相对论性磁化喷流边界处的开尔文-亥姆霍兹不稳定性
The Kelvin-Helmholtz instability at the boundary of relativistic magnetized jets
AI总结：
本文通过线性稳定性分析研究相对论性磁化喷流边界的开尔文-亥姆霍兹不稳定性，推导出色散关系解析解，并揭示波矢与磁场夹角决定喷流在亚阿尔芬或超阿尔芬条件下的不稳定性判据。
摘要：
我们研究分隔两种相对运动流体的平面界面的线性稳定性，重点关注适用于相对论性喷流边界的条件。喷流以磁场为主导，而环境风以气体压力为主导。我们推导出色散关系的最一般形式，并针对环境声速远小于喷流阿尔芬速度 $v_A$ 的情况（适用于现实系统）给出其解的解析近似。稳定性性质主要由波矢与喷流磁场之间的夹角 $ψ$ 决定。当 $ψ=π/2$ 时，磁张力不起作用，我们的解类似于以气体压力为主导的喷流的解。此时，只有亚阿尔芬喷流是不稳定的（$0<M_e\equiv(v/v_A)\cosθ<1$，其中 $v$ 是剪切速度，$θ$ 是速度与波矢之间的夹角）。当 $ψ=0$ 时，速度剪切中的自由能需要克服磁张力，只有超阿尔芬喷流是不稳定的（$1<M_e<\sqrt{(1+Γ_w^2)/[1+(v_A/c)^2Γ_w^2]}$，其中 $Γ_w$ 是风的绝热指数）。我们的结果对相对论性磁化喷流的传播和辐射具有重要影响。
英文摘要：
We study the linear stability of a planar interface separating two fluids in relative motion, focusing on conditions appropriate for the boundaries of relativistic jets. The jet is magnetically dominated, whereas the ambient wind is gas-pressure dominated. We derive the most general form of the dispersion relation and provide an analytical approximation of its solution for an ambient sound speed much smaller than the jet Alfvén speed $v_A$, as appropriate for realistic systems. The stability properties are chiefly determined by the angle $ψ$ between the wavevector and the jet magnetic field. For $ψ=π/2$, magnetic tension plays no role, and our solution resembles the one of a gas-pressure dominated jet. Here, only sub-Alfvénic jets are unstable ($0<M_e\equiv(v/v_A)\cosθ<1$, where $v$ is the shear velocity and $θ$ the angle between the velocity and the wavevector). For $ψ=0$, the free energy in the velocity shear needs to overcome the magnetic tension, and only super-Alfvénic jets are unstable ($1<M_e<\sqrt{(1+Γ_w^2)/[1+(v_A/c)^2Γ_w^2]}$, with $Γ_w$ the wind adiabatic index). Our results have important implications for the propagation and emission of relativistic magnetized jets.
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