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 Â 10 50 ergs. With the exception of 000418, which requires a jet wider than 1 2 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 À2 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 À3 range, with the exception of 990123, for which it is below 10 À2 cm À3 . 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 À6 M . Our results on the jet energy, opening Lorentz factor, and evacuation of material until breakout provide constraints on theoretical models of GRB jets.

We calculate the afterglow emission for gamma-ray bursts (GRBs) going off in an extremely low density medium, referred to as naked bursts. Our results also apply to the case where the external medium density falls off sharply at some distance from the burst. The observed afterglow flux in this case originates at high latitudes, i.e., where the angle between the fluid velocity and the observer line of sight is greater than G Ϫ1 . The observed peak frequency of the spectrum for naked bursts decreases with observer time as t Ϫ1 , and the flux at the peak of the spectrum falls off as t Ϫ2 . The 2-10 keV X-ray flux from a naked burst of average fluence should be observable by the Swift satellite for time duration of about 10 3 longer than the burst variability timescale. The high-latitude emission contributes to the early X-ray afterglow flux for any GRB, not just naked bursts, and can be separated from the shocked interstellar medium emission by their different spectral and temporal properties. Measurements of the high-latitude emission could be used to map the angular structure of GRB-producing shells.

Assuming an adiabatic evolution of a Gamma-Ray Burst (GRB) remnant interacting with an external medium, we calculate the injection, cooling, and absorption break frequencies, and the afterglow flux for plausible orderings of the break and observing frequencies. The analytical calculations are restricted to a relativistic remnant and, in the case of collimated ejecta, to the phase where there is an insignificant lateral expansion. Results are given for both a homogeneous external medium and for a wind ejected by the GRB progenitor.We compare the afterglow emission at different observing frequencies, for each type of external medium. It is found that observations at sub-millimeter frequencies during the first day provide the best way of discriminating between the two models. By taking into account the effect of inverse Compton (IC) scatterings on the electron cooling, a new possible time-dependence of the cooling break is identified. The signature of the up-scattering losses could be seen in the optical synchrotron emission from a GRB remnant interacting with a pre-ejected wind, as a temporary mild flattening of the afterglow decay. The up-scattered radiation itself should be detected in the soft X-ray emission from GRB remnants running into denser external media, starting few hours after the main event.

We calculate Gamma-Ray Burst afterglow light-curves from a relativistic jet of initial opening angle theta_0, as seen by observers at a wide range of viewing angles, theta_obs, from the jet axis. We describe three increasingly more realistic models and compare the resulting light-curves. An observer at theta_obs < theta_0 should see a light curve very similar to that for an on-axis observer. An observer at theta_obs > theta_0 should see a rising light curve at early times, the flux peaking when the jet Lorentz factor sim 1/theta_obs. After this time the flux is not very different from that seen by an on-axis observer. A strong linear polarization (<40%) may occur near the peak in the light curve, and slowly decay with time. We show that if GRB jets have a universal energy, then orphan afterglows associated with off-axis jets should be seen up to a constant theta_obs, therefore the detection rate of orphan afterglows would be proportional to the true GRB rate. We also discuss the proposed connection between supernova 1998bw and GRB 980425.Comment: 5 pages, 3 figures, to appear in ApJL. Section on GRB orphan afterglows added, section on GRB 980425/SN 1998bw association expande

We determine the basic physical characteristics of eight Gamma-Ray Bursts -- 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 3E50 ergs. In contrast, the energy release in gamma-rays, after correcting for collimated explosion, varies among bursts by more than an order of magnitude. The jet initial apertures are the 2-14 degree range, mildly correlated with the energy, half of the jets being narrower than ~3 deg. This implies that, within 100 Mpc, there are about 10 GRB remnants (expanding at ~0.1c) 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 per cc range can accommodate the broadband emission of all afterglows, with the exception of 990123, for which we find the density to be less than 0.01 per cc. 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.Comment: 4 pages, color figures. Submitted to ApJ