直接成像的多行星系统HR 8799的稳定性：共振和质量
Stability of the directly imaged multiplanet system HR 8799: resonance and masses
摘要：
直接成像太阳系外行星的新时代产生了一个三行星系统（Marois等人，2008），其中行星的质量是通过未经测试的冷却模型估计的。我们指出，行星的名义圆形、面对面的轨道导致动力学不稳定性在~10^5年，比恒星的估计年龄至少短100倍。行星质量的减少只会使小得不合理的行星（<~2 M_ Jup）产生稳定性。放松正面假设，但仍然需要圆形轨道，同时拟合观测到的位置，使不稳定时间更短。一个有希望的解决方案是，内侧的两颗行星在它们的周期之间有2：1的可调和性，并且它们通过这种共振避免彼此的近距离相遇。内部共振一直持续到现在，尽管外部行星的扰动，导致质量的限制<~10 M_Jup，除非外部两颗行星也参与2：1的平均运动共振。在双共振中，这与目前的数据一致，即使行星的质量为~20 M_Jup，该系统也可以生存到现在。拱点对准可以进一步增强平均运动谐振系统的稳定性。一个完全不同的动力学配置，大偏心率和大的行星之间的相互倾斜，是可能的，但微调。
英文摘要：
A new era of directly imaged extrasolar planets has produced a three-planet system (Marois et al. 2008), where the masses of the planets have been estimated by untested cooling models. We point out that the nominal circular, face-on orbits of the planets lead to a dynamical instability in ~10^5 yr, a factor of at least 100 shorter than the estimated age of the star. Reduced planetary masses produce stability only for unreasonably small planets (<~2 M_ Jup). Relaxing the face-on assumption, but still requiring circular orbits while fitting the observed positions, makes the instability time even shorter. A promising solution is that the inner two planets have a 2:1 commensurability between their periods, and they avoid close encounters with each other through this resonance. That the inner resonance has lasted until now, in spite of the perturbations of the outer planet, leads to a limit <~10 M_Jup on the masses unless the outer two planets are also engaged in a 2:1 mean-motion resonance. In a double resonance, which is consistent with the current data, the system could survive until now even if the planets have masses of ~20 M_Jup. Apsidal alignment can further enhance the stability of a mean-motion resonant system. A completely different dynamical configuration, with large eccentricities and large mutual inclinations among the planets, is possible but finely tuned.
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