SIMBAD references

Observations of long gamma-ray bursts (LGRBs) offer a unique opportunity to probe the history of cosmic star formation, although whether LGRBs are biased tracers remains highly debated. Based on an extensive sample of LGRBs compiled by Robertson & Ellis, we analyze various models of star formation rate, combining the possible effect of the cosmic metallicity evolution under the assumption that LGRBs preferentially occur in low-metallicity galaxies. The models of star formation rate tested in this work include empirical fits from observational data as well as a self-consistent model calculated from the hierarchical structure formation scenario. Comparing with the observational data, we find a relatively higher metallicity cut of Z ≳ 0.6 Z_☉ for the empirical fits and no metallicity cut for the self-consistent model. These results imply that there is no strong bias toward low metallicity in LGRB host galaxies, in contrast to previous studies suggesting a cut of Z ∼ 0.1-0.3 Z_☉, and that the inferred low-metallicity dependencies of LGRBs are strongly related to the specific models of star formation rate. Furthermore, a significant fraction of LGRBs that occur in small halos down to 3x10⁸ M_☉ can provide an alternative explanation for the difference between the star formation rate and the LGRB rate.