Where are the missing gamma-ray burst redshifts?

In the redshift range z = 0-1, the gamma-ray burst (GRB) redshift distribution should increase rapidly because of increasing differential volume sizes and strong evolution in the star formation rate (SFR). This feature is not observed in the Swift redshift distribution and to account for this discrepancy a dominant bias, independent of the Swift sensitivity, is required. Furthermore, despite rapid localization, about 50 per cent of Swift and pre-Swift GRBs do not have an observed optical afterglow and 60-70 per cent of GRBs are lacking redshifts. We employ a heuristic technique to extract this redshift bias using 69 GRBs localized by Swift with redshifts determined from absorption or emission spectroscopy. For the Swift and HETE + BeppoSAX redshift distributions, the best model fit to the bias at z < 1 implies that if GRB rate evolution follows the SFR, the bias cancels this rate increase. We find that the same bias is affecting both Swift and HETE + BeppoSAX measurements similarly at z < 1. Using a bias model constrained at a 98 per cent Kolmogorov-Smirnov (KS) probability, we find that 72 per cent of GRBs at z < 2 will not have measurable redshifts and about 55 per cent at z > 2. To achieve this high KS probability requires increasing the GRB rate density at small z compared to the high-z rate. This provides further evidence for a low-luminosity population of GRBs that are observed in only a small volume because of their faintness.