Probing the Cosmic Star Formation History by the Brightness Distribution of Gamma‐Ray Bursts

Brightness distribution of Gamma-Ray Bursts (GRBs) is studied in detail underthe assumption that GRB rate is related to cosmic star formation rate. The twopopulations of the long- and short-duration bursts in the 4B BATSE catalog areanalyzed separately. Taking account of current uncertainties in theobservational estimate of star formation rate (SFR), we have tried variousmodels of the cosmic star formation history and we find that the SFR evolutionin $z$ = 0--1 is strongly constrained by the GRB distribution if the standardcandle approximation is valid. The strong SFR evolution by a factor of $\sim$15 from $z$ = 0 to 1 inferred from UV observations is too steep to beconsistent with the GRB distribution for any distance scale of GRBs. Somepossibilities to reconcile this discrepancy are discussed, including theintrinsic luminosity dispersion of GRBs and/or modification of star formationhistory estimated by UV observations. We argue that SFR increase factor from$z$ = 0 to 1 may be as low as about 4 if we choose different sets ofcosmological parameters and/or take account of the evolution of metallicity anddust extinction in the UV data, and this would significantly remedy thediscrepancy.Comment: Accepted version by ApJ. Discussion on luminosity dispersion of GRBs is newly added. 30 pages including 16 figure