减速壳的相对论Rayleigh-Taylor不稳定性及其对伽马射线暴的启示
Relativistic Rayleigh-Taylor Instability of a Decelerating Shell and its Implications for Gamma Ray Bursts
摘要：
对描述相对论性壳与周围介质相互作用的自相似解进行了全局线性稳定性分析。的解决方案被证明是不稳定的对流瑞利-泰勒模式的角度尺度小于因果关系的规模。较长波长的模式是稳定的，并随时间衰减。对于足够大的球谐度$l$的模式，无量纲增长率的尺度为$\sqrt{l/Γ}$，其中$Γ$是壳的洛伦兹因子。不稳定性开始于分离冲击喷射a和冲击环境气体的接触界面，并传播到冲击。反向激波阵面对不稳定性迅速作出反应，并在早期表现出迅速增长的畸变。向前激波的传播较慢，预计在不稳定性传递到向前激波之前，接触点附近的区域将变得完全湍流。Blandford-McKee爆炸波解的非普适性表明，受冲击的周围介质中的不稳定性产生的湍流可能随时间缓慢衰减，并且可能是爆炸波演化过程中很长一段时间内磁场的起源。我们还推测这种不稳定性可能会影响伽玛暴后瞬发相早期冲击喷出物的辐射。
英文摘要：
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 $\sqrt{l/Γ}$, where $Γ$ 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.
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