Stability of the Forward/Reverse Shock System Formed by the Impact of a Relativistic Fireball on an Ambient Medium

Abstract

We analyze the stability of a relativistic double (forward/reverse) shock system which forms when the fireball of a Gamma-Ray Burst (GRB) impacts on the surrounding medium. We find this shock system to be stable to linear global perturbations for either a uniform or a wind (r^{-2}) density profile of the ambient medium. For the wind case, we calculate analytically the frequencies of the normal modes which could modulate the early short-term variability of GRB afterglows. We find that perturbations in the double shock system could induce oscillatory fluctuations in the observed flux on short (down to seconds) time scales during the early phase of an afterglow.

ApJ, submitted, 26 pages, 5 figures

References in corpus (1)

• Variability of GRB Afterglows Due to Interstellar Turbulence

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• A Numerical Gamma-Ray Burst Simulation Using Three-Dimensional Relativistic Hydrodynamics: The Transition from Spherical to Jet-like Expansion
• Self-Similar Collisionless Shocks
• Convective Instability of a Relativistic Ejecta Decelerated by a Surrounding Medium: An Origin of Magnetic Fields in GRBs?
• Relativistic Rayleigh-Taylor Instability of a Decelerating Shell and its Implications for Gamma Ray Bursts