpha \le 1.15$ matches the data.
