Relativistic Rayleigh-Taylor Instability of a Decelerating Shell and its Implications for Gamma Ray Bursts

TL;DR

This paper performs a linear stability analysis of a relativistic shell in gamma-ray bursts, revealing an instability that could generate turbulence and magnetic fields, influencing early emission phases.

Contribution

It introduces a detailed analysis of the relativistic Rayleigh-Taylor instability in GRB shells, highlighting its growth rates and potential impact on turbulence and magnetic field generation.

Findings

Unstable to convective Rayleigh-Taylor modes at small scales.

Longer wavelength modes are stable and decay over time.

Instability may influence early GRB emission and magnetic field development.

Abstract

Global linear stability analysis of a self-similar solution describing the interaction of a relativistic shell with an ambient medium is performed. The solution is shown to be unstable to convective Rayleigh-Taylor modes having angular scales smaller than the causality scale. Longer wavelength modes are stable and decay with time. For modes of sufficiently large spherical harmonic degree $l$ the dimensionless growth rate scales as $\sqrt{l/\Gamma}$, where $\Gamma$ is the Lorentz factor of the shell. The instability commences at the contact interface separating the shocked eject a and shocked ambient gas and propagates to the shocks. The reverse shock front responds promptly to the in stability and exhibits rapidly growing distortions at early times. Propagation to the forward shock is slower, and it is anticipated that the region near the contact will become fully turbulent before the instability is communicated to the forward shock. The non-universality of the Blandford-McKee blast wave solution suggests that turbulence generated by the instability in the shocked ambient medium may decay slowly with time and may be the origin of magnetic fields over a long portion of the blast wave evolution. It is also speculated that the instability may affect the emission from the shocked ejecta in the early post-prompt phase of GRBs.