Semi-analytic approach to understanding the distribution of neutral hydrogen in the Universe

Analytic derivations of the correlation function and the column density distribution for neutral hydrogen in the intergalactic medium (IGM) are presented, assuming that the nonlinear baryonic mass density distribution in the IGM is lognormal. This ansatz was used earlier by Bi & Davidsen to perform one-dimensional simulations of lines of sight and analyse the properties of absorption systems. We have taken a completely analytic approach, which allows us to explore a wide region of the parameter space for our model. The analytic results have been compared with observations to constrain various cosmological and IGM parameters, whenever possible. Two kinds of correlation functions are defined: (i) along the line of sight (LOS); and (ii) across the transverse direction. We find that the effects on the LOS correlation owing to changes in cosmology and the slope of the equation of state of the IGM, gamma, are of the same order, which means that we cannot constrain both the parameters simultaneously. However, it is possible to constrain gamma and its evolution using the observed LOS correlation function at different epochs provided that one knows the background cosmology. We suggest that the constraints on the evolution of gamma obtained using the LOS correlation can be used as an independent tool to probe the reionization history of the Universe. From the transverse correlation function, we obtain the excess probability, over random, of finding two neutral hydrogen overdense regions separated by an angle theta. We find that this excess probability is always less than 1 per cent for redshifts greater than 2. Our models also reproduce the observed column density distribution for neutral hydrogen, and the shape of the distribution depends on gamma. Our calculations suggest that one can rule out gamma > 1.6 for z similar or equal to 2.31 using the column density distribution. However, one cannot rule out higher values of gamma at higher redshifts.