Sharp H I 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 Lyα absorption systems in the redshift range 1.75 ≤ z < 3.25. We assume that the distribution of the hydrogen total (H I+H II) column density in the absorbers, NH, follows a power law KN, 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 NH/N as a function of NH. Comparison of the models and observations gave excellent fits with maximum likelihood solutions for the exponent α and X, the value of log when the Lyman limit optical depth along the line of sight is τLL = 1. The slope of the total gas column density distribution with its relative 3 σ errors is α = 2.7 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 η0 of dark matter to gas density, however, is not well constrained since log (η0) = 1.1 ± 0.8. An extrapolation of our derived power-law distribution toward systems of lower column density, the Lyα forest, tends to favor models with log(η0) ≲ 1.1 and α ~ 2.7-3.3. With α appreciably larger than 2, Lyman limit systems contain more gas than damped Lyα systems and Lyα forest clouds even more. Estimates of the cosmological gas and dark matter density due to absorbers of different column density at z ~ 2.5 are also given.