Statistics Martin A. Zwaan , Marc A. W. Verheijen , Frank H. Briggs, PASA, 16 (1), in press.
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Introduction
High column density absorbers seen in the spectra of background QSOs are referred to as Damped Ly
(DL) systems if the observed H I column density exceeds the value of
. The DL absorption lines are on the square-root part of the curve of growth where damping wings dominate the profile and column densities can be determined accurately by fitting the line profiles. Wolfe (1995) argues that these systems at high redshifts are gas-rich disks in the process of contracting to present-day spiral galaxies. This idea is supported by the fact that the characteristic velocity profiles of metal lines and Lyman series lines in DL systems are similar to those of sightlines through spiral galaxies at z=0. More recently, detailed modeling of DL absorption profiles by Prochaska & Wolfe (1998) has shown that the DL systems are consistent with rapidly rotating, thick disks. Note however that alternative models, like protogalactic clumps coalescing into dark matter halos (Haehnelt et al. 1997, Khersonsky & Turnshek 1996), can also explain the kinematics. The cosmological mass density of neutral gas in DL systems at high redshift is comparable to the mass density of luminous matter in galaxies at z=0 (e.g. Lanzetta et al. 1995).
One of the best known statistical results of the study of QSO absorption line systems is the column density distribution function (CDDF) of neutral hydrogen. The function describes the chance of finding an absorber of a certain H I column density along a random line of sight per unit distance. An observational fact from high-z Ly studies is that the differential CDDF [
] can be described by a single power law of the form
, where
over ten orders of magnitude in column density (e.g. Tytler 1987, Hu et al. 1995) from
(Ly forest) to
(DL).
An integration over the distribution function gives the total cosmological neutral gas density as a function of redshift. The H I gas density relates to as
and it is readily seen that
if 
and 
. This implies that although the high column density systems are observationally rare, they contain the bulk of the neutral gas mass in the Universe. Because so few DL systems are known (
), the uncertainties on
and the CDDF for high column densities are large, especially if the measurements are split up into different redshift bins. But following the CDDF as a function of redshift is certainly very important in constraining models of complicated physical processes like star formation or gas feedback to the interstellar medium.
There are several reasons why the determination of at the present epoch is difficult. Due to the expansion of the Universe the expected number of absorbers along a line of sight decreases with decreasing redshift, the Ly line is not observable from the ground for redshifts smaller than 1.65, and starlight and dust in the absorbing foreground galaxies hinder the identification of the background quasars. Gravitational lensing may also play a role as it can bring faint quasars into the sample which otherwise would not have been selected (e.g. Smette et al. 1997).
At the present epoch the largest repositories of neutral gas are clearly galaxies. No instance of a free-floating H I cloud not confined to the gravitational potential of a galaxy has yet been identified. It is therefore justified to use our knowledge of the local galaxy population to estimate the shape and normalization of the CDDF.
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