Binary Formation in the Orion Nebula Cluster: Exploring the Sub-stellar
  Limit
  We present results constraining the multiplicity of the very low mass stars
and sub-stellar objects in the Orion Nebula Cluster (ONC). Our sample covers
primary masses 0.012-0.1M$_{\odot}$ using archival Hubble Space Telescope data
obtained with the Advanced Camera for Surveys using multiple filters. Studying
the binary populations of clusters provides valuable constraints of how the
birth environment affects binary formation and evolution. Prior surveys have
shown that the binary populations of high-mass, high-density star clusters like
the ONC may substantially differ from those in low-mass associations. Very low
mass stellar and sub-stellar binaries at wide separations, $>$20AU, are
statistically rare in the Galactic field and have been identified in stellar
associations like Taurus-Auriga and Ophiuchus. They also may be susceptible to
dynamical interactions, and their formation may be suppressed by feedback from
on-going star formation. We implement a double point-spread function (PSF)
fitting algorithm using empirical, position dependent PSF models to search for
binary companions at projected separations $>$ 10 AU (25 mas). With this
technique, we identify 7 very low mass binaries, 5 of which are new detections,
resulting in a binary frequency of 12$^{+6}_{-3.2}$% over mass ratios of 0.5 -
1.0 and projected separations of 20 - 200 AU. We find an excess of very low
mass binaries in the ONC compared to the Galactic field, with a probability of
10$^{-6}$ that the populations are statistically consistent. The sub-stellar
population of the ONC may require further dynamical processing of the lowest
binding energy binaries to resemble the field population.
