Near-infrared emission-line imaging and long-slit spectroscopy of H2 and [Fe II] emission lines in the 1.25-2.25 μm wavelength range at multiple positions toward the Herbig-Haro objects HH 7-11 and a nearby H2 emission-line source, ASR 57, are presented. The relative line strengths are used to examine the processes responsible for exciting H2 emission in these objects. All of the H2 emission-line ratios are consistent with collisional excitation in these objects, and no evidence is seen for noncollisional excitation mechanisms. Nonetheless, the H2 level populations in HH 7-11 are inconsistent with LTE predictions and show underpopulations relative to a Boltzmann distribution in accordance with the different critical densities of each level. The level populations are consistent with either a purely molecular gas or gas containing a mixture of H and H2, provided that the gas has a range of temperatures and relatively low density. The slit positions toward HH 7-11 sample a wide range of H2 surface brightness and relative brightness of [Fe II] versus H2 emission lines. The H2 emission from HH 7 is assumed to originate in a bow shock with decreasing shock velocity from the bow shock apex to the wings. Spectra are taken across HH 7 using a series of slit positions in order to observe any changes in the spectra with velocity. The slit positions are chosen to include a wide range in shock conditions among the spectra; however, the H2 line ratios are similar at all of the observed positions, a result interpreted as evidence that the emission originates behind J-shocks.
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