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Truly eccentric. II. When can two circular planets mimic a single eccentric orbit?

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 Added by Robert Wittenmyer
 Publication date 2019
  fields Physics
and research's language is English




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When, in the course of searching for exoplanets, sparse sampling and noisy data make it necessary to disentangle possible solutions to the observations, one must consider the possibility that what appears to be a single eccentric Keplerian signal may in reality be attributed to two planets in near-circular orbits. There is precedent in the literature for such outcomes, whereby further data or new analysis techniques reveal hitherto occulted signals. Here, we perform suites of simulations to explore the range of possible two-planet configurations that can result in such confusion. We find that a single Keplerian orbit with $e>$0.5 can virtually never be mimicked by such deceptive system architectures. This result adds credibility to the most eccentric planets that have been found to date, and suggests that it could well be worth revisiting the catalogue of moderately eccentric confirmed exoplanets in the coming years, as more data become available, to determine whether any such deceptive couplets are hidden in the observational data.



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We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos occurs where mean motion resonances overlap, as in Wisdom (1980)s pioneering work. But whereas Wisdom considered only nearly circular planets, and hence examined only first order resonances, we extend his results to arbitrarily eccentric planets (up to crossing orbits) by examining resonances of all orders. We thereby arrive at a simple expression for the critical eccentricity. We do this first for a test particle in the presence of a planet, and then generalize to the case of two massive planets, based on a new approximation to the Hamiltonian (Hadden, in prep). We then confirm our results with detailed numerical simulations. Finally, we explore the extent to which chaotic two-planet systems eventually result in planetary collisions.
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