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Erik Rosolowsky edited section_Discussion_We_compare_the__.tex
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\section{Discussion}
\subsection{Mass Scales in M83}
We compare the characteristic masses and slopes derived from the empirical distributions to the characteristic masses produced by the Jeans instability and the Toomre instability. The Jeans instability is the characteristic fragmentation mass for a thin sheet of mass with support from a velocity distribution $\sigma_v$ and surface mass density $\Sigma$. Such a sheet will fragment into the characteristic (2D) Jeans mass for the system:
\begin{equation}
M_{J} = \frac{\sigma_v^4}{\pi G^2 \Sigma}.