球对称无碰撞恒星系统径向轨道不稳定性的性质
On the nature of the radial orbit instability in spherically symmetric collisionless stellar systems
摘要：
我们考虑一个中心具有非奇异密度分布的径向各向异性模型的双参数族。如果高偏心率的轨道被锁定在中心附近，不稳定性的特征增长率远小于恒星的牛仔裤和动态频率（慢模式）。不稳定性只发生在偶球谐函数上，扰动纯粹是增长的（非周期的）。相反，如果所有的轨道都接近球的外半径，那么偶次谐波和奇次谐波都是不稳定的。不稳定的奇模振荡具有动态频率（快模）量级的特征频率。不稳定偶次谐波包含一个单一的非周期模式和几个振荡模式，非周期模式是最不稳定的。径向轨道不稳定性（ROI）的性质的问题被重新讨论。在文献中提出了两种主要的解释ROI。第一个是指经典的金斯不稳定性与缺乏速度色散的恒星在横向方向。第二种是Lynden-Bell关于盘星系棒形成的轨道方法，它意味着扰动的慢性和双对称性。振荡模式，奇球谐模式，并在一个模型中发现的非慢模式表明，轨道的解释是不是唯一可能的。
英文摘要：
We consider a two-parametric family of radially anisotropic models with non-singular density distribution in the centre. If highly eccentric orbits are locked near the centre, the characteristic growth rate of the instability is much less than the Jeans and dynamic frequencies of the stars (slow modes). The instability occurs only for even spherical harmonics and the perturbations are purely growing (aperiodic). On the contrary, if all orbits nearly reach the outer radius of the sphere, both even and odd harmonics are unstable. Unstable odd modes oscillate having characteristic frequencies of the order of the dynamical frequencies (fast modes). Unstable even harmonics contain a single aperiodic mode and several oscillatory modes, the aperiodic mode being the most unstable. The question of the nature of the radial orbit instability (ROI) is revisited. Two main interpretations of ROI were suggested in the literature. The first one refers to the classical Jeans instability associated with the lack of velocity dispersion of stars in the transverse direction. The second one refers to Lynden-Bell's orbital approach to bar formation in disc galaxies, which implies slowness and bi-symmetry of the perturbation. Oscillatory modes, odd spherical harmonics modes, and non-slow modes found in one of the models show that the orbital interpretation is not the only possible.
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