Probing the Universe with the Lyα forest -: I.: Hydrodynamics of the low-density intergalactic medium

We introduce an efficient and accurate alternative to full hydrodynamic simulations, hydro-PM (HPM), for the study of the low column density Ly alpha forest (N-HI less than or similar to 10(14) cm(-2)). It consists of a particle mesh (PM) solver, modified to compute, in addition to the gravitational potential, an effective potential due to the gas pressure. Such an effective potential can be computed from the density field because of a tight correlation between density and pressure in the low-density limit (delta less than or similar to 10), which can be calculated for any photo-re-ionization history by a method outlined by Hui & Gnedin. Such a correlation exists, in part, because of minimal shock heating in the low-density limit. We compare carefully the density and velocity fields as well as absorption spectra, computed using HPM versus hydrodynamic simulations, and find good agreement. We show that HPM is capable of reproducing measurable quantities, such as the column density distribution, computed from full hydrodynamic simulations, to a precision comparable to that of observations. We discuss how, by virtue of its speed and accuracy, HPM can enable us to use the Ly alpha forest as a cosmological probe. We also discuss in detail the smoothing of the gas (or baryon) fluctuation relative to that of the dark matter on small scales due to finite gas pressure. First, it is shown that the conventional wisdom that the linear gas fluctuation is smoothed on the Jeans scale is incorrect for general re-ionization (or reheating) history; the correct linear filtering scale is in general smaller than the Jeans scale after reheating, but larger prior to it. Secondly, it is demonstrated that in the mildly non-linear regime, a PM solver, combined with suitable pre-filtering of the initial conditions, can be used to model the low-density IGM. However, such an approximation is shown to be less accurate than HPM, unless a non-uniform pre-filtering scheme is implemented.