Limits on Expanding Relativistic Shells from Gamma-Ray Burst Temporal Structure

We calculate the expected envelope of emission for relativistic shells under the assumption of local spherical symmetry. Gamma-Ray Burst envelopes rarely conform to the expected shape, which is similar to a FRED; a fast rise and exponential decay. The fast rise is determined by the time that the relativistic shell prodcues gamma rays. The decay has the form of a power law and arises from the curvature of the shell. The amount of curvature comes from the overall size of the shell so the duration of the decay phase is related to the time the shell expands before converting its energy to gamma rays. From the envelope of emission, one can estimate when the central explosion occurred and, thus, the energy required for the shell to sweep up the ISM. The energy greatly exceeds 10^{53} erg unless the bulk Lorentz factor is less than 75. This puts extreme limits on the "external" shock models. However, the alternative, "internal" shocks from a central engine, has a problem: the entire long complex time history lasting hundreds of seconds must be postulated at the central site.Comment: to appear in Proc. 18-th Texas Symposium on Relativistic Astrophysics, eds. A. Olinto, J. Frieman, and D. Schram

The Unique Signature of Shell Curvature in Gamma-Ray Bursts

As a result of spherical kinematics, temporal evolution of received gamma-ray emission should demonstrate signatures of curvature from the emitting shell. Specifically, the shape of the pulse decay must bear a strict dependence on the degree of curvature of the gamma-ray emitting surface. We compare the spectral evolution of the decay of individual GRB pulses to the evolution as expected from curvature. In particular, we examine the relationship between photon flux intensity (I) and the peak of the \nu F\nu distribution (E_{peak}) as predicted by colliding shells. Kinematics necessitate that E_{peak} demonstrate a power-law relationship with I described roughly as: I=E_{peak}^{(1-\zeta)} where \zeta represents a weighted average of the low and high energy spectral indices. Data analyses of 24 BATSE gamma-ray burst pulses provide evidence that there exists a robust relationship between E_{peak} and I in the decay phase. Simulation results, however, show that a sizable fraction of observed pulses evolve faster than kinematics allow. Regardless of kinematic parameters, we found that the existence of curvature demands that the I - E_{peak} function decay be defined by \sim (1-\zeta). Efforts were employed to break this curvature dependency within simulations through a number of scenarios such as anisotropic emission (jets) with angular dependencies, thickness values for the colliding shells, and various cooling mechanisms. Of these, the only method successful in dominating curvature effects was a slow cooling model. As a result, GRB models must confront the fact that observed pulses do not evolve in the manner which curvature demands.Comment: 3 pages, To appear in Proc. from the 2nd Workshop on Gamma-Ray Bursts in the Afterglow Er

Log N-log S in inconclusive

The log N-log S data acquired by the Pioneer Venus Orbiter Gamma Burst Detector (PVO) are presented and compared to similar data from the Soviet KONUS experiment. Although the PVO data are consistent with and suggestive of a -3/2 power law distribution, the results are not adequate at this state of observations to differentiate between a -3/2 and a -1 power law slope

Predictions for The Very Early Afterglow and The Optical Flash

According to the internal-external shocks model for $\gamma$-ray bursts (GRBs), the GRB is produced by internal shocks within a relativistic flow while the afterglow is produced by external shocks with the ISM. We explore the early afterglow emission. For short GRBs the peak of the afterglow will be delayed, typically, by few dozens of seconds after the burst. For long GRBs the early afterglow emission will overlap the GRB signal. We calculate the expected spectrum and the light curves of the early afterglow in the optical, X-ray and $\gamma$-ray bands. These characteristics provide a way to discriminate between late internal shocks emission (part of the GRB) and the early afterglow signal. If such a delayed emission, with the characteristics of the early afterglow, will be detected it can be used both to prove the internal shock scenario as producing the GRB, as well as to measure the initial Lorentz factor of the relativistic flow. The reverse shock, at its peak, contains energy which is comparable to that of the GRB itself, but has a much lower temperature than that of the forward shock so it radiates at considerably lower frequencies. The reverse shock dominates the early optical emission, and an optical flash brighter than 15th magnitude, is expected together with the forward shock peak at x-rays or $\gamma$-rays. If this optical flash is not observed, strong limitations can be put on the baryonic contents of the relativistic shell deriving the GRBs, leading to a magnetically dominated energy density.Comment: 23 pages including 4 figure