Metallicity measurements of gamma-ray burst and supernova explosion sites: lessons from H ii regions in M31

Abstract

We examine how the small-scale ($<$\,kpc) variation of metallicity within a galaxy, which is found in nearby galaxies, affect the observational estimates of metallicity in the explosion sites of transient events such as core-collapse supernovae (CC SNe) and gamma-ray bursts (GRBs). Assuming the same luminosity, metallicity, and spatial distributions of \ion{H}{ii}\ regions (hereafter HIIRs) as observed in M31, we compute the apparent metallicities that we would obtain when the spectrum of a target region is blended with those of surrounding HIIRs within the length scale of typical spatial resolution. When the spatial resolution of spectroscopy is $\lesssim$ 0.5\,kpc, which is typical for the existing studies of CC SN sites, we find that the apparent metallicities reflect the metallicities of target regions, but with significant systematic uncertainties in some cases. When the spatial resolution is $\gtrsim$ 1.0 kpc, regardless of the target regions (which has a wide range of metallicity that spans $\sim$ 0.6 dex for the M31 HIIRs), we always obtain the apparent metallicities similar to the average metallicity of the M31 HIIRs. Given that the apparent metallicities measured with $\gtrsim$\,kpc scale resolution do not necessarily reflect the immediate environment of the stellar explosions, the current observational estimates of high metallicities for some of the long GRB host galaxies do {\em not} rule out the hypothesis that the long GRBs are exclusively born in a low-metallicity environment.