Dynamical regimes of two eccentric and mutually inclined giant planets

TL;DR

This study explores the complex dynamical behaviors of two eccentric, mutually inclined giant planets around a Sun-like star, revealing two main regimes of equilibrium and resonance structures linked to initial mutual inclination.

Contribution

It introduces a comprehensive atlas of mutual mean-motion resonances and identifies two distinct dynamical regimes based on initial mutual inclination, including a critical inclination for secular resonance occurrence.

Findings

Two dynamical regimes depending on initial mutual inclination.

Identification of a critical inclination between 30 and 40 degrees for secular resonance.

Different frequency behaviors and mechanisms dominate each regime.

Abstract

We consider a basic planetary system composed by a Sun like star, a Jupiter-like planet an a Neptune-like planet in a wide range of orbital configurations not limited to the hierarchical case. We present atlases of resonances showing the domains of approx. 1300 mutual mean-motion resonances (MMRs) and their link to chaotic and regular dynamics. Following a semi-analytical method for the study of the secular dynamics we found two regimes for equilibrium configurations: one for low mutual inclinations were equilibrium is related to oscillations of the difference between the pericenter longitudes around 0 or 180 degrees, and another for high mutual inclinations where the equilibrium is given by defined values of the argument of the pericenters equal to integer multiples of 90 degrees. By numerical integration of the full equations of motion we calculate the fundamental frequencies of the systems in their diverse configurations and study their dependence with the orbital elements. According to the analysis of the fundamental frequencies we found two dynamical regimes depending on the initial mutual inclination and the limit between the two regimes occurs at some critical inclination 30<ic<40 defined by the occurrence of the secular resonance g1=g2. For i<ic the dynamics is analogue a the classic secular model for low (e,i) with well defined three fundamental frequencies and free and forced modes, conserving quasi constant the mutual inclination. For i>ic the dynamics is completely different with increasing changes in mutual inclination and emerging combinations of the fundamental frequencies and, depending on the case, dominated by the secular resonance or the vZLK mechanism.