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Alison Crocker edited sectionAnalysis___su.tex
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\label{tab1}
\end{table}
Armed with this template, we fit the J=1 through J=4 lines with the template in order to determine the maximum likelihood scale factor. All observations (even formal non-detections) are taken into account in the likelihood calculation (part of the advantage of likelihood compared to chi2). Summing
this scaled template over
the its J=1 to J=7 lines gives total integrated intensities for the detected cold components ranging from x to x.
To obtain some empirical measure of any remaining higher-J emission after this cold template is removed from the CO SLEDS of our galaxies, we simply take the residual flux in the J=5,6,7 CO lines. We decline to fit a warm template, because there is no good motivation for assuming the warm portion of these SLEDS will have any particular form. In addition, there is simply not enough informaiton in the few J>4 detected lines to fit a RADEX model with 3 free parameters. Fig.~\ref{fig:warm_vs_cold} shows the relationship between the integrated intensity of the J=6 line compared to the summed integrated intensities of the fit cold component.
\subsection{CI and CO}