Luminosity Distribution of Gamma-Ray Burst Host Galaxies at redshift z=1 in Cosmological Smoothed Particle Hydrodynamic Simulations: Implications for the Metallicity Dependence of GRBs

We study the relationship between the metallicity of gamma-ray burst (GRB) progenitors and the probability distribution function (PDF) of GRB host galaxies as a function of luminosity using cosmological hydrodynamic simulations of galaxy formation. We impose a maximum limit to the gas metallicity in which GRBs can occur, and examine how the predicted luminosity PDF of GRB host galaxies changes in the simulation. We perform the Kolmogorov-Smirnov test, and show that the result from our simulation agrees with the observed luminosity PDF of core-collapse supernovae (SNe) host galaxies when we assume that the core-collapse SNe trace star formation. When we assume that GRBs occur only in a low-metallicity environment with $Z\lesssim 0.1 \Zsun$, GRBs occur in lower luminosity galaxies, and the simulated luminosity PDF becomes quantitatively consistent with the observed luminosity PDF. The observational bias against the host galaxies of optically dark GRBs owing to dust extinction may be another reason for the lower luminosities of GRB host galaxies, but the observed luminosity PDF of GRB host galaxies cannot be reproduced solely by the dust bias in our simulation.