We present the discovery of Kepler-129 d ( yr, , ) based on six years of radial-velocity observations from Keck/HIRES. Kepler-129 also hosts two transiting sub-Neptunes: Kepler-129 b (P _b = 15.79 days, r _b = 2.40 0.04 R _⊕) and Kepler-129 c (P _c = 82.20 days, r _c = 2.52 0.07 R _⊕) for which we measure masses of m _b < 20 M _⊕ and . Kepler-129 is a hierarchical system consisting of two tightly packed inner planets and a massive external companion. In such a system, two inner planets precess around the orbital normal of the outer companion, causing their inclinations to oscillate with time. Based on an asteroseismic analysis of Kepler data, we find tentative evidence that Kepler-129 b and c are misaligned with stellar spin axis by ≳38, which could be torqued by Kepler-129 d if it is inclined by ≳19 relative to inner planets. Using N-body simulations, we provide additional constraints on the mutual inclination between Kepler-129 d and inner planets by estimating the fraction of time during which two inner planets both transit. The probability that two planets both transit decreases as their misalignment with Kepler-129 d increases. We also find a more massive Kepler-129 c enables the two inner planets to become strongly coupled and more resistant to perturbations from Kepler-129 d. The unusually high mass of Kepler-129 c provides a valuable benchmark for both planetary dynamics and interior structure, since the best-fit mass is consistent with this 2.5 R _⊕ planet having a rocky surface.

我们根据 Keck/HIRES 六年的径向速度观测结果，介绍了 Kepler-129 d ( yr, , )的发现。开普勒-129也主机上的两个中转子海王星：开普勒-129 B（P _b =15.79天，- [R _b = 2.40 0.04 - [R _⊕）和开普勒-129 C（P _{c ^} =82.20天，- [R _{c ^} = 2.52 0.07 - [R _⊕）我们测量质量m _b < 20 M _⊕和 . Kepler-129 是一个等级系统，由两个紧密排列的内部行星和一个巨大的外部伴星组成。在这样的系统中，两颗内行星围绕外伴星的轨道法线进动，导致它们的倾角随时间摆动。基于对开普勒数据的星震分析，我们发现初步证据表明开普勒 129 b 和 c 与恒星自旋轴错位 ≳38，如果开普勒 129 d 相对于内行星倾斜 ≳19，则可能会被开普勒 129 d 扭转. 使用N-body 模拟，我们通过估计两个内行星都凌日的时间分数，为 Kepler-129 d 和内行星之间的相互倾角提供了额外的约束。随着它们与 Kepler-129 d 错位的增加，两颗行星都凌日的概率会降低。我们还发现质量更大的 Kepler-129 c 使两颗内行星变得强烈耦合，并且更能抵抗来自 Kepler-129 d 的扰动。Kepler-129 c 异常高的质量为行星动力学和内部结构提供了一个有价值的基准，因为最合适的质量与这颗具有岩石表面的2.5 R _⊕行星一致。