Testing the accuracy of the hydrodynamic particle-mesh approximation in numerical simulations of the Lyman α forest

We implement the hydrodynamic particle-mesh (HPM) technique in the hydrodynamical sim- ulation code GADGET-2 and quantify the differences between this approximate method and full hydrodynamical simulations of the Lyman α forest in a concordanceCDM (cold dark matter) model. At redshifts z = 3 and 4, the differences between the gas and dark matter distributions, as measured by the one-point distribution of density fluctuations, the density power spectrum and the flux power spectrum, systematically decrease with increasing resolution of the HPM simulation. However, reducing these differences to less than a few per cent requires a signif- icantly larger number of grid cells than particles, with a correspondingly larger demand for memory. Significant differences in the flux decrement distribution remain even for very high- resolution HPM simulations, particularly at low redshift. At z = 2, the differences between the flux power spectra obtained from HPM simulations and full hydrodynamical simulations are generally large and of the order of 20-30 per cent, and do not decrease with increasing resolution of the HPM simulation. This is due to the presence of large amounts of shock-heated gas, a situation which is not adequately modelled by the HPM approximation. We confirm the results of Gnedin & Hui that the statistical properties of the flux distribution are discrepant by 5-20 per cent when compared to full hydrodynamical simulations. The discrepancies in the flux power spectrum are strongly scale- and redshift-dependent and extend to large scales. Considerable caution is needed in attempts to use calibrated HPM simulations for quantitative predictions of the flux power spectrum and other statistical properties of the Lyman α forest.