惰性奥尔特云中的混沌
Chaos in the inert Oort cloud
摘要：
背景：遥远的海王星外天体会受到行星摄动和银河潮汐的影响。前者随距离的增加而减小，后者随距离的增加而增大。在中间状态，它们具有相同的数量级（“惰性奥尔特云”），两者都很弱，导致非常长的演化时间尺度。迄今为止，有三个观测到的物体可以被认为属于这一类。目的：我们的目标是提供一个清晰的理解，这种转变发生在哪里，并在中间政权的小机构的长期动态：相关的共振，混沌区（如果有的话），并在发挥作用的时间尺度。结果：存在一个倾斜的平衡平面（拉普拉斯平面），轨道绕该平面进动。动力学在低半长轴和高半长轴区域是可积的，但在两者之间大多是混沌的。从800到1100 au，混沌几乎覆盖了所有的偏心率范围。扩散的时间尺度很大，但在4.5 Gyrs的持续时间内并没有达到难以辨别的程度：近日点距离实际上可以从几十到几百个天文单位不等。轨道变化在与明确定义的共振相对应的特定倾角范围内是有利的。从均匀分布开始，轨道角集群后4.5陀螺的半长轴大于500天文单位，因为一个非常缓慢的微分进动。结论：即使惰性奥尔特云具有很长的时间尺度，它的惰性也比它看起来的要小得多。在4.5 Gyrs以上的轨道，只有在轨道要素空间的一小部分，包括（90377）Sedna和2012VP 113，才可以被认为是惰性的。银河系潮汐的影响在半长轴约500 au的范围内是可以辨别的。我们主张将银河潮汐纳入遥远的海王星外天体的模拟中，特别是在研究分离天体的形成或轨道要素的聚集时。
英文摘要：
Context: Distant trans-Neptunian objects are subject to planetary perturbations and galactic tides. The former decrease with the distance, while the latter increase. In the intermediate regime where they have the same order of magnitude (the 'inert Oort cloud'), both are weak, resulting in very long evolution timescales. To date, three observed objects can be considered to belong to this category. Aims: We aim to provide a clear understanding of where this transition occurs, and to characterise the long-term dynamics of small bodies in the intermediate regime: relevant resonances, chaotic zones (if any), and timescales at play. Results: There exists a tilted equilibrium plane (Laplace plane) about which orbits precess. The dynamics is integrable in the low and high semi-major axis regimes, but mostly chaotic in between. From 800 to 1100 au, the chaos covers almost all the eccentricity range. The diffusion timescales are large, but not to the point of being indiscernible in a 4.5 Gyrs duration: the perihelion distance can actually vary from tens to hundreds of au. Orbital variations are favoured in specific ranges of inclination corresponding to well-defined resonances. Starting from uniform distributions, the orbital angles cluster after 4.5 Gyrs for semi-major axes larger than 500 au, because of a very slow differential precession. Conclusions: Even if it is characterised by very long timescales, the inert Oort cloud is much less inert than it appears. Orbits can be considered inert over 4.5 Gyrs only in small portions of the space of orbital elements, which include (90377) Sedna and 2012VP113. Effects of the galactic tides are discernible down to semi-major axes of about 500 au. We advocate including the galactic tides in simulations of distant trans-Neptunian objects, especially when studying the formation of detached bodies or the clustering of orbital elements.
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