Curvature Effects in Gamma‐Ray Burst Colliding Shells

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 \ⱼ \ 1/\ is considered, where \ is the Lorentz factor of the emitting shell. The shell, with comoving width \ r^\, is assumed to be illuminated for a comoving time \ t^\ and to radiate a broken power-law \ L_\ spectrum peaking at comoving photon energy \₏₊, ₀^\. Synthetic GRB pulses are calculated, and the relation between energy flux and internal comoving energy density is quantified. Curvature effects dictate that the measured \ F_\ flux at the measured peak photon energy \₏₊ is proportional to \³₏₊ 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.