We have examined some basic properties of damped Ly$alpha$ systems(DLAs) by semi-analytic model. We assume that DLA hosts are disk galaxies whose mass function is generated by Press-Schechter formulism at redshift 3. Star formation and chemical evolution undergo in the disc. We select modelled DLAs according to their observational criterion by Monte Carlo simulation using random line of sights and disk inclinations. The DLA ages are set to be 1 to 3 Gyr. By best-fitting the predicted metallicity distribution to the observed ones, we get the effective yield for DLAs about $0.25Z_{odot}$. On the basis of this constrain, we further compared our model predictions with observations at redshift 3 in the following items: number density; gas content; HI frequency distribution; star formation rate density; relationship between metallicity and HI column density. We found that the predicted number density at redshift 3 agree well with the observed value, but the gas content $Omega_{DLA}$ is about 3 times larger than observed since our model predicts more DLA systems with higher column density. The frequency distribution at higher HI column density is quite consistent with observation while some difference exists at lower HI end. The predicted star formation rate density contributed by DLAs is consistent with the most recent observations. Meanwhile, the connection between DLAs and Lyman Break galaxies(LBGs) is discussed by comparing their UV luminosity functions which shows that the DLAs host galaxies are much fainter than LBGs. However, there is a discrepancy between model prediction and observation in the correlation between metallicity and HI column density for DLAs. Further investigations are needed for the star formation mode at high redshift environments.
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