The Peak Energy Distribution of the νF_ν Spectra in the Rest Frame

Gamma-ray bursts (GRBs) are the most violent events in the universe. The peak energy of the νF_ν spectra E_p is an important quantity of the GRBs and it is dramatically different from burst to burst. The energy distribution of E_p is wide, and the distribution profile of the observed E_p from different satellites is without major differences. After calculating the peak energy E'_p=E_p,z/Γ₀ of the νF_ν spectra in the jet co-moving frame and comparing the distribution of the E_p in jet-comoving frame and observed frame, we find that the distributions show no significant difference. The result indicates that the wide distribution of the observed E_p may not be governed by the Doppler boosting effect, rather, it may be the true physical distribution of the peak energy of the GRBs.