Orbital stability of hierarchical three- and four-body systems with inclination: results for Kepler-1625, 1708, and HD 23079

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 four-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 three-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 four-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 three-body versions of two other systems, Kepler-1708 and HD 23079, while also studying a four-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 four-body study may be an incentive for studying further exomoon and submoon systems.