mass densities of the clumps are similar to those inferred from their velocity dispersions and sizes.

Finally, @Hopkins12b (see also @Escala08 and @Livermore12a) show that for a marginally stable disk of finite thickness, density structures on scales greater than $h$ will tend to be stabilised by rotation which leads to an exponential cut off of the clump mass function above $$M_0\,\simeq\,\frac{4\pi}{3}\,\rho_c(h)\,h^3\,=\,\frac{3\,\pi\,G^2}{2}\frac{\Sigma_{\rm disk}^3}{\kappa^4}
  \label{eqn:M0_1}$$ or $$\frac{M_0}{M_{\odot}}\,=\,8.6\,\times\,10^{3}\left(\frac{\Sigma_{\rm disk}}{\rm 10\,M_{\odot}\,pc^{-2}}\right)^3\,\left(\frac{\kappa}{\rm 100\,km\,s^{-1}\,kpc}\right)^{-4}
  \label{eqn:M0_2}$$ This suggests that the most massive clumps that can form in a disk (“the cut off mass”) depends strongly on the disk surface density – increasing the disk surface density increases mass of the clumps that are able to form [e.g.  @Escala11]. However, there is also a competing (stabilising) factor from the epicyclic frequency such that a fixed radius, higher circular velocities reduce the mass of the largest clumps able to form.

Applying equation \[eqn:M0\_2\] to the Milky-Way, with a cold molecular gas fraction of 10%, $f_{\sigma}$=2 [@Korchagin03], the average surface density is $\Sigma_{\rm
  disk}$=35M$_{\odot}$pc$^{-2}$ and for $\kappa$=220kms$^{-1}$/8kpc [@Feast97] the cut off mass should be $M_0\sim$10$^7$M$_{\odot}$, in good agreement with the characteristic mass of the largest galactic GMCs [e.g.  @Stark06]

How does the cut-off mass for our high-redshift sample compare to 