deletions | additions       diff --git a/section_Analysis_subsection_GMC_properties__.tex b/section_Analysis_subsection_GMC_properties__.tex  index 65a3b2c..dee0f35 100644  --- a/section_Analysis_subsection_GMC_properties__.tex  +++ b/section_Analysis_subsection_GMC_properties__.tex 
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\end{equation}  where $\alpha_{\mathrm{CO}}=4.35 M_{\odot}\mbox{ pc}^{-2}~\mathrm{(K~km~s^{-1})^{-1}}$. The velocity dispersion is the linearly-extrapolated, emission-weighted second moment of the velocity axis, corrected for the channel width. Similarly radius of the cloud is the root-mean-square of the linearly-extrapolated, emission-weighted second moments of the major and minor spatial axis of the emission. The radius is also corrected for the instrumental response by assuming an elliptical beam and subtracting its width in quadrature. See Rosolowsky \& Leroy (2006) for details. The algorithm corrects for the case where the beam and cloud position angles are not aligned.   The virial mass of the cloud is calculated from the radius and line width of the molecular cloud: $M_{\mathrm{vir}} = 5 \sigma^2 R/G$. Comparing the virial and luminous masses gives insight to the dynamical nature of the molecular clouds identified in the data. The average surface density is calculated from the luminous mass $\Sigma = M_{\mathrm{lum}}/(\pi R^2)$.Correlations of these macroscopic properties give clues to the nature of the molecular medium. We compare the properties of the molecular clouds to those seen in the Milky Way study of \citet[][;S87]{Solomon_1987} because that work measured GMC properties using similar techniques as we do here. In Figure XXX, we correlate the GMC properties and compare the result to the trend lines seen in the S87 data. First, we see that there is good agreement between the virial and luminous masses in these clouds, and this is seen throughout the system. We code each datum with the galactocentric assuming each cloud   The figure shows that the objects we identify can be associated with Milky Way molecular clouds. They have comparable sizes and mass scales, and they show the same underlying  \citet{Solomon_1987} examined GMCs in the Milky Way and described a few key relationships that characterize the properties of these clouds. We derived these properties for the M83 clouds to be confident that they are GMCs.  The M83 GMCs exhibit a similar relationship for velocity line width $\mathrm{\sigma}$ to radius $R$ as the Milky Way GMCs, which have a fit of $\sigma=\left(\frac{\pi^{1/2}R}{3.4}\right)^{0.5}$ kms$^{-1}$ (\ref{fig:rdv}). This allows us to conclude the clouds are in virial equilibrium \cite{Solomon_1987}. The virial mass $M_\mathrm{vir}$ can then be calculated from the size and velocity dispersion, while the luminous mass $M_\mathrm{lum}$ can be calculated from the luminosity and X$_\mathrm{CO}$ \cite{Rosolowsky_2006}. These masses for M83 conform to a 1:1 ratio as expected (\ref{fig:mlummvir}). Finally, the luminous mass to radius relationships are also consistent with previous findings, with \citet{Solomon_1987} finding a fit of $M=540R^2 (M_\odot)$ (\ref{fig:rm}). From this we can infer that the observations in M83 are of GMCs.