deletions | additions       diff --git a/Correlations_of_these_macroscopic_properties__.tex b/Correlations_of_these_macroscopic_properties__.tex  index 7cb2968..c5ee34b 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{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 $\langle \Sigma \rangle = 300  M_{\odot}\mbox{ pc}^{-2}$ but clouds inside this radius have a median surface density of $\langle \Sigma \rangle = 1100 M_{\odot}\mbox{ pc}^{-2}$. 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 the Milky Way relations. This relationship is roughly equivalent to the relationship plotted in Figure \ref{larson_figure}a.