| Summary: | We investigate the difference between the host galaxy properties of core-collapse supernovae and long-duration gamma-ray bursts (LGRBs), and quantify a possible metallicity dependence of the efficiency of producing LGRBs. We use a sample of 16 CC SNe and 16 LGRBs from Fruchter et al. (2006) which have similar redshift distributions to eliminate galaxy evolution biases. We make a forward prediction of their host galaxy luminosity distributions from the overall cosmic metallicity distribution of star formation. This appoach is supported by the finding that LGRB hosts follow the L-Z relations of star-forming galaxies. We then compare predictions for metallicity-dependent event efficiencies with the observed host data. We find that UV-based SFR estimates predict the hosts distribution of CC SNe perfectly well in a metallicity-independent form. In contrast, LGRB hosts are fainter on average by one magnitude, almost as faint as the Large Magellanic Cloud. Assuming this is a metallicity effect, the present data are insufficient to discriminate between a sharp metallicity cutoff and a soft decrease in efficiency towards higher metallicity. For a sharp cut-off, however, we find a best value for the cutoff metallicity, as reflected in the oxygen abundance, 12+log (O/H)_lim ~ 8.7+/-0.3 at 95% confidence including systematic uncertainties on the calibration of Kobulnicky and Kewley (2004). This value is somewhat lower than the traditionally quoted value for the Sun, but is comparable to the revised solar oxygen abundance (Asplund, Grevesse and Sauval 2005). LGRB models that require sharp metallicity cutoffs well below ~1/2 the revised solar metallicity appear to be effectively ruled out (abridged).
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