We use high resolution Eulerian hydrodynamics simulations to study kinematic properties of the low ionization species in damped Ly-alpha systems at redshift z=3. Our adaptive mesh refinement simulations include most key ingredients relevant for modeling neutral gas in high-column density absorbers: hydrodynamics, gravitational collapse, continuum radiative transfer and gas chemistry, but no star formation. We model high-resolution Keck spectra with unsaturated low ion transitions in two Si II lines (1526 and 1808 A), and compare simulated line profiles to the data from the SDSS DLA survey. We find that with increasing grid resolution the models show a trend in convergence towards the observed distribution of HI column densities. While in our highest resolution model we recover the cumulative number of DLAs per unit absorption distance, none of our models predicts DLA velocity widths as high as indicated by the data, suggesting that feedback from star formation might be important. At z=3 a non-negligible fraction of DLAs with column densities below 10^21 cm^-2 is caused by tidal tails due to galaxy-galaxy interactions in more massive halo environments. Lower column density absorbers with N_HI < 10^21.4 cm^-2 are sensitive to changes in the UV background resulting in a 10% reduction of the cumulative number of DLAs for twice the quasar background relative to the fiducial value. We find that the mass cut-off below which a large fraction of dwarf galaxies cannot retain gas after reionization is 7*10^7 msun, lower than the previous estimates. Finally, we show that models with self-shielding commonly used in the literature produce significantly lower DLA velocity widths than the full radiative transfer runs.
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