摘要：Knowledge of the bulk Lorentz factorΓ0of gamma-ray bursts (GRBs) allows us to compute their comoving frame properties shedding light on their physics. Upon collisions with the circumburst matter, the fireball of a GRB starts to decelerate, producing a peak or a break (depending on the circumburst density profile) in the light curve of the afterglow. Considering all bursts with known redshift and with an early coverage of their emission, we find 67 GRBs (including one short event) with a peak in their optical or GeV light curves at a timetp. For another 106 GRBs we set an upper limittpUL. The measure oftpprovides the bulk Lorentz factorΓ0of the fireball before deceleration. We show thattpis due to the dynamics of the fireball deceleration and not to the passage of a characteristic frequency of the synchrotron spectrum across the optical band. Considering thetpof 66 long GRBs and the 85 most constraining upper limits, we estimateΓ0or a lower limitΓ0LL. Using censored data analysis methods, we reconstruct the most likely distribution oftp. Alltpare larger than the timeTp,γwhen the promptγ-ray emission peaks, and are much larger than the timeTphwhen the fireball becomes transparent, that is,tp>Tp,γ>Tph. The reconstructed distribution ofΓ0has median value~300 (150) for a uniform (wind) circumburst density profile. In the comoving frame, long GRBs have typical isotropic energy, luminosity, and peak energy⟨Eiso⟩ = 3(8) × 1050erg,⟨Liso⟩ = 3(15) × 1047erg s-1, and⟨Epeak⟩ = 1(2)keV in the homogeneous (wind) case. We confirm that the significant correlations betweenΓ0and the rest frame isotropic energy (Eiso), luminosity (Liso), and peak energy (Ep) are not due to selection effects. When combined, they lead to the observedEp−EisoandEp−Lisocorrelations. Finally, assuming a typical opening angle of 5 degrees, we derive the distribution of the jet baryon loading which is centered around a few10-6M⊙.
