Investigating the stability of trojan and horseshoe co-orbitals in extrasolar multi-planet systems*

Trojans and horseshoes are specific types of co-orbital bodies in planetary systems. Trojans share an orbit with a planet, positioned at the stable Lagrange points L4 and L5 (60 degrees ahead or behind the planet), while horseshoes oscillate around the planet’s path in a more complex manner. At least three Solar System planets—Mars, Jupiter, and Neptune—host stable co-orbital asteroids that have shared their orbits since the early formation of the system. In contrast, Saturn and Uranus lack stable co-orbital asteroids due to their proximity to orbital resonances with Jupiter and Neptune, respectively. According to Nesvorny and Dones (2002), Saturn lacks stable Trojans because it is near 5:2 period ratio with Jupiter which results in strong gravitational perturbations that destabilize potential co-orbitals. Transiting extrasolar multi-planet systems frequently contain planets in resonance or near-resonance.

In this talk, I present numerical simulations of the stability of co-orbitals in TRAPPIST-1, Kepler-11, Kepler-80, Kepler-90/KOI-351, and HD 11067 using the TRACE integrator from the REBOUND package. We place 20 hypothetical particles for each planet 60 degrees ahead of the planet, with semi-major axes varying from that equal to the planet’s to one that is one Hill radius larger. Our simulations are limited to initially circular and planar orbits. Preliminary results indicate that co-orbitals in resonant systems, such as TRAPPIST-1, exhibit less stability compared to those in non-resonant systems. This suggests that orbital resonances play a significant role in the stability of co-orbital bodies. Full results will be presented at the conference, shedding light on the dynamics and the implications for the existence of co-orbitals in extrasolar planetary systems.