2017ApJ...834..170G

There is now strong evidence that long-duration gamma-ray bursts (LGRBs) are preferentially formed in low-metallicity environments. However, the magnitude of this effect and its functional dependence on metallicity have not been well characterized. In our previous paper, we compared the metallicity distribution of LGRB host galaxies to that of star-forming galaxies in the local universe. Here we build upon this work by in effect dividing one distribution by the other, and thus directly determine the relative rate of LGRB formation as a function of metallicity in the low-redshift universe. We find a dramatic cutoff in LGRB formation above a metallicity of log(O/H)+12~8.3 in the KK04 scale, with LGRBs forming between 10 and 50 times more frequently per unit star formation below this cutoff than above. Furthermore, our data suggest that the rate of LGRB formation per unit star formation continues to fall above this break. We estimate that the LGRB formation rate per unit star formation may drop by as much as a factor of 100 between one-third solar and solar metallicity.