We study the incidence rate of damped Ly-a systems associated with the host
galaxies of gamma-ray bursts (GRB-host-DLAs) as functions of neutral hydrogen
column density (N_HI) and projected star formation rate (SFR) using
cosmological SPH simulations. Assuming that the occurrence of GRBs is
correlated with the local SFR, we find that the median N_HI of GRB-host-DLAs
progressively shifts to lower N_HI values with increasing redshift, and the
incidence 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 IGM
attenuation in GRB afterglows increases towards higher redshift, because it
will 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 the
reionization history of the Universe. The overall incidence rate of
GRB-host-DLAs decreases monotonically with increasing redshift, whereas that of
QSO-DLAs increases up to z=6. A measurement of the difference between the two
incidence rates would enable an estimation of the value of \eta_grb, which is
the mass fraction of stars that become GRBs for a given amount of star
formation. Our predictions can be tested by upcoming high-z GRB missions,
including JANUS (Joint Astrophysics Nascent Universe Scout) and SVOM (Space
multi-band Variable Object Monitor).Comment: 5 pages, 3 figures, ApJL, in pres