Mechanical Model for Relativistic Blast Waves and Stratified Fireballs

Abstract

We propose a simple mechanical model for relativistic explosions with both forward and reverse shocks, which allows one to do fast calculations of GRB afterglow. The blast wave in the model is governed by pressures P_F and P_R at the forward and reverse shocks. We show that the simplest assumption P_F=P_R is in general inconsistent with energy conservation law. The model is applied to GRBs with non-uniform ejecta. Such "stratified fireballs" are likely to emerge with a monotonic velocity profile after an internal-shock stage. We calculate the early afterglow emission expected from stratified fireballs.