HST survey of the Orion Nebula Cluster in the H$_2$O 1.4 $\mu$m
  absorption band: II. The substellar IMF down to planetary masses
  We exploit the ability of the Hubble Space Telescope to probe near infrared
water absorption present in the atmosphere of low-mass stars, brown dwarfs and
planetary mass objects to create a very pure sample of Orion Nebula Cluster
(ONC) members, not affected by contamination from background stars and galaxies
which lack water absorption. Thanks to these data we infer the Initial Mass
Function (IMF) of the ONC in the $0.005 - 1.4$M$_{\odot}$ regime, i.e. down to
few Jupiter masses. The young age of the ONC, $\sim1$ Myr, provides a snapshot
of the outcome of star formation for the present-day conditions (metallicity,
temperature, pressure) of typical Milky Way disk molecular clouds. We
demonstrate that the IMF of the ONC is well described by either a log-normal
function or a broken power-law, with parameter values qualitatively in
agreement with the canonical Chabrier or Kroupa forms for the Milky Way disk
IMF. This continuity in the mass distribution provides clues to the fact that
the same physical processes may be regulating formation of stars, brown dwarfs,
and planetary mass objects. Both the canonical IMF forms under-predict the
observed number of very low mass members (below $0.1$ M$_\odot$), a regime
where our data allows more precise constraints. Nevertheless, we do not observe
a rise or secondary peak in the brown dwarfs or planetary mass regimes. Our
study thus contradicts findings based on broad-band near infrared ground-based
photometry, which predict an extremely high number of free-floating planets,
but likely suffer from unaccounted background contamination.
