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The majority of gamma-ray bursts exhibit a peak in their νFν photon energy spectra at an energy Ep that is in the range of ∼20-2000 keV available to the Large Area Detectors of the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory. If gamma-ray burst sources are at cosmological distances (d ≳ 1 Gpc), then the spectra of dim bursts should be redshifted to lower energies relative to those of bright bursts. The magnitude of the shift is a function of the cosmological redshifts z of both the dim and bright burst sources and hence yields the range of redshift available to the bursts; this range is further constrained by considering cosmological model fits to the burst number-intensity distribution. We have produced photon energy spectra for ∼400 bursts using data from BATSE to investigate if this expected shift in the νFν peak is observed. We find that he mean peak energies of the burst spectra are correlated with intensity: lower intensity groups of burst spectra exhibit a lower average peak energy, although the distributions of Ep are quite wide. Denoting the redshift of an event with an observed peak photon flux P (photons cm-2 s-1) by zp, we find that the maximum range consistent with the bursts of our sample is (1 + z1)/(1 + z100) = 1.86+0.36-.24.
Mallozzi et al. (Fri,) studied this question.