Characteristics of Long Gamma-Ray Bursts in the Comoving Frame

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Abstract We compile a sample of 93 long gamma-ray bursts (GRBs) from the Fermi satellite and 131 from Konus-Wind that have measured redshifts and well-determined spectra, and estimate their pseudo-Lorentz factors (Γ0) using the tight L iso–E p–Γ0 correlation. The statistical properties and pair correlations of the temporal and spectral parameters are studied in the observer frame, rest frame, and comoving frame, respectively. We find that the distributions of the duration, peak energy, isotropic energy, and luminosity in the different frames are basically log-normal, and that their distributions in the comoving frame are narrow, clustering around ∼ 4000 s, ∼ 0.7 keV, ∼ 8 × 1049 erg, and ∼ 2.5 × 1046 erg s−1, where the redshift evolution effect has been taken into account. We also find that the values of Γ0 are broadly distributed between a few tens and several hundreds, with median values of ∼270. We further analyze the pair correlations of all the quantities, confirm the E iso–E p, L iso–E p, L iso–Γ0, and E iso–Γ0 relations, and find that the corresponding relations in the comoving frame do still exist, but with large dispersions. This suggests not only that the well-known spectrum–energy relations are intrinsic correlations, but also that the observed correlations are governed by the Doppler effect. In addition, the peak energies of long GRBs are independent of duration both in the rest frame and in the comoving frame, and there is a weak anticorrelation between the peak energy and Lorentz factor.