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Description
Knowledge of the bulk Lorentz factor {Gamma}_0_ of 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 time t_p_. For another 106 GRBs we set an upper limit t_p_^UL^. The measure of t_p_ provides the bulk Lorentz factor {Gamma}_0_ of the fireball before deceleration. We show that t_p_ is 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 the t_p_ of 66 long GRBs and the 85 most constraining upper limits, we estimate {Gamma}_0_ or a lower limit {Gamma}_0_^LL^. Using censored data analysis methods, we reconstruct the most likely distribution of t_p_. All t_p_ are larger than the time T_p,{gamma}_ when the prompt {gamma}-ray emission peaks, and are much larger than the time T_ph_ when the fireball becomes transparent, that is, t_p_>T_p,{gamma}_>T_ph_. The reconstructed distribution of {Gamma}_0_ has 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 <E_iso_>=3(8)x10^50^erg, <L_iso_>=3(15)x10^47^erg/s, and <E_peak_>=1(2)keV in the homogeneous (wind) case. We confirm that the significant correlations between {Gamma}_0_ and the rest frame isotropic energy (E_iso_), luminosity (L_iso_), and peak energy (E_p_) are not due to selection effects. When combined, they lead to the observed E_p_-E_iso_ and E_p_-L_iso_ correlations. Finally, assuming a typical opening angle of 5 degrees, we derive the distribution of the jet baryon loading which is centered around a few 10^-6^M_{\sun}_.
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