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We study the incidence rate of damped Ly-a systems associated with the hostgalaxies of gamma-ray bursts (GRB-host-DLAs) as functions of neutral hydrogencolumn density (N_HI) and projected star formation rate (SFR) usingcosmological SPH simulations. Assuming that the occurrence of GRBs iscorrelated with the local SFR, we find that the median N_HI of GRB-host-DLAsprogressively shifts to lower N_HI values with increasing redshift, and theincidence rate of GRB-host-DLAs with log N_HI > 21.0 decreases rapidly at z>=6.Our results suggest that the likelihood of observing the signature of IGMattenuation in GRB afterglows increases towards higher redshift, because itwill not be blocked by the red damping wing of DLAs in the GRB host galaxies.This enhances the prospects of using high-redshift GRBs to probe thereionization history of the Universe. The overall incidence rate ofGRB-host-DLAs decreases monotonically with increasing redshift, whereas that ofQSO-DLAs increases up to z=6. A measurement of the difference between the twoincidence rates would enable an estimation of the value of \eta_grb, which isthe mass fraction of stars that become GRBs for a given amount of starformation. Our predictions can be tested by upcoming high-z GRB missions,including JANUS (Joint Astrophysics Nascent Universe Scout) and SVOM (Spacemulti-band Variable Object Monitor).

Incidence Rate of GRB-host-DLAs at High Redshift