We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in ~ 20% of the cases on a wide range of timescales (up to 5×109 orbits) and over an unexpectedly wide range of initial dynamical spacings. To identify the triggers of long-term instability in multi-planet systems, we investigated in detail the five-planet Kepler-102 system. Despite having several near-resonant period ratios, we find that mean motion resonances are unlikely to directly cause instability for plausible planet masses in this system. Instead, we find strong evidence that slow inward transfer of angular momentum deficit (AMD) via secular chaos excites the eccentricity of the innermost planet, Kepler-102 b, eventually leading to planet-planet collisions in ~ 80% of Kepler-102 simulations. Kepler-102 b likely needs a mass ≳ 0.1M ⊕, hence a bulk density exceeding about half Earth's, in order to avoid dynamical instability. To investigate the role of secular chaos in our wider set of simulations, we characterize each planetary system's AMD evolution with a "spectral fraction" calculated from the power spectrum of short integrations (~ 5 × 106 orbits). We find that small spectral fractions (≲ 0.01) are strongly associated with dynamical stability on long timescales (5 × 109 orbits) and that the median time to instability decreases with increasing spectral fraction. Our results support the hypothesis that secular chaos is the driver of instabilities in many non-resonant multi-planet systems, and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long term (in)stability of multi-planet systems from short simulations.

中文翻译：

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多个短周期行星系统的动力不稳定性可能是由长期混沌驱动的：Kepler-102 的案例研究

我们研究了高多重开普勒和 K2 行星系统的动力学稳定性。我们的数值模拟发现，大约 20% 的情况在很宽的时间尺度范围内（高达 5×109 轨道）和在出乎意料的广泛的初始动力间距范围内都存在不稳定性。为了确定多行星系统长期不稳定的触发因素，我们详细研究了五行星 Kepler-102 系统。尽管有几个近共振周期比，我们发现平均运动共振不太可能直接导致该系统中合理行星质量的不稳定。相反，我们发现强有力的证据表明，角动量赤字 (AMD) 通过长期混沌缓慢向内转移激发了最内部行星 Kepler-102 b 的离心率，最终导致约 80% 的 Kepler-102 模拟发生行星-行星碰撞。Kepler-102 b 可能需要质量 ≳ 0.1M ⊕，因此体积密度超过地球的一半左右，以避免动力学不稳定。为了研究长期混沌在我们更广泛的模拟中的作用，我们用从短积分（~ 5 × 106 轨道）的功率谱计算的“光谱分数”来表征每个行星系统的 AMD 演化。我们发现小光谱分数 (≲ 0.01) 与长时间尺度（5 × 109 轨道）上的动力学稳定性密切相关，并且不稳定的中值时间随着光谱分数的增加而减少。我们的结果支持这样一个假设，即长期混沌是许多非共振多行星系统不稳定的驱动因素，