Stability of power‐law discs — II. The global spiral modes
Stability of power‐law discs — II. The global spiral modes
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幂律圆盘的稳定性 - II. 全局螺旋模式
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
J. Read
中科院分区：
文献类型：
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作者：
N. Evans;J. Read
本文报道了自洽和截断幂函数圆盘中的面内简正模。尽管切割盘对双对称微扰非常稳定，但它们对单臂模式非常敏感。对于这种谐波，没有内部Lindblad共振，因此消除了强大的稳定影响。提出了单臂不稳定性产生的物理机制。输入的尾波在内切口处被反射为前导波，从而完成对摆动放大器的反馈。生长的三臂和四臂模式只在非常低的温度下发生。然而，对于一些光盘来说，在更高的温度下，中性m=3和m=4模式是可能的。旋转曲线指标β对稳定性有显著影响。对于所有方位向波数，如果旋转曲线上升，任何不稳定的模式都会持续到更高的温度，并增长得更强劲(β：0)。如果椎间盘的中心区域或外部被更突然地切割出来，任何不稳定因素都会变得更加致命。自洽的幂律圆盘具有许多不寻常的稳定性性质。在自洽圆盘中没有自然的时间尺度。如果一个模式以一定的模式速度和增长率被接纳，那么它必须在所有模式速度和增长率下都存在。我们的分析--尽管缺乏完整的证据--表明这种非轴对称模的二维连续体并不存在，并且自洽的幂定律盘不允许任何全局非轴对称简正模。没有反射边界或切割，就没有谐振腔，也就不可能出现不稳定的增长模。自洽的幂定律圆盘肯定允许等角螺线作为中性模，以及一维连续增长的轴对称模。
This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m = 3 and m = 4 modes are possible at higher temperatures for some discs. The rotation curve index β has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (β 0). If the central regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis — although falling short of a complete proof — suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law discs admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.