The Late Stage of Planetary System Formation: Evidence from Secular Interactions among Extra-Solar Planets

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Secular interactions among planets can keep their orbital major axes in (or librating about) alignment, a configuration that until recently was widely considered characteristic of extrasolar planetary systems. Using up-to-date orbits of extrasolar planets and our numerical integrations, we find that such librations are actually not common but in fact are quite rare; most pairs of planets' major axes are consistent with circulation relative to one another. However, the new results confirm our earlier hypothesis that two-planet systems (whether librating or circulating) tend to lie near a separatrix between libration and circulation. Similarly, in systems of more than two planets, many adjacent orbits lie near a separatrix that divides modes of circulation. A defining characteristic of near-separatrix motion is that one eccentricity periodically reaches zero. One explanation for the origin of this type of interaction, applied to the Upsilon Andromedae system, has been that a scattering event occurred as two planets on circular orbits passed by one another. This scattering event throws one planet from the system, while the other goes into the near-separatrix interaction with a third planet. Using numerical integrations, we consider hundreds of this type of scattering event and find that near-separatrix motion is rare (<5% of cases, compared with nearly 50% of observed cases), and seems to require a specific sequence of events. Also, while half of observed librating systems oscillate about aligned pericenters and half about anti-aligned, our test of the planet-planet scattering model produces nearly all the former. We propose an alternative scattering model: The disturbing body was already on a very high eccentricity orbit, scattered in from another part of the system. After it set one of the regular planets on a moderately eccentric orbit, this rogue planet might quickly be ejected from the system, leaving behind planets in near-separatrix orbits.

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