deletions | additions       diff --git a/sectionAnalysis__sub.tex b/sectionAnalysis__sub.tex  index 8fdb253..7d74ad0 100644  --- a/sectionAnalysis__sub.tex  +++ b/sectionAnalysis__sub.tex 
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In order to calculate the abundance of CS, we first must estimate the total gas column density along each line of sight. We used FIR {\bf (60$\mu$m-600$\mu$m)} imaging taken as part of the HiGal survey. Within CASA, we measured the integrated emission in all five survey bands in regions exactly coincident with the GBT beamsize, centered at each source of CS emission. The emission was then modeled as a modified blackbody:  \begin{equation*}  B_{mod} =B_0 \frac{h^2\nu^{3+\beta}}{c^3}\frac{1}{e^{\frac{h\nu}{kT}}-1} \frac{2 h \nu^{3+\beta}}{c^3}\frac{1}{e^{\frac{h\nu}{kT}}-1}  \end{equation*}  where $\beta$ is assumed to be 2 \citep{Desert2008}. B$_0$ and T were taken as free parameters and a Levenberg{\textendash}Marquardt algorithm was used to find the best-fit. The fitting was done to the flux density in Jy, so B$_0$ carries these units. The total column density was calculated following Miettinen \& Harju (2010). Briefly, we used the following relations: 
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\kappa = \kappa_{1.3mm} \left(\frac{\lambda}{1.3mm}\right)^{-\beta}\\  \end{eqnarray*}  where {\bf m$_H$ is the mass of hydrogen} and  3.73 x 10$^{-16}$ converts the surface brightness from Jy/(1\arcsec beam) to SI units. We make the following assumptions: $\kappa_{1.3mm}$ = 0.11 $\frac{m^2}{kg}$, appropriate for ice-covered dust grains from OH94, $\theta$=15.0\arcsec , the beamsize of the GBT at 49 GHz, the mean molecular weight $\mu$ = 2.3 and dust to mass ratio $R_d$ = 1/100. Note that B$_\nu$, B$_{mod}$ and $\kappa$ all require a choice of frequency or wavelength. However, these dependencies cancel in the final calculation of N$_{tot}$. These results are summarized in Table \ref{mbb}, where we report the flux density at five wavelength bands for each CS detection, the best-fit temperature, the total column density and the CS abundance. We estimate the error in determining the extended flux to be dominated by defining the edge of the object. The GBT beam is formally tapered along the edges to minimize ringing in the side-lobes. We have used a simple cut-off at the edge of the beam. This difference in beam produces a 20\% uncertainty in the fluxes reported below. To estimate the uncertainty in the model results, we fit the data after adjusting the fluxes either up or down by the 20\% uncertainty. The results indicate an uncertainty of 4 K in temperature and 20\% in column density. For those sources where the modified blackbody model was a poor fit, as judged by eye, we have excluded the temperature, column density and abundance. The cause for the poor fit in these cases appeared to be caused by the Herschel band emission extending well outside the the GBT beam. For these poorly-fit sources, the fluxes reported here probably do not represent the emission from the same object. For those sources with a double-Gaussian CS line profile, we add the CS column densities calculated using both Gaussians. If this shape is caused by optical depth effects, as we discuss below, than the reported column density would be a lower limit.