Recent observational surveys of the outer solar system provide evidence that Neptune's distant n:1 mean motion resonances may harbor relatively large reservoirs of trans-Neptunian objects (TNOs). In particular, the discovery of two securely classified 9:1 resonators, 2015 KE₁₇₂ and 2007 TC₄₃₄, by the Outer Solar System Origins Survey is consistent with a population of order 10⁴ such objects in the 9:1 resonance with absolute magnitude H _r < 8.66. This work investigates whether the long-term stability of such populations in Neptune’s n:1 resonances can be used to constrain the existence of distant 5–10 M _⊕ planets orbiting at hundreds of au. The existence of such a planet has been proposed to explain a reported clustering in the orbits of highly eccentric “extreme” trans-Neptunian objects (or eTNOs), although this hypothesis remains controversial. We engage in a focused computational case study of the 9:1 resonance, generating synthetic populations and integrating them for 1 Gyr in the presence of 81 different test planets with various masses, perihelion distances, eccentricities, and inclinations. While none of the tested planets are incompatible with the existence of 9:1 resonators, our integrations shed light on the character of the interaction between such planets and nearby n:1 resonances, and we use this knowledge to construct a simple heuristic method for determining whether or not a given planet could destabilize a given resonant population. We apply this method to the currently estimated properties of Planet 9, and find that a large primordial population in the 15:1 resonance (or beyond), if discovered in the future, could potentially constrain the existence of this planet.

中文翻译：

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海王星的遥远平均运动共振能否限制太阳系中未被发现的行星？ 9:1 共振案例研究的教训

最近对外太阳系的观测调查提供了证据表明海王星距离遥远n:1 平均运动共振可能蕴藏着相对较大的海王星外天体（TNO）。特别是，外太阳系起源巡天发现的两个安全分类的 9:1 谐振器 2015 KE ₁₇₂和 2007 TC _{434与绝对星等的 9:1 谐振中的 10} ^{4 个}此类物体的数量一致。H _r < 8.66。这项工作调查了海王星中此类种群的长期稳定性是否n:1 共振可用于限制远距离 5–10 的存在中号 _⊕绕轨道运行数百个天文单位的行星。人们提出这样一颗行星的存在来解释据报道的高度偏心“极端”海王星天体（或 eTNO）轨道上的聚集，尽管这一假设仍然存在争议。我们对 9:1 共振进行了集中的计算案例研究，生成合成种群，并在 81 个具有不同质量、近日点距离、偏心率和倾角的不同测试行星的存在下将它们整合为 1 Gyr。虽然所有经过测试的行星都与 9:1 谐振器的存在不相容，但我们的集成揭示了此类行星与附近行星之间相互作用的特征n:1 共振，我们利用这些知识构建了一个简单的启发式方法来确定给定的行星是否会破坏给定的共振群体的稳定。我们将这种方法应用于目前估计的第 9 号行星的属性，发现如果将来发现 15:1 共振（或更高）的大量原始种群，可能会限制这颗行星的存在。