Lyman limit and damped Ly \alpha absorption systems probe the distribution of collapsed , cold gas at high redshift .
Numerical simulations that incorporate gravity and gas dynamics can predict the abundance of such absorbers in cosmological models .
We develop a semi-analytical method to correct the numerical predictions for the contribution of unresolved low mass halos , and we apply this method to the Katz et al .
( 1996 ) simulation of the standard cold dark matter model ( \Omega = 1 , h = 0.5 , \Omega _ { b } = 0.05 , \sigma _ { 8 } = 0.7 ) .
Using this simulation and higher resolution simulations of individual low mass systems , we determine the relation between a halo ’ s circular velocity v _ { c } and its cross section for producing Lyman limit or damped Ly \alpha absorption .
We combine this relation with the Press-Schechter formula for the abundance of halos — itself calibrated against the simulated halo population — to compute the number of absorbers per unit redshift .
The resolution correction increases the predicted abundances by about a factor of two at z = 2 , 3 , and 4 , bringing the predicted number of damped Ly \alpha absorbers into quite good agreement with observations .
Roughly half of these systems reside in halos with circular velocities v _ { c } \geq 100 { km } { s } ^ { -1 } and half in halos with 35 { km } { s } ^ { -1 } \leq v _ { c } \leq 100 { km } { s } ^ { -1 } .
Halos with v _ { c } > 150 { km } { s } ^ { -1 } typically harbor two or more systems capable of producing damped absorption .
Even with the resolution correction , the predicted abundance of Lyman limit systems is a factor of three below observational estimates , signifying either a failure of the standard cold dark matter model or a failure of these simulations to resolve most of the systems responsible for Lyman limit absorption .
By comparing simulations with and without star formation , we find that depletion of the gas supply by star formation affects absorption line statistics at z \geq 2 only for column densities exceeding N _ { HI } = 10 ^ { 22 } { cm } ^ { -2 } , even though half of the cold , collapsed gas has been converted to stars by z = 2 .