Probing the Universe with the Lyman-alpha Forest: I. Hydrodynamics of the Low Density IGM

We introduce an efficient and accurate alternative to full hydrodynamic simulations, Hydro-PM (HPM), for the study of the low column density Lyman-alpha forest. It consists of a Particle-Mesh 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, which can be calculated for any photo-reionization history by a method outlined in Hui & Gnedin (1997). 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 Lyman-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. It is shown the conventional wisdom that the linear gas fluctuation is smoothed on the Jeans scale is incorrect for general reionization (or reheating) history; the correct linear filtering scale is in general smaller than the Jeans scale after reheating, but larger prior to it. (abridged)