论文标题
混乱的基本限制对紧凑的行星系统的不稳定性时间预测
Fundamental limits from chaos on instability time predictions in compact planetary systems
论文作者
论文摘要
紧凑的行星系统中的不稳定性通常由混乱的动力学驱动。这意味着通过直接N体积分测量的不稳定时间并不精确，而是代表同样有效的混乱轨迹的分布中的单个平局。为了在直接n体积分中表征报告的不稳定性时间的“错误”，我们研究了不稳定时间分布的形状和参数（ITD）的阴影轨迹集合，这些轨迹最初会彼此彼此互相扰动。我们发现，与Lyapunov（混乱）时间尺度相比，不稳定时间长的限制，ITD的方法非常相似，具有标准偏差的lognormal分布〜0.43 $ \ pm $ 0.16 DEX，尽管我们的样本中的不稳定时间从$ 10^4-10^8 $ Orbits中变化为$ 10^4-10^8美元。我们发现了这些预测之间的极好的一致性，这些预测来自三个行星的约450个密切包装的配置，以及〜20,000个集成的较广泛验证，以及〜20,000个以前出版的五个平面系统紧密包装的集成，以及基于Trappist-1的七个平面物共振链，尽管它们是基于Trappist-1的不稳定性泰晤士报，但不稳定的时间表超出了我们的范围。我们还测试了结果在太阳系的动态激发版本上的适用性。这些分布定义了混乱对这种行星系统中不稳定性时代的可预测性的基本极限。它提供了固有误差的定量估计值，这是混乱印记的N体不稳定性时间，这两个方向都大约为3倍。
Instabilities in compact planetary systems are generically driven by chaotic dynamics. This implies that an instability time measured through direct N-body integration is not exact, but rather represents a single draw from a distribution of equally valid chaotic trajectories. In order to characterize the "errors" on reported instability times from direct N-body integrations, we investigate the shape and parameters of the instability time distributions (ITDs) for ensembles of shadow trajectories that are initially perturbed from one another near machine precision. We find that in the limit where instability times are long compared to the Lyapunov (chaotic) timescale, ITDs approach remarkably similar lognormal distributions with standard deviations ~0.43 $\pm$ 0.16 dex, despite the instability times varying across our sample from $10^4-10^8$ orbits. We find excellent agreement between these predictions, derived from ~450 closely packed configurations of three planets, and a much wider validation set of ~10,000 integrations, as well as on ~20,000 previously published integrations of tightly packed five-planet systems, and a seven-planet resonant chain based on TRAPPIST-1, despite their instability timescales extending beyond our analyzed timescale. We also test the boundary of applicability of our results on dynamically excited versions of our Solar System. These distributions define the fundamental limit imposed by chaos on the predictability of instability times in such planetary systems. It provides a quantitative estimate of the intrinsic error on an N-body instability time imprinted by chaos, approximately a factor of 3 in either direction.
