Modeling the secular evolution of migrating planet pairs

TL;DR

This paper develops a qualitative model for the secular evolution of migrating planet pairs under dissipative forces, analyzing energy and angular momentum exchange without specifying force types, and links final states to initial configurations.

Contribution

It introduces a general secular model for migrating planets that accounts for energy and angular momentum exchange, independent of specific dissipation mechanisms.

Findings

Migration paths follow conservative secular solutions under weak dissipation

Final system states can be used to infer initial configurations and migration history

Evolution converges along Mode I and Mode II secular solutions

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.