A comprehensive statistical analysis of the gas distribution in Lyman limit and damped Ly alpha absorption systems

In this paper we show how to use data on Lyman limit and damped Ly alpha ab sorption systems to derive the hydrogen ionization fractions and the distri bution of the face-on total gas column density. We consider axially symmetr ic, randomly oriented absorbers, ionized by an external background radiatio n field in order to relate the face-on total gas distribution to that of th e neutral hydrogen observed along the line of sight. We devise a statistica l procedure based on the maximum likelihood criterion, which is able to tre at simultaneously data coming from different surveys and statistically reco vers the "true" column densities in the presence of large uncertainties: th is is especially important for Lyman limit systems that leave an unmeasurab le residual flux at wavelengths shorter than the Lyman break. We make use o f simulated data to look for possible observational biases and extensively test our procedure. For a large statistical sample of real data in the reds hift range 1.75-3.25 (collected from all published surveys) our maximum lik elihood procedure gives a power-law slope for the total hydrogen distributi on of -2.7. All together Lyman limit systems therefore contain more gas tha n damped Lya systems. Analysis of data at other redshifts shows that more o bservations are needed to reach compelling evidence for a cosmological evol ution of the slope of the gas distribution.