Revisiting Metallicity of Long Duration Gamma-Ray Burst Host Galaxies: The Role of Chemical Inhomogeneity within Galaxies

We predict the metallicity probability distribution function (PDF) of long gamma-ray burst (GRB) host galaxies at low-redshifts ($z \la 0.3$) when GRBs occur only in low-metallicity environment, assuming empirical formulations of galaxy properties. We discuss contribution of high-metallicity galaxies to the cosmic rate of low-metallicity GRBs, taking internal dispersion of metallicity within each galaxy into account. Assuming GRBs trace low-metallicity star formation $< \Zcrit$: 12+log$_{10}$(O/H) = 8.2, we find that GRB host galaxies may have systematically higher-metallicity than that of GRB progenitors. Furthermore, we expect $\ga$ 10% of the host galaxies to have 12+log$_{10}$(O/H) $> 8.8$, if galaxies have 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 the recent discoveries of the high-metallicity host galaxies of GRBs. We also show possible bimodality in the host metallicity PDF that results from the single progenitor model of GRBs. If found in future observation, the bimodality can be a clue to constrain the nature of GRB progenitors.