Convergence of small scale Ly\(\alpha\) structure at high-\(z\) under different reionization scenarios

The Ly\(\alpha\) forest (LAF) at \(z>5\) probes the thermal and reionization history of the intergalactic medium (IGM) and the nature of dark matter, but its interpretation requires comparison to cosmological hydrodynamical simulations. At high-\(z\), convergence of these simulations is more exacting since transmission is dominated by underdense voids that are challenging to resolve. With evidence mounting for a late end to reionization, small structures down to the sub-kpc level may survive to later times than conventionally thought due to the reduced time for pressure smoothing to impact the gas, further tightening simulation resolution requirements. We perform a suite of simulations using the Eulerian cosmological hydrodynamics code Nyx, spanning domain sizes of 1.25-10 \(h^{-1}\) Mpc and 5-80 \(h^{-1}\) kpc cells, and explore the interaction of these variables with the timing of reionization on the properties of the matter distribution and the simulated LAF at \(z=5.5\). In observable Ly\(\alpha\) power, convergence within 10% is achieved for \(k< 0.1\) s/km, but larger \(k\) shows deviation of up to 20 percent. While a later reionization retains more small structure in the density field, because of the greater thermal broadening there is little difference in the convergence of LAF power between early (\(z=9\)) and later (\(z=6\)) reionizations. We conclude that at \(z\sim5.5\), resolutions of 10 kpc are necessary for convergence of LAF power at \(k