Resonant capture of multiple planet systems under dissipation and stable orbital configurations

TL;DR

This paper investigates how dissipative forces can lead to planetary systems being captured into resonances during migration, and examines the stability of these resonant configurations, including two- and three-planet systems.

Contribution

It analyzes the conditions for resonant capture and stability in multi-planet systems using phase space and periodic orbit families, extending understanding of long-term planetary configurations.

Findings

High probability of 2:1 and 3:1 resonant capture at low eccentricities

Resonant capture of three-planet systems is possible under specific conditions

Stable three-planet configurations can be identified from migration paths

Abstract

Migration of planetary systems caused by the action of dissipative forces may lead the planets to be trapped in a resonance. In this work we study the conditions and the dynamics of such resonant trapping. Particularly, we are interested in finding out whether resonant capture ends up in a long-term stable planetary configuration. For two planet systems we associate the evolution of migration with the existence of families of periodic orbits in the phase space of the three-body problem. The family of circular periodic orbits exhibits a gap at the 2:1 resonance and an instability and bifurcation at the 3:1 resonance. These properties explain the high probability of 2:1 and 3:1 resonant capture at low eccentricities. Furthermore, we study the resonant capture of three-planet systems. We show that such a resonant capture is possible and can occur under particular conditions. Then, from the migration path of the system, stable three-planet configurations, either symmetric or asymmetric, can be determined.