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Christer Watson edited Results.tex
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\section{Results}
Eighteen sources displayed emission greater than 3$\sigma$. A typical spectrum is shown in Figure \ref{N92spectrum}. Emission lines were fit using the standard Gaussian fitting routine in GBTIDL. Fitting parameters (amplitude in T$_A^*$ units, central velocity and velocity width) are listed in Table \ref{fitting}. For sources that displayed a double peak, two simultaneous gaussian functions were fit to the emission and are listed in consecutive rows. Column densities were calculated assuming LTE, optically thin emission and an excitation temperature T$_{ex}$=15 K. CS has been observed to be optically thick (citation), which would make our calculated column density a lower limit. Given these assumptions we used the following
relations: relation:
\begin{equation}
N(mol) = \frac{3 k_B \epsilon_0}{2 \pi^2}\frac{1}{\nu \mu^2_{el}S}\frac{Z_{rot}(T_{ex})}{g_K g_I}\frac{e^{E_u/k_B T_{ex}}}{1-\frac{F(T_{bg})}{F(T_{ex})}}\int T_{MB}dv
\end{equation}
where
\begin{eqnarray}
g_K= g_I = 1\\
\mu^2_{el} S = 3.8 Debye^2\\
Z_{rot} = .8556 T_{ex}-0.10\\
F(T) = \frac{1}{e^{h\nu/k_BT}-1\\
\end{eqnarray}
\begin{table}[]
\label{fitting}
\caption{Gaussian fitting parameters for CS detections.}