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arXiv 1901.04487astro-ph.HE
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有吸积的弱激波传播。II。径向扰动自相似解的稳定性

Weak Shock Propagation with Accretion. II. Stability of Self-similar Solutions to Radial Perturbations

Eric R. Coughlin, Stephen Ro, Eliot Quataert

摘要:

Coughlin等人(2018)(论文I)推导并分析了一种新的自相似机制,该机制描述了质点的引力场中的弱激波(单位阶马赫数)。这些解与低能爆炸有关,包括失败的超新星。在本文中,我们开发了一个形式主义的稳定性分析的冲击径向扰动,我们证明了自相似的解决方案文件I是非常弱的不稳定,这样的径向扰动。具体来说,我们表明,扰动的冲击波速度和冲击后的流体量(速度,密度和压力)的增长随着时间的$t^α$,其中$α\le 0.12$,这意味着这种扰动的十倍的时间尺度大约是十个数量级的时间。我们通过进行高分辨率,随时间变化的数值模拟来证实这些预测。使用相同的形式主义,我们还表明,Sedov-Taylor爆炸波是平凡稳定的径向扰动提供的自相似,Sedov-Taylor解决方案延伸到原点,我们推导出简单的表达式的扰动后冲击波的速度,密度和压力。最后,我们证明了描述稀疏波的流体方程存在第三种自相似解(除了论文I中的解和Sedov-Taylor解之外),即,振幅极小的向外传播的声波。我们解释了这三个不同的自相似解决方案的冲击波传播的稳定性。

英文摘要:

Coughlin et al. (2018) (Paper I) derived and analyzed a new regime of self-similarity that describes weak shocks (Mach number of order unity) in the gravitational field of a point mass. These solutions are relevant to low energy explosions, including failed supernovae. In this paper, we develop a formalism for analyzing the stability of shocks to radial perturbations, and we demonstrate that the self-similar solutions of Paper I are extremely weakly unstable to such radial perturbations. Specifically, we show that perturbations to the shock velocity and post-shock fluid quantities (the velocity, density, and pressure) grow with time as $t^α$, where $α\le 0.12$, implying that the ten-folding timescale of such perturbations is roughly ten orders of magnitude in time. We confirm these predictions by performing high-resolution, time-dependent numerical simulations. Using the same formalism, we also show that the Sedov-Taylor blastwave is trivially stable to radial perturbations provided that the self-similar, Sedov-Taylor solutions extend to the origin, and we derive simple expressions for the perturbations to the post-shock velocity, density, and pressure. Finally, we show that there is a third, self-similar solution (in addition to the the solutions in Paper I and the Sedov-Taylor solution) to the fluid equations that describes a rarefaction wave, i.e., an outward-propagating sound wave of infinitesimal amplitude. We interpret the stability of shock propagation in light of these three distinct self-similar solutions.

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