Explaining the gamma-ray burst Epeak distribution

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 Gamma) 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 Gamma(N) and E-rest varies as Gamma(M), the observed E-peak will 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-peak on L and z results in E-peak being roughly constant for bursts of similar peak flux, P-256. 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 Gamma) and a nearby distance (and hence a small cosmological redshift). Quantitatively E-peak, should vary roughly as P-2.56(0.36), 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 similar to 10) should all appear with E-peak at approximate to200 keV. A further prediction of this model is that normal bursts with P-256 below the BATSE trigger threshold will appear as X-ray flashes with E-peak approximate to 70 keV, just as is reported by Kippen et al. and Heise et al.