Properties of Relativistic Jets in Gamma-Ray Burst Afterglows

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Abstract
We extend our calculation of physical parameters of 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 ten 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 5E50erg. With the exception of 000418, which requires a jet wider than 1/2 radians, the jet initial half-angle in the other cases ranges from 2 deg to 20 deg. We find that, in half of the cases, a homogeneous ambient medium accommodates the afterglow emission better than the wind-like 1/r^2 profile medium expected around massive stars. The two types of media give fits of comparable quality in four cases, a wind medium providing a better description only for 970508. The circumburst densities we obtain are in the 0.1-100 per cc range, with the exception of 990123, for which it is below 0.01 per cc. If in all ten cases the observed GRB durations are a good measure of the ejecta deceleration timescale, then the parameters obtained here lead to jet initial bulk Lorentz factors between 70 and 300, anticorrelated with the jet initial aperture, and jet masses around 1E-6 M_sun. Our results on the jet energy, opening Lorentz factor, and evacuation of material until break-out provide constraints on theoretical models of GRB jets.

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