Secular Orbital Dynamics of Hierarchical Two Planet Systems

TL;DR

This study analyzes the long-term orbital evolution of five multi-planet systems using N-body simulations, revealing complex dynamics, potential high eccentricities and inclinations, and the influence of general relativity on system stability.

Contribution

It provides a comprehensive dynamical analysis of five known multi-planet systems, incorporating observational data, inclination variations, and relativistic effects, which was not extensively done before.

Findings

Hierarchical systems can develop high eccentricities and inclinations.

Relativistic effects can significantly alter system dynamics.

Multiple dynamical regimes are probable for each system.

Abstract

The discovery of multi-planet extrasolar systems has kindled interest in using their orbital evolution as a probe of planet formation. Accurate descriptions of planetary orbits identify systems which could hide additional planets or be in a special dynamical state, and inform targeted follow-up observations. We combine published radial velocity data with Markov Chain Monte Carlo analyses in order to obtain an ensemble of masses, semimajor axes, eccentricities and orbital angles for each of 5 dynamically active multi-planet systems: HD 11964, HD 38529, HD 108874, HD 168443, and HD 190360. We dynamically evolve these systems using 52,000 long-term N-body integrations that sample the full range of possible line-of-sight and relative inclinations, and we report on the system stability, secular evolution and the extent of the resonant interactions. We find that planetary orbits in hierarchical systems exhibit complex dynamics and can become highly eccentric and maybe significantly inclined. Additionally we incorporate the effects of general relativity in the long-term simulations and demonstrate that can qualitatively affect the dynamics of some systems with high relative inclinations. The simulations quantify the likelihood of different dynamical regimes for each system and highlight the dangers of restricting simulation phase space to a single set of initial conditions or coplanar orbits.