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Secular Behavior of Exoplanetary Systems: Self-Consistency and Comparisons With The Planet-Planet Scattering Hypothesis

Miles Timpe
Rory Barnes
Ravikumar Kopparapu
Sean N. Raymond
Richard Greenberg
The Astrophysics Journal, vol. 146 (2011), pp. 53
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Planet-planet scattering has been suggested as a mechanism to explain the disproportionate number of planet-planet pairs found to lie on or near an apsidal separatrix, in which one planet's eccentricity periodically drops to near-zero. We present the results of numerical simulations of 2-planet systems having arisen from dynamically unstable 3-planet systems. We show that the distribution of near-separatrix systems arising after an instability is consistent with the observed systems, further strengthening the planet-planet scattering hypothesis. We also note that many observed systems have been found near their extreme eccentricity values. Such a pattern may suggest a bias in exoplanet observations, as planets should have an equal probability of being discovered at any point in their secular cycle. We test this possibility by numerically integrating known multiplanet systems and determining the relative time each planet spends in a given eccentricity range and then comparing this distribution of eccentricity values to the observational uncertainty. We find that planets tend to spend more time near their minimum and maximum values as they represent turning points in the oscillations. Moreover, the uncertainties for many eccentricities are so large that we cannot make strong statements regarding the possibility that planets are being discovered at their extreme eccentricities too often. However, as uncertainties become smaller and more multiplanet systems are discovered, this potential bias should be revisited.

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