Orbital Stability of Hierarchical 3 and 4-Body Systems with Inclination: Results for Kepler-1625, 1708, and HD 23079

TL;DR

This study analyzes the orbital stability of hierarchical 3- and 4-body systems with inclination, focusing on exomoon candidates like Kepler-1625, and identifies stable regions and resonances using numerical and analytical methods.

Contribution

It provides a comprehensive framework for assessing the stability of exomoon and submoon systems, including new resonance analysis techniques.

Findings

Identification of stable and unstable regions in 3- and 4-body systems.

Discovery of secular resonance patterns affecting stability.

Application of combined numerical and analytical methods for stability analysis.

Abstract

As the number of potential exomoon candidates grows, there is a heightened motivation of pursing orbital stability analyses. In this work, we provide an in-depth investigation into 4-body systems, consisting of a star, planet, moon, and submoon by using the N-body simulator rebound. Particularly, we focus on the system of Kepler-1625, where evidence of a possible exomoon has been obtained. We investigate the 3-body star--planet--moon system for the proposed exomoon parameters allowing us to identify stable regions associated with most of the space parameters. Thereafter, we consider a 4-body system including a potential submoon. We find that there are both stable and unstable regions, as expected, as well as resonance patterns that are further explored using numerical and analytical methods including secular perturbation theory. We are able to identify these resonances as secular in nature. In addition, we investigate 3-body versions of two other systems, Kepler-1708 and HD 23079, while also studying a 4-body version of HD 23079. Our work may serve as a generalized framework for exploring other planet--moon cases in the future while noting that the current 4-body study may be an incentive for studying further exomoon and submoon systems.