Other
Scientific paper
Jul 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dda....38.1507z&link_type=abstract
American Astronomical Society, DDA meeting #38, #15.07
Other
Scientific paper
We investigate the long-term orbital evolution of exoplanets in a planar two-planet system, subject to an applied dissipative force. Without dissipation, the orbits of the two planets oscillate with two fundamental eigenmodes due to their secular gravitational interactions: a slow mode in which the two pericenters are aligned and a fast mode in which they are anti-aligned. In each mode, the two orbits precess as a rigid body at a rate determined purely by planet masses and orbital semi-major axes. In addition, the ratio between the two eccentricities is fixed. Any system of two planets can be represented by a linear combination of these two modes, with initial conditions (eccentricities and longitudes of pericenters) determining the precise mix.
When eccentricities are slowly damped by perturbations such as planetary tides or disk interactions, the mode frequencies and eccentricity ratios shift slightly, and the two modes decay separately at different rates. We solve for these rates analytically -- usually one mode damps much faster than the other, and the system ends up locked in either an apsidally aligned or anti-aligned state. Numerical integrations of both the first-order secular equations and direct N-body equations show close agreement with our analytical results. This mechanism provides a possible explanation for the nonzero eccentricities of "hot-Jupiters", assuming that they have companions in more eccentric orbits. Some perturbations may also cause planetary migration. For slow migration rates, adiabatic invariants exist, which are functions of mode parameters (frequencies and amplitudes). Similar invariants can be found for the case where mass loss is important. Through analytical study of these integrals, we seek to explain the diverse appearance of planetary orbits.
Hamilton Douglas P.
Zhang Ke
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