The First Stars: formation under cosmic ray feedback
  We explore the impact of a cosmic ray (CR) background generated by supernova
explosions from the first stars on star-forming metal-free gas in a minihalo at
$z\sim25$. Starting from cosmological initial conditions, we use the smoothed
particle hydrodynamics code GADGET-2 to follow gas collapsing under the
influence of a CR background up to densities of $n=10^{12}\,{\rm cm}^{-3}$, at
which point we form sink particles. Using a suite of simulations with two sets
of initial conditions and employing a range of CR background models, we follow
each simulation for $5000\,$yr after the first sink forms. CRs both heat and
ionise the gas, boosting ${\rm H}_2$ formation. Additional ${\rm H}_2$ enhances
the cooling efficiency of the gas, allowing it to fulfil the Rees-Ostriker
criterion sooner and expediting the collapse, such that each simulation reaches
high densities at a different epoch. As it exits the loitering phase, the
thermodynamic path of the collapsing gas converges to that seen in the absence
of any CR background. By the time the gas approaches sink formation densities,
the thermodynamic state of the gas is thus remarkably similar across all
simulations. This leads to a robust characteristic mass that is largely
independent of the CR background, of order $\sim$ a few $\times10\,{\rm
M}_{\odot}$ even as the CR background strength varies by five orders of
magnitude.
