Hydrodynamics of a Relativistic Fireball: the Complete Evolution

Abstract

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 non-relativistic 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 $\gamma \sim 5$, and a reasonable approximation even down to $\gamma \sim 2$ though the solution is rigorous only for $\gamma \gg 1$. We examine the transition into the Blandford-McKee solution, and the transition from the solution to the non-relativistic self similar Sedov-Taylor solution. These simulations demonstrate the attractive nature of the Blandford-McKee solution and its stability to radial perturbations.

Submitted to ApJ, 35 pages, latex, 14 figures

References in corpus (2)

• Gamma-ray bursts from internal shocks in a relativistic wind: temporal and spectral properties
• Radiative Regimes in Gamma-Ray Bursts and Afterglows

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