Self-shielding Effects on the Column Density Distribution of Damped Lyman Alpha Systems

We calculate the column density distribution of damped Lyman alpha systems, modeled as spherical isothermal gaseous halos ionized by the external cosmic background. The effects of self-shielding introduce a hump in this distribution, at a column density N_{HI} \sim 1.6x10^{17} X^{-1} cm^{-2}, where X is the neutral fraction at the radius where self-shielding starts being important. The most recent compilation of the column density distribution by Storrie-Lombardi & Wolfe shows marginal evidence for the detection of this feature due to self-shielding, suggesting a value X \sim 10^{-3}. Assuming a photoionization rate \Gamma \sim 10^{-12} s^{-1} from the external ionizing background, the radius where self-shielding occurs is inferred to be about 3.8kpc. If damped Lyman alpha systems consist of a clumpy medium, this should be interpreted as the typical size of the gas clumps in the region where they become self-shielding. Clumps of this size with typical column densities N_H \sim 3x10^{20} cm^{-2} would be in hydrostatic equilibrium at the characteristic photoionization temperature \sim 10^4 K if they do not contain dark matter. Since this size is similar to the overall radius of damped \lya systems in Cold Dark Matter models, where all halos are assumed to contain similar gas clouds producing damped absorbers, this suggests that the gas in damped absorbers is in fact not highly clumped.