太阳系类似物的命运与一个额外的遥远行星
The fates of Solar system analogues with one additional distant planet
摘要：
太阳系中可能存在一颗遥远的行星（“行星九”），这促使人们重新思考行星系的演化。当太阳从一颗主序星转变为一颗白矮星时，木星、土星、天王星和海王星目前被认为会在膨胀但其他方面不变的轨道上生存下来。然而，一个非常遥远和非常巨大的额外行星将通过太阳巨星分支质量损失和银河系潮汐的综合影响改变这种静止的结局。在这里，我估计一个遥远的额外行星的质量和轨道的界限，这将煽动未来的不稳定系统与太阳一样的恒星和巨大的行星与质量和轨道相当于木星，土星，天王星和海王星。我发现，这个边界是弥漫的，强烈依赖于每个遥远的行星的轨道参数。尽管如此，我认为，当行星质量与木星一样大，半长轴超过300 au，或者质量与超级地球相当，半长轴超过3000 au时，不稳定性往往会发生。这些结果适用于从100到至少400 au的轨道近心点。这种不稳定的情况可能是一种常见的现象，整个银河系白矮星大气中普遍存在的金属污染可能就是明证。
英文摘要：
The potential existence of a distant planet ("Planet Nine") in the Solar system has prompted a re-think about the evolution of planetary systems. As the Sun transitions from a main sequence star into a white dwarf, Jupiter, Saturn, Uranus and Neptune are currently assumed to survive in expanded but otherwise unchanged orbits. However, a sufficiently-distant and sufficiently-massive extra planet would alter this quiescent end scenario through the combined effects of Solar giant branch mass loss and Galactic tides. Here, I estimate bounds for the mass and orbit of a distant extra planet that would incite future instability in systems with a Sun-like star and giant planets with masses and orbits equivalent to those of Jupiter, Saturn, Uranus and Neptune. I find that this boundary is diffuse and strongly dependent on each of the distant planet's orbital parameters. Nevertheless, I claim that instability occurs more often than not when the planet is as massive as Jupiter and harbours a semimajor axis exceeding about 300 au, or has a mass of a super-Earth and a semimajor axis exceeding about 3000 au. These results hold for orbital pericentres ranging from 100 to at least 400 au. This instability scenario might represent a common occurrence, as potentially evidenced by the ubiquity of metal pollution in white dwarf atmospheres throughout the Galaxy.
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