deletions | additions       diff --git a/Correlations_of_these_macroscopic_properties__.tex b/Correlations_of_these_macroscopic_properties__.tex  index c5ee34b..c6e30ed 100644  --- a/Correlations_of_these_macroscopic_properties__.tex  +++ b/Correlations_of_these_macroscopic_properties__.tex 
...
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 appear  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 that  show line widths and surface densities that depart significantly from the Milky Way relations. This relationship is thus  roughly equivalent to the relationship plotted in Figure \ref{larson_figure}a. From this analysis, we conclude that we are observing GMCs that show properties comparable to those found in the Milky Way, though we see real variations across the face of the galaxy. In particular clouds located within 500 pc of the galaxy center have significantly higher line widths and surface densities for a given radius, but the local increases in these quantities in the galaxy center balance such that the clouds retain a good balance between gravitational and kinetic energies.