Orbital Evolution of Exoplanets Caused by Scattering and Tides

Mathematics – Probability

Scientific paper

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Scientific paper

We have investigated formation of Hot-Jupiters by a combination of mutual scattering, secular effects and tidal circularization. We perform N-body simulations of three gas giant planets including the effect of the general relativity and inclusion of inertial modes in additions to fundamental modes in the tides.
We found that in about 350 cases out of 1200 runs (about 30%), the eccentricity of one of planets is excited highly enough for the tidal circularization by mutual close scatterings followed by Kozai effect or the effect of secular chaos due to outer planets and the planet becomes a close-in planet. The formation probability of close-in planets is the same order of that of simulations without the general relativity and the inertial modes. The formation probability of close-in planets is about 20-30%
almost independent of planetary mass/radius except in the cases of massive/compact planets.
The fraction of formation of eccentric close-in planets is about 4% in all the close-in planets. They are formed by long term secular perturbations between remaining two planets after ejection of one planet (two-body circularization), rather than chaotic perturbations among three planets before the ejection (three-body circularization).The fraction we get here is the minimum value of a limit of unstable system. If the 3-planets' system is kept in a tentatively stable stage for longer time, the portion of eccentric close-in planets would be enhanced.
We found in our simulations that as much as 29% of close-in planets have retrograde orbits. The retrograde planets are formed by three-body circularization and tend to have small eccentricities due to the exchange of eccentricities and inclinations.
This work was supported by MEXT-KAKENHI(21740324) Grant-in-Aid for Young Scientists (B).

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