Slow Modes in Keplerian Disks
Slow Modes in Keplerian Disks
复制标题
开普勒圆盘中的慢速模式
DOI：
10.1086/319398
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
S. Tremaine
中科院分区：
文献类型：
--
作者：
S. Tremaine
围绕大质量天体运行的小质量圆盘可以支持“慢”简正模式，在这种模式下，本征频率远小于轨道频率。慢模是不对称的，即方位向波数m=1。我们用软化的自引力作为圆盘中集体效应的简单模型，研究了慢模的性质。我们同时使用WKB近似和线性本征值方程的数值解。我们发现所有的慢模都是稳定的。离散慢模可以分为两类，我们称之为g-模和p-模。G模包括长前波和长尾波，具有由圆盘的自引力决定的性质，并且仅存在于进动速率由外部势主导的窄环或圆盘中。相反，p模的性质是由自引力和其他集体效应的相互作用决定的。P模包括长波和短波，在WKB近似下，出现简并的前导和拖尾对。磁盘支持有限数量--有时为零--的离散慢模式和连续的奇异模式。
Low-mass disks orbiting a massive body can support "slow" normal modes, in which the eigenfrequency is much less than the orbital frequency. Slow modes are lopsided, i.e., the azimuthal wavenumber m = 1. We investigate the properties of slow modes, using softened self-gravity as a simple model for collective effects in the disk. We employ both the WKB approximation and numerical solutions of the linear eigenvalue equation. We find that all slow modes are stable. Discrete slow modes can be divided into two types, which we label g-modes and p-modes. The g-modes involve long leading and long trailing waves, have properties determined by the self-gravity of the disk, and are only present in narrow rings or in disks where the precession rate is dominated by an external potential. In contrast, the properties of p-modes are determined by the interplay of self-gravity and other collective effects. P-modes involve both long and short waves, and in the WKB approximation appear in degenerate leading and trailing pairs. Disks support a finite number—sometimes zero—of discrete slow modes and a continuum of singular modes.