The Lyman-$\alpha$ forest in optically-thin hydrodynamical simulations

We study the statistics of the Lyman-$\alpha$ forest in a flat LCDM cosmology with the N-body + Eulerian hydrodynamics code Nyx. We produce a suite of simulations, covering the observationally relevant redshift range $2 \leq z \leq 4$. We find that a grid resolution of 20 kpc/h is required to produce one percent convergence of Lyman-$\alpha$ flux statistics, up to k = 10 h/Mpc. In addition to establishing resolution requirements, we study the effects of missing modes in these simulations, and find that box sizes of L > 40 Mpc/h are needed to suppress numerical errors to a sub-percent level. Our optically-thin simulations with the ionizing background prescription of Haardt & Madau (2012) reproduce an IGM equation of state with $T_0 \approx 10^4 K$ and $\gamma \approx 1.55$ at z=2, with a mean transmitted flux close to the observed values. When using the ionizing background prescription of Faucher-Giguere et al. (2009), the mean flux is 10-15 per cent below observed values at z=2, and a factor of 2 too small at z = 4. We show the effects of the common practice of rescaling optical depths to the observed mean flux and how it affects convergence rates. We also investigate the common practice of `splicing' results from a number of different simulations to estimate the 1D flux power spectrum and show it is accurate at the 10 percent level. Finally, we find that collisional heating of the gas from dark matter particles is negligible in modern cosmological simulations.