Metallicity and HI Column Density Properties of Damped Lyman-$α$ Systems

Based on the disk galaxy formation theory within the framework of standard LCDM hierarchical picture, we selected modelled DLAs, according to their observational criterion, by Monte Carlo simulation with the random inclinations being considered, to examine their observed properties. By best-fitting the predicted metallicity distribution to the observed ones, we get the effective yield for DLAs about 0.25Z_sun, which is comparable to those for SMC and LMC. And the predicted distribution is the same as that of observation at the significant level higher than 60%. The predicted column density distribution of modelled DLAs is compared with the observed ones with the corresponding number density, gas content being discussed. We found that the predicted number density n(z) at redshift 3 agree well with the observed value, but the gas content Ω_DLA is about 3 times larger than observed since our model predicts more DLA systems with higher column density. It should be noted that the predicted star formation rate density contributed by DLAs is consistent with the most recent observations if the star formation timescale in DLAs is assumed to be 1 to 3 Gyr. Meanwhile, the connection between DLAs and LBGs is discussed by comparing their UV luminosity functions which shows that the DLAs host galaxies are much fainter than LBGs. We also predict that only few percent of DLAs can host LBGs which is also consistent with current observations. However, there is a discrepancy between model prediction and observation in the correlation between metallicity and HI column density for DLAs. We suggest that this could result from either the inadequacy of Schmidt-type star formation law at high redshift, the diversities of DLA populations, or the model limitations.