The expected redshift distribution of gamma-ray bursts

We predict the redshift distribution of gamma-ray bursts (GRBs), assuming that they trace the cosmic star formation history. We find that a fraction greater than or similar to50% of all GRBs on the sky originate at a redshift zgreater than or similar to5, even though the fraction of the total stellar mass formed by zsimilar to5 is only similar to15%. These two fractions are significantly different, because they involve different cosmological factors when integrating the star formation rate over redshift. Hence, deep observations of transient events, such as GRB afterglows or supernovae, provide an ideal strategy for probing the high-redshift universe. We caution, however, that existing or planned flux-limited instruments are likely to detect somewhat smaller fractions of high-redshift bursts. For example, we estimate that the fraction of all bursts with redshifts zgreater than or similar to5 is similar to10% in the case of the BATSE instrument and similar to25% in the case of Swift. We also show that the intrinsic distribution of GRB durations is bimodal but significantly narrower and shifted toward shorter durations than the observed distribution.