deletions | additions       diff --git a/why 12 gives good image but bad data.tex b/why 12 gives good image but bad data.tex  index 9305d03..56a080f 100644  --- a/why 12 gives good image but bad data.tex  +++ b/why 12 gives good image but bad data.tex 
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To correct for the fact that \textsuperscript{12}CO is opticaly thick, we use the following equation:  \begin{equation} \label{eqn:mass-energy} Tmb_12 T_{\rm mb 12}  / Tmb_13 T_{mb13}  = [12_CO] [^{12}{\rm CO}]  / [13_CO] [^{13}{\rm CO}]  * (1 - e ^ -tau_12) e^{-\tau_{12})  / tau_12\end{equation} \tau_{12}  \end{equation}  taken from the Dunhan paper. This provides a correction for the optical depth of each \textsuperscript{12}CO voxel based on the \textsuperscript{13}CO equivalent voxel. Using this scaling, we obtained the following results.