Modelling the IGM and the Lyα forest at high redshift from the dark matter distribution

A variety of approximate schemes for modelling the low-density intergalactic medium (IGM) in the high-redshift Universe are compared with the results of a large high-resolution hydrodynamical simulation. These schemes use either an analytical description of the dark matter distribution and the IGM or numerical simulations of the dark matter (DM) distributions combined with different approximate relations between dark matter field and the gas distribution. Schemes based on a filtering of the dark matter distribution with a global Jeans scale result in a rather poor description of the gas distribution. An adaptive filtering which takes into account the density/temperature dependence of the Jeans scale is required. A reasonable description of the gas distribution can be achieved using a fit of the mean relation between the dark matter and gas densities in the hydrodynamical simulation to relate dark matter and gas distribution. In the hydrodynamical simulations deviations from this mean relation are correlated with gradients in the dark matter peculiar velocity field indicative of shocks in the gas component. A scheme which takes into account this correlation results in a further improved gas distribution. Such adaptive filtering schemes applied to dark matter simulations will be very well suited for studies of statistical properties of the Lyalpha forest which investigate the IGM and the underlying dark matter distribution and require a large dynamic range and/or an extensive parameter study.