Semi analytic approach to understanding the distribution of neutral hydrogen in the universe

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Abstract
Analytic derivations of the correlation function and the column density distribution for neutral hydrogen in the intergalactic medium (IGM) are presented, assuming that the non-linear baryonic mass density distribution in the IGM is lognormal. We have compared the analytic results with observations and explored the possibility of constraining various cosmological and IGM parameters. Two kinds of correlation functions are defined : (i) along the line-of-sight (LOS) and (ii) across the transverse direction. Comparison of the observed LOS correlation with our analytical models suggests that unique recovery of power spectrum is difficult without a prior knowledge of the IGM parameters. However, we show that it is possible to constrain the slope of the equation of state of the IGM, \gamma, and its evolution using the observed LOS correlation function at different epochs. From the transverse correlation function, we obtain the excess probability, over random, of finding two neutral hydrogen overdense separated by an angle \theta. We find that this excess probability is always less than 1% for redshifts greater than 2. Our models also reproduce the observed column density distribution for neutral hydrogen. We show that the shape of the distribution depends on \gamma. Our calculations suggest that one can rule out \gamma > 1.6 for z > 2.31 using the column density distribution. We suggest that the constraints on the evolution of \gamma (obtained using both the LOS correlation and the column density distribution) can be used as an independent tool to probe the reionisation history of the universe.

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