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F. Marzari (Univ. di Padova and Planetary Science Institute), S. J. Weidenschilling (Planetary Science Institute)
Extrasolar planets (ESPs) seem to be divided into two groups: circular orbits very close to their stars, or eccentric orbits at larger distances. The latter may be the result of gravitational scattering of planets that formed in unstable orbits (Weidenschilling and Marzari 1996, Nature 384, 619). For systems of three Jupiter-mass planets, the most common outcome is ejection of one planet, leaving the others in stable orbits with significant eccentricities and mutual inclinations. We have compiled statistics for orbital elements of the survivors. At the time of ejection, the eccentricity of the inner one has a broad distribution with modal value ~0.5, ranging from about 0.1 to 0.9; smaller and larger values are rare. In contrast, among observed eccentric ESPs only 2 of 11 have e > 0.5, and none have e > 0.7, although there is no observational bias against detection of planets on eccentric orbits. One possible explanation is a large cross-section for young gas giant planets still in their contraction phase, so that non-collisional encounters yield smaller velocity changes. However, even if the effective radius is twice Jupiter's present value, the eccentricity distribution does not change significantly. The "snapshot" distribution at the time one planet is ejected may be misleading. The orbits of the remaining planets are subject to mutual perturbations. The inner planet's eccentricity may oscillate with large amplitude on timescales of 107 - 108 y. Peak values bring some periastrons low enough for tides to circularize orbits. For planets with large initial eccentricities, the time-averaged e is lower, yielding better agreement with the observed distribution. Still, some orbits with eccentricities up to 0.9, should be detected in a large enough sample of ESPs. If none are found, their absence would argue against gravitational scattering as a general phenomenon in planetary systems.