The HIDEEP survey (Minchin et al. 2003) was done in an attempt to find objects having low inferred neutral hydrogen column densities, yet they found a distribution which was strongly peaked at 10^20.65 cm^-2. In an attempt to understand this distribution and similar survey results, we model HI profiles of gas discs and use simple simulations of objects having a wide range of HI properties in the presence of an ionizing background. We find that inferred column density (N_HI^o) values, which are found by averaging total HI masses over some disc area, do not vary strongly with central column density (N_max) for detectable objects, so that even a population having a wide range of N_max values will give rise to a strongly peaked distribution of N_HI^o values. We find that populations of objects, having a wide range of model parameters, give rise to inferred column density distributions around 10^20.6+/-0.3 cm^-2. However, populations of fairly massive objects having a wide range of central column densities work best in reproducing the HIDEEP data, and these populations are also consistent with observed Lyman limit absorber counts. It may be necessary to look two orders of magnitude fainter than HIDEEP limits to detect ionized objects having central column densities <10^20 cm^-2, but the inferred column densities of already detected objects might be lower if their radii could be estimated more accurately.
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