the excitation temperature does depend on the optical depth, and is quite different for  and . Nevertheless, the likely error in the trapping predicted by the LVG and other models is relatively modest compared to other uncertainties inherent in this analysis.

**\[!htbp\] ![image](f5.pdf)**

**\[!htbp\] ![image](f6.pdf)**

In mask 0, after averaging $\simeq$ 10$^6$ spatial pixels, we are able to detect both isotopologues, and we thus analyze the emission for the region as if it were a single spatial entity. The general analysis follows the procedure described above for mask 1. The fact that the integrated / ratio is $\simeq$ 19 indicates that the  is almost certainly optically thin. This is also the case for mask 1, and here as well results in the  and  having quite different excitation temperatures due to the radiative trapping for the more abundant isotopologue.

Again, we fix the kinetic temperature to be 15 K, reflecting increased heating in regions of low extinction, and assume that the average line width is 2 , similar to that observed for the low excitation gas of mask 1. Note that the average mask 0 spectrum (Figure \[3masks\_spectra\]) is much broader than 2 , but the large value of the line 