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A B S T R A C TWe investigate the importance of several numerical artefacts such as lack of resolution on spectral properties of the Lya 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 hydrodynamical 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 8 , 1:8 × 10 7 , 2:2 × 10 6 and 2:1 × 10 5 M ᭪ . 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 He ii transmission is demanding. When progressively smaller haloes are resolved at better resolution, a larger fraction of low-density gas contracts to moderate overdensities in which He ii is already optically thick, and this increases the net transmission, making it difficult to simulate He ii reliably. Our highest resolution simulation gives a mean effective optical depth in He ii 5 per cent lower than the simulation with eight times lower mass resolution, illustrating the degree to which the He ii optical depth has converged. In contrast, the hydrogen mean optical depth for these runs is identical. As many properties of the simulated Lya 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 photoionizing background inferred from quasars as computed by Haardt & Madau, with observations. The simulation reproduces both the H I column density and b parameter distribution when we assume a high baryon density, Q B h 2 տ 0:028. In addition we need to impose a higher intergalactic medium (IGM) temperature than predicted within our basic set of assumptions. We argue that such a higher temperature could be caused by differences between the assumed and true reionization history. The simulated H I optical depth is in good agreement with observations, but the He ii optical depth is lower than observed. Fitting the He ii optical depth requires a larger jump, ϳ14, b...

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