The population of damped Ly alpha and Lyman limit systems in the cold dark matter model

Lyman limit and damped Ly alpha absorption systems probe the distribution of collapsed, cold gas at high redshift. Numerical simulations that incorporate gravity and gasdynamics can predict the abundance of such absorbers in cosmological models. We develop a semianalytical method to correct the numerical predictions for the contribution of unresolved low-mass halos, and we apply this method to the Katz et al. simulation of the standard cold dark matter model (Ohm = 1, h = 0.5, Ohm(b) = 0.05, and sigma(g) = 0.7). Using this simulation and higher resolution simulations of individual low-mass systems, we determine the relation between a halo's circular velocity upsilon(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-in order to compute the number of absorbers per unit redshift. The resolution correction increases the predicted abundances by about a factor of 2 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 upsilon(c) greater than or equal to 2 100 km s(-1), and half in halos with 35 km s(-1) less than or equal to upsilon(c) less than or equal to 100 km s(-1). Halos with upsilon(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 3 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 the depletion of the gas supply by star formation affects absorption-line statistics at z greater than or equal to 2 for column densities exceeding N-HI = 10(22) cm(-2) only, even though half of the cold, collapsed gas has been converted to stars by z = 2.