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.
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