We calculate the column density distribution of damped Ly \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 1.6 \times 10 ^ { 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 \simeq 10 ^ { -3 } .
Assuming a photoionization rate \Gamma \simeq 10 ^ { -12 } { s } ^ { -1 } from the external ionizing background , the radius where self-shielding occurs is inferred to be \sim 3.8 { kpc } .
If damped Ly \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 3 \times 10 ^ { 20 } { cm } ^ { -2 } would be gravitationally confined 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 Ly \alpha 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 .