2001ApJ...552..386B

In this paper we show how to use data on Lyman limit and damped Lyα absorption systems to derive the hydrogen ionization fractions and the distribution of the face-on total gas column density. We consider axially symmetric, randomly oriented absorbers, ionized by an external background radiation field in order to relate the face-on total gas distribution to that of the neutral hydrogen observed along the line of sight. We devise a statistical procedure based on the maximum likelihood criterion, which is able to treat simultaneously data coming from different surveys and statistically recovers the ``true'' column densities in the presence of large uncertainties: this is especially important for Lyman limit systems that leave an unmeasurable residual flux at wavelengths shorter than the Lyman break. We make use of simulated data to look for possible observational biases and extensively test our procedure. For a large statistical sample of real data in the redshift range 1.75-3.25 (collected from all published surveys) our maximum likelihood procedure gives a power-law slope for the total hydrogen distribution of -2.7. All together Lyman limit systems therefore contain more gas than damped Lyα systems. Analysis of data at other redshifts shows that more observations are needed to reach compelling evidence for a cosmological evolution of the slope of the gas distribution.