2011MNRAS.417..567N

We predict the metallicity probability distribution function (PDF) of long gamma-ray burst (GRB) host galaxies at low redshifts (z ≲ 0.3) when GRBs occur only in low-metallicity environments, assuming empirical formulations of galaxy properties. We discuss the contribution of high-metallicity galaxies to the cosmic rate of low-metallicity GRBs, taking the internal dispersion of metallicity within each galaxy into account. Assuming that GRBs trace low-metallicity star formation <Z_crit: 12+log₁₀(O/H) = 8.2, we find that GRB host galaxies may have systematically higher metallicity than GRB progenitors. Furthermore, we expect >rsim10 per cent of the host galaxies to have 12+log₁₀(O/H) > 8.8, if galaxies have an internal dispersion of metallicity comparable to that observed in the Milky Way. Our results show that the low-metallicity scenario of GRB progenitors can be reconciled with recent discoveries of the high-metallicity host galaxies of GRBs. We also show a possible bimodality in the host metallicity PDF that results from the single-progenitor model of GRBs. If found in future observations, the bimodality might be a clue to constrain the nature of GRB progenitors.