2004ApJ...614..284D

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 θ_j≫1/Γ is considered, where Γ is the Lorentz factor of the emitting shell. The shell, with comoving width Δr', is assumed to be illuminated for a comoving time Δt' and to radiate a broken-power-law νL_νspectrum peaking at comoving photon energy ε'_pk,0. Synthetic gamma-ray burst (GRB) pulses are calculated, and the relation between energy flux and internal comoving energy density is quantified. Curvature effects dictate that the measured νF_νflux at the measured peak photon energy ε_pkbe proportional to ε³_pkin the declining phase of a GRB pulse. Possible reasons for discrepancies with observations are discussed, including adiabatic and radiative cooling processes that extend the decay timescale, a nonuniform jet, and 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.