Abstract
Long-duration gamma-ray bursts(LGRBs) are believed to be linked with the star formation. We adopt a galactic evolution model, in which the star formation process inside the virialized dark halo at given redshift can be achieved. In this paper, the gamma-ray burst(GRB) host galaxies are assumed to be the star-forming galaxies within the small dark halos. The star formation rates(SFRs) in the host galaxies of LGRBs at different redshifts have been derived from our model with the galactic evolutionary time about a few times of $10^7$ yr and the dark halo mass of about $5\times 10^{11}M_\odot$. The related stellar masses, luminosities and metallicities of these hosts are estimated as well. We further calculate the X-ray and optical absorption of GRB afterglow emission. From our model calculation, at higher redshift, the SFR of host galaxy is larger, the absorption in X-ray band and optical band of GRB afterglow is stronger, in the condition that the dust and metal components are released locally, surrounding the GRB environment. These model predictions are compared with the {\it Swift} and other observational data. At lower redshift $z<1$, as the merger and interaction of some host galaxies are involved, one monolithic physical process is not sufficient to fully explain all kinds of observed phenomena.
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