Expanding Relativistic Shells and Gamma‐Ray Burst Temporal Structure

Many models of cosmological gamma-ray bursts involve the sudden release of$\sim 10^{51}$ erg which produce shells which expand at relativistic speeds(Lorentz $\Gamma$ factors of $10^{2-3}$). We investigate the kinematic limitson the source size due to the observed time structure in three types of bursts:short spikes, FREDs (Fast Rise, Exponentail decay), and long complex bursts.The emitting shell keeps up with the photons it produces reducing apparentdurations by $\Gamma^2$ so that source sizes can be very large ($2c\Gamma^2T_{dur}). However, the thickness of the emitting region is not effected by theshell motion so it must always be small, $c\Delta T$ where $\Delta T$ is thesubpeak time scale. We argue that one can only view the bulk motion head-on soit is inappropriate to treat GRBs as viewing the sides of a jet. Althoughphotons come from a region within an angle $\Gamma^{-1}$, we show that thecurvature of the shell within that angle creates delays comparable to thoseassociated with the duration of the event. As a result, most bursts should belike FREDs with sharp rises related to how long the shell emits and power lawdecays related to how long the shell expanded before becoming gamma-ray active.Few bursts have the long decay phases required for large shells resulting inunacceptable high densities for ISM objects to cause the observed subpeaks. Tobe consistent with the observations, perhaps very thick shells (which act asparallel slabs) are required to avoid the effects of the curvature, or theduration is dictated by a central engine.Comment: Tex file, 30 pages, 7 Postscript figures, in press ApJ, Vol 47