derived 2 density is a factor of 2.5 lower, for an assumed value of $R$. The same trends of carbon monoxide column density and 2 density as a function of $R$ are seen for the higher kinetic temperature as for the lower. The uncertainty resulting from the assumption of a fixed kinetic temperature is thus of the same order as resulting from our choosing a best value of $R$, and combining these could yield a factor of 2 uncertainty in $N$(CO). Observations of multiple transitions of carbon monoxide isotopologues would provide a more accurate estimate of the molecular column density. However, observations of these transitions over a region of comparable size would pose a formidable challenge for currently available telescopes and receiver systems.

To obtain the column density for each line of sight, we utilize an analytic fit to the relationship between the CO column density per unit line width and the excitation temperature obtained for the set of $T_{ex}$ bins, $N(^{12}CO)/\delta v = (-1.473\times 10^{16}+4.672\times 10^{15}T_{ex})$. We multiply the results by the observed FWHM  line width $\Delta v$ from the data. The use of the LVG model introduces some uncertainty because the carbon monoxide excitation is quite subthermal, and 