On the operation of the chemothermal instability in primordial
  star-forming clouds
  We investigate the operation of the chemothermal instability in primordial
star-forming clouds with a suite of three-dimensional, moving-mesh simulations.
In line with previous studies, we find that the gas at the centre of
high-redshift minihaloes becomes chemothermally unstable as three-body
reactions convert the atomic hydrogen into a fully molecular gas. The
competition between the increasing rate at which the gas cools and the
increasing optical depth to H2 line emission creates a characteristic dip in
the cooling time over the free-fall time on a scale of 100 au. As a result, the
free-fall time decreases to below the sound-crossing time, and the cloud may
become gravitationally unstable and fragment on a scale of a few tens of au
during the initial free-fall phase. In three of the nine haloes investigated,
secondary clumps condense out of the parent cloud, which will likely collapse
in their own right before they are accreted by the primary clump. In the other
haloes, fragmentation at such an early stage is less likely. However, given
that previous simulations have shown that the infall velocity decreases
substantially once the gas becomes rotationally supported, the amount of time
available for perturbations to develop may be much greater than is evident from
the limited period of time simulated here.
