deletions | additions       diff --git a/The_stellar_clusters_are_well__.tex b/The_stellar_clusters_are_well__.tex  index fccd536..6a90681 100644  --- a/The_stellar_clusters_are_well__.tex  +++ b/The_stellar_clusters_are_well__.tex 
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\end{equation}  Similarly, a thin shearing disk with rotation curve $V(R)$ as a function of galactocentric radius $R$ will fragement into a characteristic mass set by the Toomre instability. The characteristic scale of the Toomre instability is $\lambda_T = 4\pi^2 G \Sigma \varkappa^{-1}$ where $\varkappa$ is the epicyclic frequency.   Measuring $\sigma_v$ and $\varkappa$ for the gas disk requires measuring the rotation curve.  We compare adopt  the results rotation curve analysis  of our method \citet{Lundgren_2004}, who used low resolution ($27''$) CO mapping to derive a rotation curve. They find the rotation curve is well modeled by an exponential disk. We confirm this by using their kinematic parameters (i.e., inclination and position angle)  to estimate the amplitudes of the rotational motion for the {\sc Hi} 21-cm map of the galaxy that is part of the THINGS \cite{Walter_2008} survey. In Figure \ref{fig:profiles}, we show \citet{Lundgren_2004} rotation curve and the median absolute deviation of inferred rotational velocities for the 21-cm data around the rotation curve (grey region).