Modeling the secular evolution of migrating planet pairs

Abstract

The subject of this paper is the secular behaviour of a pair of planets evolving under dissipative forces. In particular, we investigate the case when dissipative forces affect the planetary semi-major axes and the planets move inward/outward the central star, in a process known as planet migration. To perform this investigation, we introduce fundamental concepts of conservative and dissipative dynamics of the three-body problem. Based on these concepts, we develop a qualitative model of the secular evolution of the migrating planetary pair. Our approach is based on analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces is invoked. We show that, under assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the Mode I and Mode II stationary solutions of the conservative secular problem. The ultimate convergence and the evolution of the system along one of these secular modes of motion is determined uniquely by the condition that the dissipation rate is sufficiently smaller than the proper secular frequency of the system. We show that it is possible to reassemble the starting configurations and migration history of the systems on the basis of their final states and consequently to constrain the parameters of the physical processes involved.

20 pages, 17 figures. Accepted for publication in MNRAS

References in corpus (2)

• Long-term tidal evolution of short-period planets with companions
• On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets

Cited by in corpus (11)

• Two planets around Kapteyn's star : a cold and a temperate super-Earth orbiting the nearest halo red-dwarf
• Spin-orbit coupling for tidally evolving super-Earths
• Dynamical Stability of Terrestrial Planets in the Binary α Centauri System
• Tidal evolution of close-in exoplanets in co-orbital configurations
• Angular momentum exchange during secular migration of two-planet systems
• Secular Dynamics of S-type Planetary Orbits in Binary Star Systems: Applicability Domains of First- and Second-Order Theories
• Vertical instability and inclination excitation during planetary migration
• Dynamics of the 3/1 planetary mean-motion resonance. An application to the HD60532 b-c planetary system
• Past and present dynamics of the circumbinary moons in the Pluto-Charon system
• The generalized non-conservative model of a 1-planet system - revisited
• Secular Dynamics of Multiplanetary Circumbinary Systems