Fundamental Physical Parameters of Collimated Gamma-ray Burst Afterglows

We determine the basic physical characteristics of eight Gamma-Ray Bursts (GRB) – 980519, 990123, 990510, 991028, 991216, 000301c, 000926 and 010222 – by modelling the broadband emission of their afterglows. We find that the burst kinetic energies after the GRB phase are well clustered around a mean value of 3 × 10 ergs. In contrast, the energy release in γ-rays, after correcting for collimated explosion, varies among bursts by more than an order of magnitude. The jet initial apertures are the 2 − 14 range, mildly correlated with the energy, half of the jets being narrower than ∼ 3. This implies that, within 100 Mpc, there are about 10 GRB remnants (expanding at∼ 0.1 c) which can be resolved with VLBA. For all eight afterglows the total energy in the shock-accelerated electrons is close to equipartition with protons. However the slope of the power-law electron distribution is not universal, varying between 1.4 and 2.8. In at least half of the cases, the density structure of the medium is inconsistent with an r−2 profile. A homogeneous medium with density in the 0.1 − 50 cm−3 range can accommodate the broadband emission of all afterglows, with the exception of 990123, for which we find the density to be less than 10−2 cm−3. If GRBs arise from the core collapse of massive stars, then such low densities indicate the existence of superbubbles created by the supernovae and winds within a cluster of massive stars.