Herschel observations of Extra-Ordinary Sources: H2S as a Probe of Dense
  Gas and Possibly Hidden Luminosity Toward the Orion KL Hot Core
  We present Herschel/HIFI observations of the light hydride H$_{2}$S obtained
from the full spectral scan of the Orion Kleinmann-Low nebula (Orion KL) taken
as part of the HEXOS GT key program. In total, we observe 52, 24, and 8
unblended or slightly blended features from H$_{2}$$^{32}$S, H$_{2}$$^{34}$S,
and H$_{2}$$^{33}$S, respectively. We only analyze emission from the so called
hot core, but emission from the plateau, extended ridge, and/or compact ridge
are also detected. Rotation diagrams for ortho and para H$_{2}$S follow
straight lines given the uncertainties and yield T$_{\rm rot}$=141$\pm$12 K.
This indicates H$_{2}$S is in LTE and is well characterized by a single kinetic
temperature or an intense far-IR radiation field is redistributing the
population to produce the observed trend. We argue the latter scenario is more
probable and find that the most highly excited states (E$_{\rm up}$>1000 K) are
likely populated primarily by radiation pumping. We derive an H$_{2}$$^{32}$S
column density, N$_{\rm tot}$(H$_{2}$$^{32}$S)=9.5$\pm$1.9$\times$10$^{17}$
cm$^{-2}$, gas kinetic temperature, T$_{\rm kin}$=120$\pm^{13}_{10}$ K, and
constrain the H$_{2}$ volume density, n$_{H2}$>9$\times$10$^{7}$ cm$^{-3}$, for
the H$_{2}$S emitting gas. These results point to an H$_{2}$S origin in
markedly dense, heavily embedded gas, possibly in close proximity to a hidden
self-luminous source (or sources), which are conceivably responsible for Orion
KL's high luminosity. We also derive an H$_{2}$S ortho/para ratio of
1.7$\pm$0.8 and set an upper limit for HDS/H2S of <4.9$\times$10$^{-3}$.
