林德布拉德区：共振偏心轨道，以帮助酒吧和螺旋形成星系盘
Lindblad Zones: resonant eccentric orbits to aid bar and spiral formation in galaxy discs
摘要：
在固定的引力势中，拱点进动频率随着轨道的径向范围（偏心率）而增加。虽然频率的增加是适度的，但它可能对星系盘中的波动动力学产生重要影响，这在以前没有被详细探索过。最有趣的结果之一是，对于给定的模式频率，每个Lindblad共振并不孤立存在，而是一个连续序列的共振半径，一个Lindblad区，在这个区域的每个半径的特点是一个特定的偏心率的父。在周转近似中，岁差或周转频率不依赖于周转点的大小，并且这种现象没有被捕获。偏心轨道的一个更好的近似是由p椭圆曲线（Struck 2006）提供的，它确实表现出这种效果。在这里的p-椭圆近似和岁差偏心率的关系被用作工具，用于寻找从各种Lindblad父共振产生的共振半径。简单的，理想化的例子，在平坦的旋转曲线和近固体盘，被用来表明，合奏的偏心共振轨道激发Lindblad区可以提供一个骨干产生各种（运动）酒吧和螺旋波。在平衡半径相关的圆频率和偏心率相关的进动的情况下，一系列的共振轨道可以保持它们在图案框架中的形式，并且不会卷起。偏心共振轨道需要一个强扰动来激发它们，并且可能主要在星系相互作用或强烈的内部扰动中产生。
英文摘要：
The apsidal precession frequency in a fixed gravitational potential increases with the radial range of the orbit (eccentricity). Although the frequency increase is modest it can have important implications for wave dynamics in galaxy discs, which have not been previously explored in detail. One of the most interesting consequences is that for a given pattern frequency, each Lindblad resonance does not exist in isolation, but rather is the parent of a continuous sequence of resonant radii, a Lindblad Zone, with each radius in this zone characterized by a specific eccentricity. In the epicyclic approximation the precession or epicyclic frequency does not depend on epicycle size, and this phenomenon is not captured. A better approximation for eccentric orbits is provided by p-ellipse curves (Struck 2006), which do exhibit this effect. Here the p-ellipse approximation and precession-eccentricity relation are used as tools for finding the resonant radii generated from various Lindblad parent resonances. Simple, idealized examples, in flat rotation curve and near solid-body discs, are used to show that ensembles of eccentric resonant orbits excited in Lindblad Zones can provide a backbone for generating a variety of (kinematic) bars and spiral waves. In cases balancing radius-dependent circular frequencies and eccentricity-dependent precession, a range of resonant orbits can maintain their form in the pattern frame, and do not wind up. Eccentric resonance orbits require a strong perturbation to excite them, and may be produced mostly in galaxy interactions or by strong internal disturbances.
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