We present the first systematic investigation of the [NeV] (14um/24um) and [SIII] (18um/33um) infrared line flux ratios, traditionally used to estimate the density of the ionized gas, in a sample of 41 Type 1 and Type 2 active galactic nuclei (AGNs) observed with the Infrared Spectrograph on board Spitzer. The majority of galaxies with both [NeV] lines detected have observed [NeV] line flux ratios consistent with or below the theoretical low density limit, based on calculations using currently available collision strengths and ignoring absorption and stimulated emission. We find that Type 2 AGNs have lower line flux ratios than Type 1 AGNs and that all of the galaxies with line flux ratios below the low density limit are Type 2 AGNs. We argue that differential infrared extinction to the [NeV] emitting region due to dust in the obscuring torus is responsible for the ratios below the low density limit and we suggest that the ratio may be a tracer of the inclination angle of the torus to our line of sight. Because the temperature of the gas, the amount of extinction, and the effect of absorption and stimulated emission on the line ratios are all unknown, we are not able to determine the electron densities associated with the [NeV] line flux ratios for the objects in our sample. We also find that the [SIII] emission from the galaxies in our sample is extended and originates primarily in star forming regions. Since the emission from low-ionization species is extended, any analysis using line flux ratios from such species obtained from slits of different sizes is invalid for most nearby galaxies.
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