Expanding Relativistic Shells and Gamma‐Ray Burst Temporal Structure

Abstract

Many models of gamma-ray bursts (GRBs) involve a shell expanding at extreme relativistic speeds. The shell of material expands in a photon-quiet phase for a period and then becomes gamma-ray t 0 active, perhaps 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-active phases. We initially assume local spherical symmetry wherein, on average, the same conditions prevail over the shells surface within angles the order of !~1, where ! is the Lorentz factor for the bulk motion. The contribution of the curvature to the temporal structure is comparable to the contribution from the overall expansion. As a result, GRB time histories from a shell should have an envelope similar to "" FRED (fast rise, exponential decay) events in which the rise time is related to the duration of the photon-active phase and the fall time is related to the duration of the photon-quiet phase. This result 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 that expected for a relativistic expanding shell.