The intensity distribution of faint gamma-ray bursts detected with BATSE

We have recently completed a search of 6 years of archival BATSE data for g amma-ray bursts (GRBs) that were too faint to activate the real-time burst detection system running on board the spacecraft. These "nontriggered" burs ts can be combined with the "triggered" bursts detected on board to produce a GRB intensity distribution that reaches peak fluxes a factor of similar to 2 lower than could be studied previously. The value of the [V/V-max] sta tistic (in Euclidean space) for the bursts we detect is 0.177 +/- 0.006. Th is surprisingly low value is obtained because we detected very few bursts o n the 4.096 s and 8.192 s timescales (where most bursts have their highest signal-to-noise ratio) that were not already detected on the 1.024 s timesc ale. If allowance is made for a power-law distribution of intrinsic peak lu minosities, the extended peak flux distribution is consistent with models i n which the redshift distribution of the gamma-ray burst rate approximately traces the star formation history of the universe. We argue that this clas s of models is preferred over those in which the burst rate is independent of redshift. We use the peak flux distribution to derive a limit of 10% (99 % confidence) on the fraction of the total burst rate that could be contrib uted by a spatially homogeneous (in Euclidean space) subpopulation of burst sources, such as type Ib/c supernovae. These results lend support to the c onclusions of previous studies predicting that relatively few faint "classi cal" GRBs will be found below the BATSE onboard detection threshold.