Curvature Effects in Gamma Ray Burst Colliding Shells

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  • 21 March 2004
Abstract
An elementary kinematic model for emission produced by relativistic spherical colliding shells is studied. The case of a uniform blast-wave shell with jet opening angle \theta_j \gg 1/\Gamma is considered, where \Gamma is the Lorentz factor of the emitting shell. The shell, with comoving width \Delta r^\prime, is assumed to be illuminated for a comoving time \Delta t^\prime and to radiate a broken power-law \nu L_\nu spectrum peaking at comoving photon energy \e_{pk,0}^{\prime}. Synthetic GRB pulses are calculated, and the relation between energy flux and internal comoving energy density is quantified. Curvature effects dictate that the measured \nu F_\nu flux at the measured peak photon energy \e_{pk} is proportional to \e^3_{pk} in the declining phase of a GRB pulse. Possible reasons for discrepancy with observations are discussed, including adiabatic and radiative cooling processes that extend the decay timescale, a nonuniform jet, or the formation of pulses by external shock processes. A prediction of a correlation between prompt emission properties and times of the optical afterglow beaming breaks is made for a cooling model, which can be tested with Swift.

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