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.
