  We present a deep near-infrared spectrum of the Orion Bar Photodissociation
Region (PDR) taken with the Immersion Grating INfrared Spectrometer (IGRINS) on
the 2.7 m telescope at the McDonald Observatory. IGRINS has high spectral
resolution (R~45000) and instantaneous broad wavelength coverage (1.45-2.45
microns), enabling us to detect 87 emission lines from rovibrationally excited
molecular hydrogen (H_2) that arise from transitions out of 69 upper
rovibration levels of the electronic ground state. These levels cover a large
range of rotational and vibrational quantum numbers and excitation energies,
making them an excellent probe of the excitation mechanisms of H_2 and physical
conditions within the PDR. The Orion Bar PDR is thought to consist of cooler
high density clumps or filaments (T=50-250 K, n_H = 10^5 - 10^7 cm^-3) embedded
in a warmer lower density medium (T=250-1000 K, n_H=10^4 - 10^5 cm^-3). We fit
a grid of simple constant-temperature and constant-density Cloudy models, which
recreate the observed H_2 level populations well, to constrain the temperature
to a range of 600 to 650 K and the density to n_H = 2.5 x 10^3 to 10^4 cm^-3.
The best fit model gives T = 625 K and n_H = 5x10^3 cm^-3. This well
constrained warm temperature is consistent with kinetic temperatures found by
other studies for the Orion Bar's lower density medium. However, the range of
densities well fit by the model grid is marginally lower than those reported by
other studies. We could be observing lower density gas than the surrounding
medium, or perhaps a density-sensitive parameter in our models is not properly
estimated.
