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P 3 M-SPH simulations of the Lyman-α Forest

We investigate the importance of several numerical artifacts such as lack of resolution on spectral properties of the Lyman-α -forest as computed from cosmological hydrodynamic simulations in a standard cold dark matter universe. We use a new simulation code which is based on a combination of a hierarchical particle-particle– particle-mesh (P3M) scheme for gravity and smoothed particle hydrodynamics (SPH) for gas dynamics. We have performed extensive comparisons between this new code and a modified version of the HYDRA code of Couchman et al. and find excellent agreement. We have also rerun the TREESPH simulations of Hernquist et al. using our new codes and find very good agreement with their published results. This shows that results from hydro dynamical simulations that include cooling are reproducible with different numerical algorithms. We then use our new code to investigate several numerical effects such as resolution on spectral statistics deduced from Voigt profile fitting of lines by running simulations with gas particle masses of 1.4× 10, 1.8× 10, 2.2 × 10 and 2.1 × 105M⊙. When we increase the numerical resolution the mean effective hydrogen optical depth converges and so does the column density distribution. However, higher resolution simulations produce narrower lines and consequently the b-parameter (velocity width) distribution has only marginally converged in our highest resolution run. Obtaining numerical convergence for the mean Heii transmission is demanding. When progressively smaller halos are resolved at better resolution, a larger fraction of low density gas contracts to moderate over densities in which Heii is already optically thick, and this increases the net transmission, making it difficult to simulate Heii reliably. Our highest resolution simulation gives a mean effective optical depth in Heii 5% lower than the simulation with eight times lower mass resolution, illustrating the degree to which the Heii optical depth has converged. In contrast, the hydrogen mean optical depth for these runs is identical. Since many properties of the simulated Lyman-α -forest depend on resolution, one should be careful when deducing physical parameters from a comparison of the simulated forest with the observed one. We compare predictions from our highest resolution simulation in a cold dark matter universe with a photo-ionising background inferred from quasars as computed by Haardt & Madau (1996), with observations. The simulation reproduces both the Hi column density and b-parameter distribution when we assume a high baryon density, ΩBh 2 > ∼ 0.028. In addition we need to impose a higher IGM temperature than predicted within our basic set of assumptions. We argue that such a higher temperature could be due to differences between the assumed and true reionization history. The simulated Hi optical depth is in good agreement with observations but the Heii optical depth is lower than observed. Fitting the Heii optical depth requires a larger jump ∼ 14 between the photon flux at the Hi and Heii edge than is present in the Haardt & Madau spectrum.