The First Stars: formation under X-ray feedback

We investigate the impact of a cosmic X-ray background (CXB) on Population III stars forming in a minihalo at $z\simeq25$. Using the smoothed particle hydrodynamics code GADGET-2, we attain sufficient numerical resolution to follow gas collapsing into the centre of the minihalo from cosmological initial conditions up to densities of $10^{12}\,{\rm cm}^{-3}$, at which point we form sink particles. This allows us to study how the presence of a CXB affects the formation of H$_2$ and HD in the gas prior to becoming fully molecular. Using a suite of simulations for a range of possible CXB models, we follow each simulation for 5000\yr after the first sink particle forms. The CXB provides two competing effects, with X-rays both heating the gas and increasing the free electron fraction, allowing more H$_2$ to form. X-ray heating dominates below $n\sim1\,{\rm cm}^{-3}$, while the additional H$_2$ cooling becomes more important above $n\sim10^2\,{\rm cm}^{-3}$. The gas becomes optically thick to X-rays as it exits the quasi-hydrostatic `loitering phase,' such that the primary impact of the CXB is to cool the gas at intermediate densities, resulting in an earlier onset of baryonic collapse into the dark matter halo. At the highest densities, self-shielding results in similar thermodynamic behaviour across a wide range of CXB strengths. Consequently, we find that star formation is relatively insensitive to the presence of a CXB; both the number and the characteristic mass of the stars formed remains quite similar even as the strength of the CXB varies by several orders of magnitude.