Pressure-driven fragmentation of clouds at high redshift
  The discovery of a hyper metal-poor star with total metallicity of $\le
10^{-5}$ Z$_\odot$, has motivated new investigations of how such objects can
form from primordial gas polluted by a single supernova. In this paper we
present a shock-cloud model which simulates a supernova remnant interacting
with a cloud in a metal-free environment at redshift $z=10$. Pre-supernova
conditions are considered, which include a multiphase neutral medium and H II
region. A small dense clump ($n=100$ cm$^{-3}$), located 40 pc from a 40
M$_\odot$ metal-free star, embedded in a $n=10$ cm$^{-3}$ ambient cloud. The
evolution of the supernova remnant (explosion energy $10^{52}$ erg) and its
subsequent interaction with the dense clump is examined. This is the first
study to include a comprehensive treatment of the non-equilibrium chemistry and
associated radiative cooling that is occurring at all stages of the shock-cloud
model. We have included a primordial chemistry network that covers the
temperature range $10-10^9$ K, and is coupled to thermal models of atomic &
molecular cooling. We find $\times10^{3}$ density enhancement of the clump (i.e
maximum density $\sim 78000$ cm$^{-3}$) within this metal-free model. This is
consistent with Galactic shock-cloud models considering solar metallicity gas
with equilibrium cooling functions. Despite this strong compression, the cloud
does not become gravitationally unstable. We find that the small cloud modelled
here is destroyed for shock velocities $\gtrsim 50\,$km s$^{-1}$, and not
significantly affected by shocks with velocity $\lesssim 30\,$km s$^{-1}$.
Rather specific conditions are required to make such a cloud collapse.
