2003ApJ...583L..71S

The characteristic photon energy for gamma-ray bursts (GRBs), E_peak, has a remarkably narrow distribution for bursts of similar peak flux, with values between 150 and 600 keV for most faint bursts. This result is surprising within the framework of internal shock models, since spectral shifts associated with the jet's blueshift (by a Lorentz factor of Γ) and the cosmological redshift (by a factor of 1+z) should cause substantial smearing in the distribution of the spectral peak in the jet's comoving frame, E_rest. For the general case where the luminosity (L) varies as Γ^N and E_restvaries as Γ^M, the observed E_peakwill vary as L^(M+1)/N(1+z)^–1. For two independent sets of 20 and 84 bursts, E_peak(1+z) varies as a power law of the luminosity with an index of (M+1)/N=0.36±0.03. With this measured value, the above functional dependence of E_peakon L and z results in E_peakbeing roughly constant for bursts of similar peak flux, P₂₅₆. Thus, the kinematic smearing will be small, hence allowing the E_peak distribution to be narrow. This model also predicts that bright bursts will have high E_peak-values because they all have some combination of high luminosity (and hence a large blueshift Γ) and a nearby distance (and hence a small cosmological redshift). Quantitatively, E_peakshould vary roughly as P^0.36₂₅₆, and this model prediction is strikingly confirmed with BATSE data by Mallozzi et al. A prediction of this model is that GRBs at very high redshift (z∼10) should all appear with E_peakat ~200 keV. A further prediction of this model is that normal bursts with P₂₅₆below the BATSE trigger threshold will appear as X-ray flashes with E_peak~70 keV, just as is reported by Kippen et al. and Heise et al.