Properties of Relativistic Jets in Gamma‐Ray Burst Afterglows

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Abstract
We extend our calculation of physical parameters of gamma-ray burst (GRB) jets by modeling the broadband emission of the afterglows 970508, 980519, 991208, 000926, 000418, and 010222. Together with 990123, 990510, 991216, and 000301c, there are 10 well-observed afterglows for which the initial opening angle of the GRB jet can be constrained. The jet energies (after the GRB phase) obtained for this set of afterglows are within one decade around 5 × 1050 ergs. With the exception of 000418, which requires a jet wider than rad, the jet initial half-angle in the other cases ranges from 2° to 20°. We find that in half of the cases, a homogeneous ambient medium accommodates the afterglow emission better than the windlike r-2 profile medium expected around massive stars. The two types of media give fits of comparable quality in four cases, with a wind medium providing a better description only for 970508. The circumburst densities we obtain are in the 0.1-100 cm-3 range, with the exception of 990123, for which it is below 10-2 cm-3. If in all 10 cases the observed GRB durations are a good measure of the ejecta deceleration timescale, then the parameters obtained here lead to jet Lorentz factors at the deceleration radius between 70 and 300, anticorrelated with the jet initial aperture, and jet masses around 10-6 M☉ . Our results on the jet energy, opening Lorentz factor, and evacuation of material until breakout provide constraints on theoretical models of GRB jets.