Expanding Relativistic Shells and Gamma-Ray Burst Temporal Structure

E. E. Fenimore; Claudine Madras; Sergei Nayakshin

doi:10.1086/178210

paper

Expanding Relativistic Shells and Gamma-Ray Burst Temporal Structure

arXiv:astro-ph/9607163 · doi:10.1086/178210

Abstract

Many models of cosmological gamma-ray bursts involve the sudden release of $\sim 1 0^{51}$ erg which produce shells which expand at relativistic speeds (Lorentz $Γ$ factors of $1 0^{2 - 3}$ ). We investigate the kinematic limits on 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 apparent durations by $Γ^{2}$ so that source sizes can be very large ( $2 c Γ^{2} T_{d u r}) . H o w e v er, t h e t hi c k n esso f t h ee mi tt in g r e g i o ni s n o t e f f ec t e d b y t h es h e l l m o t i o n so i t m u s t a l w a y s b es ma l l,$ cΔT $w h er e$ ΔT $i s t h es u b p e ak t im esc a l e . W e a r g u e t ha t o n ec an o n l y v i e w t h e b u l k m o t i o nh e a d - o n so i t i s ina pp r o p r ia t e t o t r e a tGR B s a s v i e w in g t h es i d eso f aj e t . A l t h o ug h p h o t o n sco m e f r o ma r e g i o n w i t hinanan g l e$ Γ^{-1}$, we show that the curvature of the shell within that angle creates delays comparable to those associated with the duration of the event. As a result, most bursts should be like FREDs with sharp rises related to how long the shell emits and power law decays related to how long the shell expanded before becoming gamma-ray active. Few bursts have the long decay phases required for large shells resulting in unacceptable high densities for ISM objects to cause the observed subpeaks. To be consistent with the observations, perhaps very thick shells (which act as parallel slabs) are required to avoid the effects of the curvature, or the duration is dictated by a central engine.

Tex file, 30 pages, 7 Postscript figures, in press ApJ, Vol 473

Expanding Relativistic Shells and Gamma-Ray Burst Temporal Structure

Abstract

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