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We use hydrodynamic cosmological simulations to study damped Lyα (DLA) and Lyman limit (LL) absorption at redshifts z = 2-4 in five variants of the cold dark matter scenario: COBE-normalized (CCDM), cluster-normalized (SCDM), and tilted (n = 0.8) Ωm = 1 models, as well as open (OCDM) and flat (LCDM) Ωm = 0.4 models. Our standard simulations resolve the formation of dense concentrations of neutral gas in halos with circular velocity vcvc,res 140 km s-1 for Ωm = 1 and 90 km s-1 for Ωm = 0.4, at z = 2; an additional LCDM simulation resolves halos down to vc,res 50 km s-1 at z = 3. We find a clear relation between H I column density and projected distance to the center of the nearest galaxy, with DLA absorption usually confined to galactocentric radii less than 10-15 kpc and LL absorption arising out to projected separations of 30 kpc or more. If we consider only absorption in the halos resolved by our standard simulations, then all five models fall short of reproducing the observed abundance of DLA and LL systems at these redshifts. To estimate the absorption from lower mass halos, we fit a power law to the relation between absorption area α and halo circular velocity vc in our simulations and extrapolate using the Jenkins et al. halo mass function; we do not apply this method to the TCDM model because it has too few halos at the level resolved by our simulation. In the two LCDM simulations, for which DLA results agree well in the mass regime of overlap, the mean cross section for DLA absorption is α π(0.3Rvir)2, much larger than the simple estimate α ~ π(0.1Rvir)2 based on collapse of the baryons to a centrifugally supported disk (Rvir is the halo virial radius). The cross sections for LL absorption are α π(0.6Rvir)2, with a dependence on numerical resolution at the ~25% level. Detailed examination provides further evidence of nonequilibrium effects on absorption cross section: for example, individual absorbers can be slightly smaller in more massive halos because gas sinks deeper into the potential wells, but more massive halos nonetheless have larger average cross sections because they are more likely to have multiple gas concentrations. Our extrapolation procedure implies that all four models are consistent with the observed abundance of DLA systems if the fitted α(vc) extends to vc 50-80 km s-1, and they may produce too much absorption if the relation continues to vc 40 km s-1. Matching the observed abundance of LL systems requires absorption in halos down to vc 30-50 km s-1. Our results suggest that LL absorption is closely akin to DLA absorption, arising in less massive halos or at larger galactocentric radii but not caused by processes acting on a radically different mass scale. Robust tests of cosmological models against the observed amount of high column density absorption will require simulations of representative volumes that resolve halos at the low-mass limit where they cease to harbor high column density absorbers, 30 vc 60 km s-1.


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