Relativistic Rayleigh-Taylor in a GRB Fireball

Author: Paul Duffell

Abstract: We numerically calculate the growth and saturation of the Rayleigh-Taylor instability caused by the deceleration of a shockwave from a relativistic fireball with Lorentz factor ∼ 100. We calculate afterglow emission from the explosion and find the reverse shock emission to be significantly altered by the instability. The reverse shock emission peaks at a later time but is still distinguishable from the forward shock. Rayleigh-Taylor generates turbulence whose scale exhibits strong dependence on Lorentz factor, as only modes within the causality scale (1/gamma) can grow. We develop a simple diagnostic to measure the fraction of energy in turbulent eddies and use it to estimate magnetic field amplification by the instability. We estimate a magnetic energy fraction ∼ 0.01 due to Rayleigh-Taylor in a region behind the forward shock. The instability completely diffuses out the contact discontinuity between the ejecta and the swept up circumburst medium. The reverse shock is stable, but is impacted by Rayleigh-Taylor fingers, which strengthen the shock and push it away from the forward shock. The forward shock is causally disconnected from the unstable region and is hence unaffected, but Rayleigh-Taylor fingers can penetrate about 10% of the way into the energetic region behind the shock during the two-shock phase of the explosion. These calculations are performed using a novel numerical technique that includes a moving computational grid. The moving grid is essential as it maintains contact discontinuities to high precision and can easily evolve flows with Lorentz factors upwards of 300.