Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

TL;DR

This paper uses periodic orbits in the three-body problem to validate and constrain the orbital parameters of near-resonant exoplanet systems, enhancing understanding of their long-term stability.

Contribution

It introduces a method leveraging the stability properties of periodic orbits to validate and refine orbital elements of two-planet systems near resonance.

Findings

Mean-motion resonance locking stabilizes K2-21 and K2-24.

Kepler-9 stability is maintained through apsidal anti-alignment.

Kepler-108 stability may involve resonance or inclination effects.

Abstract

Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data.