The redshift distribution of gamma-ray bursts revisited

In this Letter, we calculate the redshift distribution of gamma-ray bursts assuming that they trace (i) the globally averaged star formation rate or (ii) the average metallicity in the Universe. While at redshifts 5 and below both the star formation rate and the metallicity are observationally determined modulo some uncertainties, at higher redshifts there are few constraints. We extrapolate the star formation rate and metallicity to higher redshifts and explore models that are broadly consistent with bounds on the optical depth from WMAP results. In addition, we also include parametric descriptions of the luminosity function, and the typical spectrum for gamma-ray bursts (GRBs). With these essential ingredients included in the modelling, we find that a substantial fraction (75 per cent) of GRBs are expected to originate at redshifts below 4, in variance with some previous estimates. Conversely, if we assume as expected for the collapsar model that gamma-ray bursts favour a low-metallicity environment, and therefore relate the GRB rate to a simple model of the average metallicity as a function of redshift, we find that a higher fraction of bursts, about 40 per cent, originate from z > 4. We conclude with the implications of Swift GRB detections.