Protostars and Planets VI, Heidelberg, July 15-20, 2013
THE ORBITAL STABILITY OF PLANETS IN THE FIRST-ORDER MEAN- MOTION RESONANCES
Matsumoto, Yuji (Tokyo Tech)
Nagasawa, Makiko (Tokyo Tech)
Ida, Shigeru (Tokyo Tech)
Many extrasolar planetary systems containing multiple super-Earths have been discovered near the central stars. Kepler Mission reports 885 of those multiples in 361 systems (e.g., Batalha et al., 2012). Period ratios of pairs of planets show some peaks at commensurable ratios (e.g., Fabrycky et al., 2012). N-body simulations concerning standard type I migration suggest that protoplanets are captured into mean-motion resonances near the inner edge where the migration is halted (Terquem & Papaloizou 2007). Ogihara & Ida (2009) showed that in the case of migration that is slow compared to the rates predicted for linear calculations of type I migration, protoplanets are captured in the resonances and cause orbital instability after gas removal. Through close scattering and merging among protoplanets, non-resonant systems are formed. We investigated the orbital stability of planets trapped in first-order resonances. We calculated the crossing time of systems in resonances, with changing the total number of planets, the orbital separations in mutual Hill radius, and planetary masses. We found that when the total number of planets is larger than the critical number, the crossing time is similar to that of non-resonant cases, while the orbital instability never occurs within calculation time (10^8 Kepler time) when the total number of planets is equal to or less than the critical number. When 10^-5 solar mass planets are trapped in 7:6 resonances around the solar mass star, the orbital separations are equal to 5.456 Hill radius. In this case, the critical number is equal to 4. The critical number increases with increasing the orbital separation in mutual Hill radii with fixed planetary mass and increases with increasing planetary mass with fixed the orbital separation in mutual Hill radii. When 10^-4 solar mass planets are trapped in 3:2 resonances, the orbital separations become 6.626 Hill radius, and the critical number is over 15. Many observed planets close to the central star and not in resonances are suggested that protoplanets over the critical number are trapped in resonances due to migration and these protoplanets cause instability. When the planetary systems whose planets are in resonances have wide orbital separations, large mass planets, and small number of planets, the planets are left in resonant orbits.
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