Herschel HIFI observations of O$_2$ toward Orion: special conditions for
  shock enhanced emission
  We report observations of molecular oxygen (O$_2$) rotational transitions at
487 GHz, 774 GHz, and 1121 GHz toward Orion Peak A. The O2 lines at 487 GHz and
774 GHz are detected at velocities of 10-12 km/s with line widths 3 km/s;
however, the transition at 1121 GHz is not detected. The observed line
characteristics, combined with the results of earlier observations, suggest
that the region responsible for the O$_2$ emission is 9" (6e16 cm) in size, and
is located close to the H2 Peak 1position (where vibrationally-excited H$_2$
emission peaks), and not at Peak A, 23" away. The peak O2 column density is
1.1e18/cm2. The line velocity is close to that of 621 GHz water maser emission
found in this portion of the Orion Molecular Cloud, and having a shock with
velocity vector lying nearly in the plane of the sky is consistent with
producing maximum maser gain along the line-of-sight. The enhanced O$_2$
abundance compared to that generally found in dense interstellar clouds can be
explained by passage of a low-velocity C-shock through a clump with preshock
density 2e4/cm3, if a reasonable flux of UV radiation is present. The postshock
O$_2$ can explain the emission from the source if its line of sight dimension
is ~10 times larger than its size on the plane of the sky. The special geometry
and conditions required may explain why O$_2$ emission has not been detected in
the cores of other massive star-forming molecular clouds.
