  Using the Texas Echelon Cross Echelle Spectrograph (TEXES) we mapped emission
in the H_2 v = 0-0 S(1) and S(2) lines toward the Orion Bar PDR at 2"
resolution. We also observed H_2 v = 0-0 S(4) at selected points toward the
front of the PDR. Our maps cover a 12" by 40" region of the bar where H_2
ro-vibrational lines are bright. The distributions of H_2 0-0 S(1), 0-0 S(2),
and 1-0 S(1) line emission agree in remarkable detail.
  The high spatial resolution (0.002 pc) of our observations allows us to probe
the distribution of warm gas in the Orion Bar to a distance approaching the
scale length for FUV photon absorption. We use these new observational results
to set parameters for the PDR models described in a companion paper (Draine et
al. 2005, in prep). The best-fit model can account for the separation of the
H_2 emission from the ionization front and the intensities of the ground state
rotational lines as well as the 1-0 S(1) and 2-1 S(1) lines. This model
requires significant adjustments to the commonly used values for the dust UV
attenuation cross section and the photoelectric heating rate.
