AI 中文总结
本研究通过分析开普勒望远镜数据，发现开普勒-50系统受一颗非凌日行星扰动，其两颗近共振凌日行星的质量、偏心率等参数被精确约束，该系统为行星形成理论提供了重要基准。
AI 中文摘要
开普勒-50拥有两颗处于6:5平均运动共振附近的凌日行星。我们利用动力学拟合方法分析开普勒望远镜数据测得的凌日时间，将残差信号归因于该系统中一颗近共振的非凌日第三行星。第三行星的参数存在简并性；我们为外部摄动天体识别出55个感兴趣区域，为内部摄动天体识别出15个感兴趣区域，并对每个感兴趣区域内的系统参数进行后验采样表征。我们发现，剔除非长期稳定的样本不会为后验分布提供额外约束，且凌日时间未证实这两颗凌日行星很可能处于两体共振态——约68%的可能稳定后验样本也处于天平动状态。我们还识别出一小部分处于三体天平动的样本。尽管存在参数简并性，我们仍得到了约束严格的开普勒-50 b和c的质量，分别为2.35(+0.48,-0.43)M⊕和4.43(+0.45,-0.49)M⊕，并以高置信度探测到开普勒-50 b和c存在非零相对偏心率，其中(e_c cosϖ_c - e_b cosϖ_b)= -0.045±0.003，(e_c sinϖ_c - e_b sinϖ_b)= -0.030±0.004。这两颗邻近行星分别位于半径谷和亚海王星尺寸（半径分别为1.750±0.038R⊕和2.079±0.060R⊕）。作为已知轨道间距最近的行星系统之一，且接近一阶平均运动共振，开普勒-50系统是行星形成理论的重要基准。
英文摘要
Kepler-50 has two transiting planets close to the 6:5 commensurability. We analyze transit times measured from Kepler data with dynamical fits. We attribute the residual signal to a near-resonance non-transiting third planet in the system. The parameters of the third planet are degenerate. We identified 55 (15) regions of interest for an exterior (interior) perturber, and characterize system parameters in each region of interest with posterior sampling. We find that removing samples that are not long-term stable provides few additional constraints on posteriors, and that the transit times do not confirm the likely 2-body resonant state of the transiting planets as $\approx$ 68\% of posterior samples that are likely stable are also likely in libration. We identify a small fraction of samples that are in 3-body libration. Despite the degeneracies, we recover robust, tightly constrained masses for Kepler-50 b and c ($2.35^{+0.48}_{-0.43}$ $M_{\oplus}$ and $4.43^{+0.45}_{-0.49}$ $M_{\oplus}$, respectively) and strongly detected non-zero relative eccentricity for Kepler-50 b and c with ($e_c\cos\varpi_c$ - $e_b\cos\varpi_b$) = -0.045 $\pm 0.003$, and ($e_c\sin\varpi_c$ - $e_b\sin\varpi_b$) = -0.030 $\pm 0.004$. These close neighbors are in the radius valley and sub-Neptune by size, respectively ($1.750 \pm 0.038$ $R_{\oplus}$ and $2.079 \pm 0.060$ $R_{\oplus}$). With one of the closest planet pairs known and one of the closest to first-order commensurability, the Kepler-50 system is an especially valuable benchmark for planet formation theory.
