Circular periodic orbits, resonance capture and inclination excitation during type II migration

TL;DR

This paper investigates how planetary systems undergoing type II migration can experience resonance capture and inclination excitation at vertical critical orbits, leading to stable, mutually inclined resonant configurations.

Contribution

It establishes a direct link between circular orbit families, VCOs, and the emergence of inclined resonant planetary systems, expanding understanding of planetary migration outcomes.

Findings

Inclination excitation occurs at VCOs during migration.

More VCOs appear with higher multiplicity in circular families.

Resonant planets on circular orbits can evolve into stable inclined systems.

Abstract

We consider planetary systems evolving under the effect of a Stokes-type dissipative force mimicking the outcome of a type II migration process. As inward migration proceeds and the planets follow the circular family (they start on circular orbits) and even though they are initially almost coplanar, resonance capture can be realized. Then, at the \textit{vertical critical orbits} (VCOs), that the circular family possesses, the inclination excitation can abruptly take place. The planets are now guided by the spatial elliptic families, which bifurcate from those critical orbits. We herein, perform a direct link of mutually inclined stable planetary systems on circular orbits trapped in \textit{mean-motion resonance} (MMR) with the existence of VCOs of high values of multiplicity. It is shown that the more the multiplicity of the periodic orbits of the circular family increases, the more VCOs (corresponding to more MMRs) appear. In this way, we can provide a justification for the existence of resonant planets on circular orbits, which could, even further to that, evolve stably if they were mutually inclined.