EXPANDING RELATIVISTIC SHELLS AND GAMMA-RAY BURST TEMPORAL STRUCTURE

Many models of gamma-ray bursts (GRBs) involve a shell expanding at ex treme relativistic speeds. The shell of material expands in a photon-q uiet phase for a period t(0) and then becomes gamma-ray active, perhap s due to inhomogeneities in the interstellar medium or the generation of shocks. Based on kinematics, we relate the envelope of the emission of the event to the characteristics of the photon-quiet and photon-ac tive phases. We initially assume local spherical symmetry wherein, on average, the same conditions prevail over the shell's surface within a ngles the order of Gamma(-1), where Gamma is the Lorentz factor for th e bulk motion. The contribution of the curvature to the temporal struc ture is comparable to the contribution from the overall expansion. As a result, GRB time histories from a shell should have an envelope simi lar to ''FRED'' (fast rise, exponential decay) events in which the ris e time is related to the duration of the photon-active phase and the f all time is related to the duration of the photon-quiet phase. This re sult depends only on local spherical symmetry and, since most GRBs do not have such envelopes, we introduce the ''shell symmetry'' problem: the observed time history envelopes of most GRBs do not agree with tha t expected for a relativistic expanding shell. Although FREDs have the signature of a relativistic shell, they may not be due to a single sh ell, as required by some cosmological models. Some FREDs have precurso rs in which the peaks are separated by more than the expansion time re quired to explain FRED shape. Such a burst is most likely explained by a central engine; that is, the separation of the multiple peaks occur s because the central site produced multiple releases of energy on tim escales comparable to the duration of the event. Alternatively, there still could be local spherical symmetry of the bulk material, but with a low ''filling factor''; that is, only a few percent of the viewable surface (which is already very small, 4 pi Gamma(-2)) ever becomes ga mma-ray active. Long complex bursts present a myriad of problems for t he models. The duration of the event at the detector is similar to t(0 )/(2 Gamma(2)). The long duration cannot be due to large t(0), since i t requires too much energy to sweep up the interstellar medium. Nor ca n it be due to small Gamma if the time variation is due to ambient obj ects, since the density of such objects is unreasonable (similar to 10 (18)Gamma(-4) pc(-3) for typical parameters). Long events must explain why they almost always violate local spherical symmetry or why they h ave low filling factors. Both precursor and long complex events are li kely to be ''central engines'' that produce multiple releases of energ y over similar to 100 s. One promising alternative scenario is one in which the shell becomes thicker than the radius of the curvature withi n Gamma(-1). Then it acts as a parallel slab, eliminating the problems associated with local spherical symmetry.