Formulations Of Planetary Migration In A Planetesimal Disk

Astronomy and Astrophysics – Astronomy

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Formulations of planetary migration are developed. Solar system experienced planetary migration when its formation stage. Especially, an outward orbital migration of Neptune in early solar system history provides an efficient mechanism for shortening the planet growth time as well as sweeping up large numbers of Trans-Neptunian objects into Neptune's mean-motion resonances. In some previous researches, they show that migration of Neptune occurred as a result of angular momentum exchange between planetesimal disk and Neptune. But there are two difficulties to migrate the Neptune outward in normal disk.First problem is that surface density of the disk thins by going outside. Second, synodic period of the inner region of a planet is shorter than outer region. As a result, Neptune encounters inner planetesimals more than outer planetesimals. For the outward migration of Neptune, it needs inner heavy planet like Jupiter. In this situation, planetesimals around Neptune are scattered and stochastically increase their eccentricities and some of them are finally scattered by Jupiter and remove from feeding zone of Neptune. Then the net angular momentum can be deemed it transferred from the removed planetesimals to Neptune. On these grounds we paid attention to three timescales κi, κo, and κs to formulate the planetary migration. κi is the timescale takes to planetesimal jump into outer gravitational region from inner region of planet. κo is the opposite term of κi. κs is the timescale takes to scattering planetesimal by Jupiter.In our formulations of planetary migration, these three timescale and the mass in the gravitational region determined the aspects of migration and it consistent with the results of N-body calculations in several mass distributions.

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