一般多方同调坍缩星核的摄动分析
Perturbation Analysis of a General Polytropic Homologously Collapsing Stellar Core
摘要：
对于Goldreich & Weber和Lou & Cao的动力学背景模型，我们研究了多变指数为4/3的相对论性热介质的一般多变同系坍缩星核的振荡和不稳定性的三维扰动性质.我们识别声学p模式和表面f模式以及内部重力g $^{+}-$和g $^{-}-$模式。我们证明，全球能源标准的Ehrasehkar是不够的，以保证稳定的一般多方平衡。我们证实了Goldreich & Weber的声学p模稳定性，即使他们的p模本征值出现在系统误差中。不稳定模式包括g $^{-}-$模式和高阶g $^{+}-$模式。这种不稳定性发生在恒星核心反弹之前，与其他超新星爆炸模型中的不稳定性形成对比。到目前为止，球对称性的破坏比数值模拟中预期的要早。中央致密物体的形成和运动被推测受到这种g模式不稳定性的影响。通过典型参数的估计，不稳定的低阶l=1 g模可能会产生中心紧凑对象的初始踢。
英文摘要：
For dynamic background models of Goldreich & Weber and Lou & Cao, we examine 3-dimensional perturbation properties of oscillations and instabilities in a general polytropic homologously collapsing stellar core of a relativistic hot medium with a polytropic index of 4/3. We identify acoustic p-modes and surface f-modes as well as internal gravity g$^{+}-$ and g$^{-}-$modes. We demonstrate that the global energy criterion of Chandrasehkar is insufficient to warrant the stability of general polytropic equilibria. We confirm the acoustic p-mode stability of Goldreich & Weber, even though their p-mode eigenvalues appear in systematic errors. Unstable modes include g$^{-}-$modes and high-order g$^{+}-$modes. Such instabilities occur before the stellar core bounce, in contrast to instabilities in other models of supernova explosions. The breakdown of spherical symmetry happens earlier than expected in numerical simulations so far. The formation and motion of the central compact object are speculated to be much affected by such g-mode instabilities. By estimates of typical parameters, unstable low-order l=1 g-modes may produce initial kicks of the central compact object.
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