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 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, Erest. For the general case where the luminosity (L) varies as ΓN and Erest varies as Γ M, the observed Epeak 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 Epeak on L and z results in Epeak being roughly constant for bursts of similar peak flux, P256. Thus, the kinematic smearing will be small, hence allowing the Epeak distribution to be narrow. This model also predicts that bright bursts will have high Epeak-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, Epeak should vary roughly as P2560.36, 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 ∼ 10) should all appear with Epeak at ≈200 keV. A further prediction of this model is that normal bursts with P256 below the BATSE trigger threshold will appear as X-ray flashes with Epeak ≈70 keV, just as is reported by Kippen et al. and Heise et al.
Publication Source (Journal or Book title)
Schaefer, B. (2003). Explaining the gamma-ray burst Epeak distribution. Astrophysical Journal, 583 (2 II) https://doi.org/10.1086/368106