Other
Scientific paper
Jul 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dda....38.1301t&link_type=abstract
American Astronomical Society, DDA meeting #38, #13.01
Other
Scientific paper
We investigate the evolution of hierarchical four-body systems in which a secondary star orbits the planet-hosting star and two planets in an inclined orbit. With the presence of the other planet, the orbital evolution of a planet is typically estimated by the ratio of two precession frequencies: the one caused by the binary companion (ξKoz= dωKoz/dt) due to the Kozai mechanism and the other caused by the mutual interaction between planets (ξM.I.= dωM.I./dt). The former can be derived from the quadupole-order secular perturbation equations, and the latter can be estimated from the classical Laplace-Lagrange secular solutions. When the timescale of the secular interaction between planets is significantly shorter than the Kozai precession rate (ξM.I./ξKoz 100 or greater), the orbital precession is suppressed, and the planetary orbits remain nearly circular. However, when the two precession frequencies are comparable to within a factor 100, the orbital elements of the planets evolve in a highly chaotic manner. Most likely, the system will become unstable, either by (i) orbital crossing due to the excited eccentricity, (ii) secular drift in the eccentricity of the less massive planet caused by the eccentricity oscillation of the more massive planet, or (iii) stochastic instability induced by close encounters between planets. However, in some cases, planets may undergo stable, large-amplitude, synchronized eccentricity oscillations. This synchronized oscillation is a combined effect of the Kozai eccentricity oscillation of the outer planet and the secular apsidal alignment of the two planets. If the conditions ξM.I., 2/ξKoz, 2 < 100 and ξM.I., 1 > ξKoz, 2 are satisfied, the libration of Δ ω=| ◜-◛| can lock the planetary orbits, resulting in synchronous eccentricity oscillations.
Kita Ryosuke
Rasio Frederic A.
Takeda Genya
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