Analysis

If the absorption coefficients of two lines (one of which is assigned and thus has known lower state energy and linestrength) are measured at two temperatures, the lower state energy and line strength for the unassigned line can be calculated [1]. Since these reference lines have known strengths $S_{ij}\mu^2$ and lower state energy levels $E_l$ from the QM analyses, and Doppler widths $d\nu_D$ and line frequencies $n_0$ from the known temperature and measured frequencies of our experiment, we can use a fit of their measured peak absorbance, $$\begin{equation}A_{peak} = L\alpha_{peak}\left(T \right) = \frac{nL}{Q}\frac{8\pi^3}{3ch}\left(1 - e^{-\frac{h\nu_0}{kT}}\right)S_{ij}\mu^2e^{-\frac{E_l}{kT}}\sqrt{\frac{ln(2)}{\pi}}\frac{\nu_0}{\delta\nu_D}\end{equation}$$ to obtain the spectroscopic temperature $T$ and $nL/Q$, where $n$ is the number density of the molecules, $L$ the effective path length of the spectroscopic cell, and $Q$ the molecular partition function. This fit is performed for each of the 400 - 1200 spectra obtained over the temperature range.

Next we use two complimentary analysis procedures, both based on the equation above to provide astrophysically meaningful data.