Dynamics of the 3/1 planetary mean-motion resonance. An application to the HD60532 b-c planetary system

TL;DR

This paper presents a semi-analytical method to analyze the phase space of the 3/1 planetary mean-motion resonance, revealing stable configurations and dynamical structures relevant to exoplanetary systems without extensive numerical simulations.

Contribution

It introduces a novel semi-analytical framework using two key parameters to study the resonance's phase space, including stability and topology, applicable to systems with high eccentricities.

Findings

Identification of stable Apsidal Corotation Resonances (ACR) families.

Construction of dynamical maps showing evolution of stable regions.

Analysis of the influence of angular momentum and mass ratio on resonance stability.

Abstract

In this paper, we use a semi-analytical approach to analyze the global structure of the phase space of the planar planetary 3/1 mean-motion resonance, in cases where the outer planet is more massive than its inner companion. We show that the resonant dynamics can be described using only two fundamental parameters, the total angular momentum and the scaling parameter. The topology of the Hamiltonian function describing the resonant behaviour is studied on the representative planes that allows us to investigate a large domain of the phase space of the three-body problem without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The families of the well known Apsidal Corotation Resonances (ACR) parameterized by the planetary mass ratio are obtained and their stability is analyzed. The main dynamical features in the domains around ACR are also investigated in detail by means of spectral analysis techniques, which allow us to detect the regions of different regimes of motion of resonant systems. The construction of dynamical maps for various values of the total angular momentum shows the evolution of domains of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems.