Long-Duration Gamma-Ray Bursts (GRBs) are powerful probes of the Universe star formation history, but correlation between the two depends on the highly debated presence/strength of a metallicity bias. To investigate this correlation, we use a phenomenological model that successfully describes star formation rates, luminosities and stellar masses of star forming galaxies, applying it to GRB production. We predict luminosities, stellar masses, and metallicities of host galaxies depending on the metallicity bias. Our best-fitting model includes a moderate metallicity bias, broadly consistent with the large majority of long-duration GRBs in metal-poor environments originating from collapsars (probability ~83%), but with a secondary contribution (~17%) from metal-independent production channels, such as binary evolution. Because of the mass-metallicity relation of galaxies, the maximum likelihood model predicts that the metal-independent channel becomes dominant at z<2, where hosts have higher metallicities and collapsars are suppressed. This possibly explains why some studies find no clear evidence of a metal-bias based on low-z samples. However, while metallicity predictions match observations well at high redshift, there is tension with low redshift observations, since a significant fraction of GRB hosts are predicted to have (near-)solar metallicity. This is in contrast to observations, unless obscured, metal-rich hosts are preferentially missed in current datasets, and suggests that lower efficiencies of the metal-independent GRB channel might be preferred following a comprehensive fit from complete samples. Overall, we are able to establish the presence of a metallicity bias for GRB production, but continued characterization of GRB host galaxies is needed to quantify its strength.
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