Optical flashes and radio flares in GRB afterglows: Numerical study

Abstract

We numerically study the evolution of an adiabatic relativistic fireball interacting with an ambient uniform medium, both in the initial energy transfer stage and in its late evolution. It is shown that the Blandford-McKee solution adequately describes the evolution of the shocked ejecta quite early on and for as long as the fire-ball material has relativistic temperatures. In the case where the reverse shock is only mildly relativistic, the shocked ejecta becomes cold almost immediately and the evolution deviates from the Blandford-McKee solution. We derive analytical expressions for the ejecta evolution in its cold regime. This solution gives a good approximation to the numerical results. We estimate the radiation from the fireball ejecta using the numerical hydrodynamic evolution in both cases: cold and hot ejecta. Surprisingly, we find that both evolutions give rather similar light curves, decaying approximately as t^–2 in the optical and peaking after about one day in the radio, even though the hydrodynamics is different.