2008ApJ...684..430D

An analysis of the interaction between a spherical relativistic blast-wave shell and a stationary cloud with a spherical cap geometry is performed assuming that the cloud width Δ_cl≪x, where x is the distance of the cloud from the gamma-ray burst (GRB) explosion center. The interaction is divided into three phases: (1) a collision phase with both forward and reverse shocks; (2) a penetration phase when either the reverse shock has crossed the shell while the forward shock continues to cross the cloud, or vice versa; and (3) an expansion phase when, both shocks having crossed the cloud and shell, the shocked fluid expands. Temporally evolving spectral energy distributions (SEDs) are calculated for the problem of the interaction of a blast-wave shell with clouds that subtend large and small angles compared with the Doppler (-cone) angle θ₀=1/Γ₀, where Γ₀ is the coasting Lorentz factor. The Lorentz factor evolution of the shell/cloud collision is treated in the adiabatic limit. The behavior of the light curves and SEDs on, e.g., Γ₀, shell-width parameter η, where Δ₀+ηx/Γ²₀ is the blast-wave shell width, and properties and locations of the cloud is examined. Short-timescale variability in GRB light curves, including ∼100 keV γ-ray pulses observed with BATSE and delayed ∼1 keV X-ray flares found with Swift, can be explained by emissions from an external shock formed by the GRB blast wave colliding with small density inhomogeneities in the ``frozen-pulse'' approximation (η⟶0), and perhaps in the thin-shell approximation (η~1/Γ₀), but not when η~1. If the frozen-pulse approximation is valid, then external shock processes could make the dominant prompt and afterglow emissions in GRB light curves consistent with short-delay two-step collapse models for GRBs.