Sharp H Ι edges at high z:: The gas distribution from damped Lyα to Lyman limit absorption systems

We derive the distribution of neutral and ionized gas in high-redshift clouds, which are optically thick to hydrogen ionizing radiation, using published data on Lyman limit and damped Ly alpha absorption systems in the redshift range 1.75 less than or equal to z < 3.25. We assume that the distribution of the hydrogen total (H I + H II) column density in the absorbers, N-H, follows a power law KNH-alpha, whereas the observed H I column density distribution deviates from a pure power law as a result of ionization from a background radiation field. We use an accurate radiative transfer code for computing the rapidly varying ratio N-H/N-H I as a function of N-H. Comparison of the models and observations gave excellent fits with maximum likelihood solutions for the exponent alpha and X, the value of log (N-H/N-H I) when the Lyman limit optical depth along the line of sight is tau (LL) = 1. The slope of the total gas column density distribution tion with its relative 3 sigma errors is alpha = 2.7(-0.7)(+1.0) and X = 2.75 +/- 0.35. This value of X is much lower than what would be obtained for a gaseous distribution in equilibrium under its own gravity. The ratio eta (0) of dark matter to gas density, however, is not well constrained since log (eta (0)) = 1.1 +/- 0./8. An extrapolation of our derived power-law distribution toward systems of lower column density, the Ly alpha forest, tends to favor models with log (eta (0)) less than or similar to 1.1 and alpha similar to 2.7-3.3. With alpha appreciably larger than 2, Lyman limit systems contain more gas than damped Ly alpha systems and Ly alpha forest clouds even more. Estimates of the cosmological gas and dark matter density due to absorbers of different column density at z similar to 2.5 are also given.