周期性使星系激波不稳定。线性分析
Periodicity makes galactic shocks unstable - I. Linear analysis
摘要：
我们研究了静止星系螺旋激波的动力学稳定性。定常平衡流包含罗伯茨在紧绕近似中导出的那类激波。我们发现边界条件是决定解是否稳定的关键。如果施加周期性边界条件，冲击是不稳定的。对于中等强度的螺旋势，如果施加边界条件，使上游流保持不变，如D 'yakov和Kontorovich的经典分析那样，不稳定性消失。这调和了先前作者关于螺旋冲击稳定性的明显矛盾的发现。这也表明，不稳定性是不同的Kelvin-Helmholtz不稳定性，确认Kim等人的研究结果。我们认为，不稳定性是一个一般的特征周期性冲击，无论剪切的存在，并提供了一个物理图片，为什么是这种情况。对于强螺旋势，无论边界条件如何，高的激波后剪切都会使系统不稳定，也会导致寄生Kelvin-Helmholtz不稳定。我们的分析是在一个简化的问题，同时保留所有的重要特征的原始问题，剥离它不必要的复杂性，并假设气体是等温的，非自引力，非磁化的情况下进行的。
英文摘要：
We study the dynamical stability of stationary galactic spiral shocks. The steady-state equilibrium flow contains a shock of the type derived by Roberts in the tightly wound approximation. We find that boundary conditions are critical in determining whether the solutions are stable or not. Shocks are unstable if periodic boundary conditions are imposed. For intermediate strengths of the spiral potential, the instability disappears if boundary conditions are imposed such that the upstream flow is left unperturbed as in the classic analysis of D'yakov and Kontorovich. This reconciles apparently contradictory findings of previous authors regarding the stability of spiral shocks. This also shows that the instability is distinct from the Kelvin-Helmholtz instability, confirming the findings of Kim et al. We suggest that instability is a general characteristics of periodic shocks, regardless of the presence of shear, and provide a physical picture as to why this is the case. For strong spiral potentials, high post-shock shear makes the system unstable also to parasitic Kelvin-Helmholtz instability regardless of the boundary conditions. Our analysis is performed in the context of a simplified problem that, while preserving all the important characteristics of the original problem, strips it from unnecessary complications, and assumes that the gas is isothermal, non self-gravitating, non-magnetised.
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