deletions | additions       diff --git a/The_stellar_clusters_are_well__.tex b/The_stellar_clusters_are_well__.tex  index a3dfbdc..73a6429 100644  --- a/The_stellar_clusters_are_well__.tex  +++ b/The_stellar_clusters_are_well__.tex 
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The stellar clusters are well described by a truncation for the three outer bins \cite{Adamo_2015}. The indices found for the GMCs are along the same magnitude as those found for GMCs in other nearby galaxies \cite{Fukui_2010}. The indices are smaller than those for the stellar clusters in M83 but similarly increase outwards (Table 1).  \begin{table}   \begin{tabular}{ c c c c c c c c c c}  Bin & GMC $\alpha$ & R & p & GMC $M_c$ & GMC $M_s$ & Largest GMC & 5th largest GMC & Stellar cluster $\alpha$ & Stellar cluster $M_c$ \\ (kpc) & & & & ($10^6$ M$_\odot$) & ($10^6$ M$_\odot$) & ($10^6$ M$_\odot$) & ($10^6$ M$_\odot$) & & ($10^5$ M$_\odot$) \\  0-0.45 & -1.37 & -18.5 & 1.2e-9 & 33.4 & & 47.7 & 22.0 & N/A & N/A \\   0.45-2.3 & -1.65 & -33.9 & 2.2e-16 & 4.95 & & 19.4 & 6.82 & -1.90 & 4.00\\  
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3.2-3.9 & -1.75 & -4.12 & 0.0041 & 3.34 & & 7.59 & 2.38 & -2.20 & 0.55\\   3.9-4.5 & -1.84 & -2.69 & 0.020 & 2.24 & & 3.84 & 1.48 & -2.70 & 0.25\\   \end{tabular}   \caption{The power law indices $\alpha$ and truncation masses $M_c$ for giant molecular clouds properties of GMCs  and stellar clusters (from Adamo et al. 2015) in M83, for  bins of equal area. The properties Values  were derived for clouds more massive than $3\times 10^5 M_\odot$, and clusters more massive than 5000 M$_\odot$.} \end{table}  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: