the clumps identified in strongly lensed $z\sim
$1.5–3 galaxies from @Jones10 and @Stark08.

Despite the scatter, the radius–$\sigma$ and $\sigma$–Luminosity relations of the high-redshift clumps approximately follow the same scaling relations as those locally, but extending up to $\sim $kpc scales. Indeed, including all of the data-points in the fits, we derive the scaling between size ($r$), luminosity ($L$) and velocity dispersion ($\sigma$) of $$\log\left(\frac{r}{\rm kpc}\right)\,=\,(1.01\,\pm\,0.08)\,\log\left(\frac{\sigma}{\rm km\,s^{-1}}\right)\,+\,(0.8\,\pm\,0.1)
  \label{eqn:rs}$$ and $$\log\left(\frac{L}{\rm erg\,s^{-1}}\right)\,=\,(3.81\,\pm\,0.29)\log\left(\frac{\sigma}{\rm km\,s^{-1}}\right)\,+\,(34.7\pm0.4)
  \label{eqn:Ls}$$ Equation  \[eqn:rs\] suggests $\sigma\propto R$. If the clouds are self-gravitating clouds with $\sigma\propto R$, then the virial density is constant. The relation L$\propto\sigma^{3.81\pm0.29}$ is in reasonable agreement with the early work from @Terlevich81, and steeper than that found for super-giant H[ii]{} regions in local galaxies [@Rozas06], although the large error bars (on both the local and high-redshift data) preclude any firm conclusions. Clearly a larger sample is required to confirm this result and/or test whether the scatter in the data is intrinsic.

If the star-forming regions we have identified are short lived, then these scaling relations effectively reflect initial collapse conditions of the clump as it formed, since a clump can not evolve far from those initial conditions [e.g.  @Ceverino10]. In this case, the relation between radius, 