Hydrodynamics of a Relativistic Fireball: The Complete Evolution

We study numerically the evolution of an adiabatic relativistic fireball expanding into a cold uniform medium. We follow the stages of initial free expansion and acceleration, coasting, and then deceleration and slowing down to a nonrelativistic velocity. We compare the numerical results with simplified analytical estimates. We show that the relativistic self-similar Blandford-McKee solution describes well the relativistic deceleration epoch. It is an excellent approximation throughout the relativistic deceleration stage, down to γ~5, and a reasonable approximation even down to γ~2, though the solution is rigorous only for γ>>1. We examine the transition into the Blandford-McKee solution and the transition from the solution to the nonrelativistic self-similar Sedov-Taylor solution. These simulations demonstrate the attractive nature of the Blandford-McKee solution and its stability to radial perturbations.