Modelling the Lyman-α forest with Eulerian and SPH hydrodynamical methods

We compare two state-of-the-art numerical codes to study the overall accuracy in modelling the intergalactic medium and reproducing Lyman-α forest observables for DESI and high-resolution data sets. The codes employ different approaches to solving both gravity and modelling the gas hydrodynamics. The first code, Nyx, solves the Poisson equation using the Particle-Mesh (PM) method and the Euler equations using a finite-volume method. The second code, CRK-HACC , uses a Tree-PM method to solve for gravity, and an improved Lagrangian smoothed particle hydrodynamics (SPH) technique, where fluid elements are modelled with particles, to treat the intergalactic gas. We compare the convergence behaviour of the codes in flux statistics as well as the degree to which the codes agree in the converged limit. We find good agreement overall with differences being less than observational uncertainties, and a particularly notable ≲1 per cent agreement in the 1D flux power spectrum. This agreement was achieved by applying a tessellation methodology for reconstructing the density in CRK-HACC instead of using an SPH kernel as is standard practice. We show that use of the SPH kernel can lead to significant and unnecessary biases in flux statistics; this is especially prominent at high redshifts, z ∼ 5, as the Lyman-α forest mostly comes from lower-density regions that are intrinsically poorly sampled by SPH particles.