  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, Graham & Fruchter (2013), we compared the
metallicity distribution of LGRB host galaxies to the 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
ten and fifty times more frequently per unit star-formation below this cutoff
than above. Furthermore, our data suggests that the rate of LGRB formation per
unit star formation continues to fall above this break. We estimate the LGRB
formation rate per unit star formation may drop by as much as a factor of one
hundred between one-third solar and solar metallicity.
