deletions | additions       diff --git a/Correlations_of_these_macroscopic_properties__.tex b/Correlations_of_these_macroscopic_properties__.tex  index 0d59250..a00d9be 100644  --- a/Correlations_of_these_macroscopic_properties__.tex  +++ b/Correlations_of_these_macroscopic_properties__.tex 
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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 \ref{larson_figure}, we correlate the GMC properties and compare the result to the trends seen in the S87 data. First, we see (panel a) that there is good agreement between the virial and luminous masses in these clouds, and this is seen throughout the system. We color each datum by the galactocentric radius to highlight the variation in cloud properties across the face of the disk. The most massive clouds are found in the center of the galaxy, but these extreme clouds still show good agreement between the two mass estimates. Both mass estimates will be subject to $\sim 0.3~\mathrm{ dex}$ uncertainties, but even in high quality data, there remains about 0.5 dex of scatter \cite{Heyer_2009}.   The radius-velocity dispersion plot (Figure \ref{larson_figure}b) shows the size-line width scalings in these clouds. The Milky Way relationship shows a good lower bound for the population, but there is significant scatter to higher line widths at a give radius. These offset clouds are found in the center of the galaxy, and are also associated with the higher mass clouds. Such objects are typically seen in molecule rich environments, where the surface densities of clouds increase significantly \citep{Oka_2001,Rosolowsky_2005,Heyer_2009,Leroy_2015}. Such clouds are also seen as outliers in the mass-radius plot (Figure \ref{larson_figure}c). Clouds at $R_{\mathrm{gal}}>0.5\mbox{ kpc}$ have a median surface density of $\langle \Sigma \rangle = M_{\odot}\mbox{ pc}^{-2}$ but clouds inside this radius have a median surface density of $\langle \Sigma \rangle = 1100 M_{\odot}\mbox{ pc}^{-2}$.  The figure Even with these changes across the face of the galaxy, the clouds all appears to show gravitational binding energies comparable to their kinetic energies. Figure \ref{larson_figure}d shows the correlation between surface density and the turbulent line width on 1 pc scales $\sigma_0 = \sigma_v/R^{1/2}$ (the $y$-axis  shows the square of this quantity). \citet{Heyer_2009} noted  that these quantities correlate even in clouds which show line widths and surface densities that depart significantly from  theobjects we identify can be associated with  Milky Way molecular clouds. They have comparable sizes and mass scales, and they show relations. This relationship is roughly equivalent to  the same underlying relationship plotted in Figure \ref{larson_figure}a.  \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 From this analysis, we conclude  that they we  are GMCs.  The M83 observing  GMCs exhibit a similar relationship for velocity line width $\mathrm{\sigma}$ that show properties comparable  to radius $R$ as those found in  the Milky Way GMCs, which have a fit Way, though we see real variations across the face  of$\sigma=\left(\frac{\pi^{1/2}R}{3.4}\right)^{0.5}$ kms$^{-1}$ (\ref{fig:rdv}). This allows us to conclude  the galaxy. In particular  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 located within 500 pc of  the luminosity galaxy center have significantly higher line widths  and X$_\mathrm{CO}$ \cite{Rosolowsky_2006}. These masses surface densities  forM83 conform to  a 1:1 ratio as expected (\ref{fig:mlummvir}). Finally, given radius, but  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 local increases in these quantities in the galaxy center balance such  that the observations in M83 are of GMCs. clouds retain a good balance between gravitational and kinetic energies.