Results

CS Point Sources

Eighteen sources displayed emission greater than 3\(\sigma\). A typical spectrum is shown in Figure \ref{N92spectrum}. Emission lines were fit using fitgauss, the standard Gaussian fitting routine in GBTIDL. Fitting parameters (amplitude in T\({}_{mb}\) units, central velocity and FWHM) 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. CS column densities, \(N_{CS}\), were calculated assuming LTE, optically thin emission and an excitation temperature T\({}_{ex}\)=15 K, a typical ISM value (see review in \citet{Zinnecker2007}). Increasing or decreasing the assumed excitation temperature by 5 K changes the column density by about 30%. If CS(1-0) is optically thick, as we assume for three sources in section 4.2 below, then our calculation would be a lower limit. Given these assumptions we used the following relation (see \citet{Miettinen2012} for a detailed discussion of the relations below):

\begin{equation} N_{CS}=\frac{3k_{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\nonumber \\ \end{equation}

where

\begin{aligned} g_{K}=g_{I} & =1 & \nonumber \\ \mu^{2}_{el}S & =3.8\;\mathrm{Debye}^{2} & \nonumber \\ Z_{rot} & =.8556\;T_{ex}-0.10 & \nonumber \\ F(T) & =\frac{1}{e^{h\nu/k_{B}T}-1}. & \nonumber \\ \end{aligned}

Here \(\epsilon_{0}\) is the vacuum permittivity, \(\mu_{el}\) is the permanent electric dipole moment, S is the line strength, Z\({}_{rot}\) is the rotational partition function, \(\nu\) is the frequency, g\({}_{K}\) is the K-level degeneracy, g\({}_{I}\) is the reduced nuclear spin degeneracy, E\({}_{u}\) is the energy of the upper-transition state, T\({}_{ex}\) is the excitation temperature and T\({}_{bg}\) is the background temperature. The dipole moment line strength (\(\mu^{2}_{el}\) S) is taken from the JPL spectral line catalog \citep{Pickett1998}. The partition function (Z\({}_{rot}\)) is a linear fit to JPL data between T=37 to 75 K. T\({}_{bg}\) was taken to be the cosmic microwave background temperature, 2.725 K. The uncertainty in the fit amplitudes and derived column densities is dominated by our flux-calibration uncertainty. Since the relationships are linear, we estimate the uncertainty in both as 20%.