Damped Lyman-$\alpha$ Systems at High Redshift and Models of Protogalactic Disks

We employ observationally determined intrinsic velocity widths and column densities of damped Lyman-alpha systems at high redshift to investigate the distribution of baryons in protogalaxies within the context of a standard cold dark matter model. We proceed under the assumption that damped Lyman alpha systems represent a population of cold, rotationally supported, protogalactic disks and that the abundance of protogalactic halos is well approximated by a cold dark matter model with critical density and vanishing cosmological constant. Using conditional cross sections to observe a damped system with a given velocity width and column density, we compare observationally inferred velocity width and column density distributions to the corresponding theoretically determined distributions for a variety of disk parameters and CDM normalizations. In general, we find that the observations can not be reproduced by the models for most disk parameters and CDM normalizations. Whereas the column density distribution favors small disks with large neutral gas fraction, the velocity width distribution favors large and thick disks with small neutral gas fraction. The possible resolutions of this problem in the context of this CDM model may be: (1) an increased contribution of rapidly rotating disks within massive dark matter halos to damped Lyman-alpha absorption or (2) the abandoning of simple disk models within this CDM model for damped Lyman-alpha systems at high redshift. Here the first possibility may be achieved by supposing that damped Lya system formation only occurs in halos with fairly large circular velocities and the second possibility may result from a large contribution of mergers and double-disks to damped Lya absorption at high redshift