1302.7306 (Paul C. Duffell et al.)

Rayleigh-Taylor Instability in a Relativistic Fireball on a Moving Computational Grid    [PDF]

Paul C. Duffell, Andrew I. MacFadyen

We numerically calculate the growth and saturation of the Rayleigh-Taylor instability caused by the deceleration of relativistic outflows with Lorentz factor \Gamma = 10, 30, and 100. The instability generates turbulence whose scale exhibits strong dependence on Lorentz factor, as only modes within the causality scale \Delta \theta ~ 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 turbulence in a shock-heated region behind the forward shock. The instability completely disrupts the contact discontinuity between the ejecta and the swept up circumburst medium. The reverse shock is stable, but is impacted by the Rayleigh-Taylor instability, which strengthens the reverse shock and pushes it away from the forward shock. The forward shock front is unaffected by the instability, 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. 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. 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.

View original: http://arxiv.org/abs/1302.7306