HST survey of the Orion Nebula Cluster in the H$_2$O 1.4 $\mu$m
  absorption band: III. The population of sub-stellar binary companions
  We present new results concerning the sub-stellar binary population in the
Orion Nebula Cluster (ONC). Using the Karhunen-Lo\`{e}ve Image Projection
(KLIP) algorithm, we have reprocessed images taken with the IR channel of the
Wide Field Camera 3 mounted on the Hubble Space Telescope to unveil faint close
companions in the wings of the stellar PSFs. Starting with a sample of $1392$
bona-fide not saturated cluster members, we detect $39$ close-pairs cluster
candidates with separation $0.16''-0.77''$. The primary masses span a range
M$_p$ $\sim 0.015-1.27$ M$_{\odot}$ whereas for the companions we derive M$_c$
$\sim 0.004-0.54$ M$_{\odot}$. Of these $39$ binary systems, $18$ were already
known while the remaining $21$ are new detections. Correcting for completeness
and combining our catalog with previously detected ONC binaries, we obtain an
overall binary fraction of $11.5\% \pm 0.9\%$. Compared to other star forming
regions, our multiplicity function is $\sim 2$ smaller than e.g. Taurus, while
compared to the binaries in the field we obtain comparable values. We analyze
the mass function of the binaries, finding differences between the mass
distribution of binaries and single stars and between primary and companion
mass distributions. The mass ratio shows a bottom-heavy distribution with
median value of $M_c/M_p \sim 0.25$. Overall our results suggest that ONC
binaries may represent a template for the typical population of field binaries,
supporting the hypothesis that the ONC may be regarded as a most typical star
forming region in the Milky Way.
