We investigate the nature of the mass-metallicity (M-Z) relation for long gamma-ray burst (LGRB) host galaxies. Recent studies suggest that the M-Z relation for local LGRB host galaxies may be systematically offset towards lower metallicities relative to the M-Z relation defined by the general star forming galaxy (SDSS) population. The nature of this offset is consistent with suggestions that low metallicity environments may be required to produce high mass progenitors, although the detection of several GRBs in high-mass, high-metallicity galaxies challenges the notion of a strict metallicity cut-off for host galaxies that are capable of producing GRBs. We show that the nature of this reported offset may be explained by a recently proposed anti-correlation between the star formation rate (SFR) and the metallicity of star forming galaxies. If low metallicity galaxies produce more stars than their equally massive, high-metallicity counterparts, then transient events that closely trace the SFR in a galaxy would be more likely to be found in these low metallicity, low mass galaxies. Therefore, the offset between the GRB and SDSS defined M-Z relations may be the result of the different methods used to select their respective galaxy populations, with GRBs being biased towards low metallicity, high SFR, galaxies. We predict that such an offset should not be expected of transient events that do not closely follow the star formation history of their host galaxies, such as short duration GRBs and SN Ia, but should be evident in core collapse SNe found through upcoming untargeted surveys.
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