An off-line scan for nontriggered gamma-ray bursts (GRBs) in the BATSE daily records at 1024 ms time resolution covering about 7 yr of observations gave 1353 nontriggered and 1581 triggered GRBs. The scan efficiency was measured by adding artificial test bursts to the data. The distribution could be extended log N-log P down to peak fluxes, photons cm Ϫ2 s Ϫ1 . Previous indications of a turnover at small P are not confirmed. P ∼ 0.1 The distribution cannot be fitted with a standard candle model with a nonevolving GRB source log N-log P population, assuming that there are no large non-GRB contaminations. It is likely that the intrinsic luminosity function of GRBs is wide.
The source population of gamma-ray bursts (GRBs) declines toward the present epoch, being consistent with the measured decline of the star formation rate. We show this using the brightness distribution of 3255 long BATSE GRBs found in an off-line scan of the BATSE continuous 1.024 s count rate records. The significance of this conclusion is enhanced by the detection of three GRBs with known redshifts brighter than 10 52 ergs s À1 during the last two years. This is an argument in favor of the generally believed idea that GRBs are strongly correlated with star production, at least on cosmological timescales, and favors the association of long GRBs with collapses of supermassive stars. However, we still cannot rule out neutron star mergers if the typical delay time for binary system evolution is relatively short. If we assume a steep decline of the GRB population at z > 1:5, then their luminosity function can be clearly outlined. The luminosity function is close to a power law, dN=dL / L À1:4 , for low luminosities over at least 1.7 orders of magnitude. Then, the luminosity function breaks to a steeper slope or to an exponential decline around L $ 3 Â 10 51 ergs s À1 in the 50-300 keV range, assuming isotropic emission.
Before the BATSE/GRO launch GRBs seem to be a uniform phenomenon with duration up to ∼100 seconds. The BATSE has detected many events longer than 100 s and a few longer than 500s. We performed the off-line scan of the 1024 ms continuous BATSE records and revealed several non-triggered episodes of the BATSE GRB triggers which confidently belong to the same GRBs. There are also several pairs of bursts which are candidates to single very long ("superlong") GRBs lasting up to ∼2000s. Their emission on 500-2000s is prompt emission rather than afterglow. These superlong GRBs probably belong to the class of "long" GRBs constituting the tail of their duration distribution. The existence of such events can constrain some models and should be taken into account in the studies of hard X-ray afterglows.
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