Constellations of co-orbital planets: horseshoe dynamics, long-term stability, transit timing variations, and potential as SETI beacons

Abstract: Co-orbital systems contain two or more bodies sharing the same orbit around a planet or star. The best-known flavors of co-orbital systems are tadpoles (in which two bodies' angular separations oscillate about the L4/L5 Lagrange points $60^\circ$ apart) and horseshoes (with two bodies periodically exchanging orbital energy to trace out a horseshoe shape in a co-rotating frame). Here, we use N-body simulations to explore the parameter space of many-planet horseshoe systems. We show that up to 24 equal-mass, Earth-mass planets can share the same orbit at 1 au, following a complex pattern in which neighboring planets undergo horseshoe oscillations. We explore the dynamics of horseshoe constellations, and show that they can remain stable for billions of years and even persist through their stars' post-main sequence evolution. With sufficient observations, they can be identified through their large-amplitude, correlated transit timing variations. Given their longevity and exotic orbital architectures, horseshoe constellations may represent potential SETI beacons.

• The paper explores the dynamics and long-term stability of co-orbital planet constellations, finding that up to 24 Earth-like planets can share an orbit stably in horseshoe configurations.
• Using N-body simulations, the study shows these systems' stability depends on initial spacing and highlights their potential detection via significant Transit Timing Variations (TTVs).
• The research suggests that the unique stability and observable signatures of these co-orbital systems could potentially serve as artificial beacons for Search for Extraterrestrial Intelligence (SETI).

Co-orbital Constellations: Dynamics, Stability, and Astrobiological Implications

The paper by Raymond et al. presents an in-depth exploration of constellations of co-orbital planets, specifically focusing on those occupying horseshoe orbits. This study leverages $N$-body simulations to elucidate the intricate dynamics and potential stability of such systems over astronomical timescales. The paper also examines the observational feasibility of detecting these systems via transit timing variations (TTVs) and speculates on their potential as beacons for the Search for Extraterrestrial Intelligence (SETI).

Dynamics and Stability of Horseshoe Orbits

Co-orbital configurations in planetary systems are characterized by bodies sharing the same orbital path around a central mass. Two well-known types are the tadpole and horseshoe configurations. This research primarily focuses on the latter, revealing that it is feasible for up to 24 equal-mass Earth-like planets to share the same orbit at 1 AU, engaging in complex horseshoe oscillations with their nearest neighbors.

Key findings from the simulations include:

• Co-orbital systems of up to 24 planets can exhibit stable horseshoe dynamics over billions of years, enduring even through the evolutionary phases of their host stars.
• Stability of these systems is critically contingent on the initial spacing of the planets, expressed in mutual Hill radii, with horseshoe constellations demonstrating unique dynamical behavior compared to two-planet systems like the Janus and Epimetheus configuration around Saturn.
• Horseshoe systems are inherently robust, illustrating persistent stability across diverse conditions, including different masses and numbers of constituent planets.

Observational Prospects and SETI Implications

The paper underscores that horseshoe constellations might be identified via their significant TTV signatures. These signals, which result from the periodic exchanges of angular momentum between the planets, can be distinguished from other astrophysical phenomena given adequate observational baselines. Specifically, the correlated and high-amplitude nature of TTVs in such systems presents a distinct signature that could be challenging to interpret but potentially recognizable as non-natural configurations.

Intriguingly, the discussion extends to the field of astrobiology and SETI. The enduring stability and exotic nature of horseshoe constellations suggest that they could serve as intentional constructs or markers by technologically advanced civilizations. The study conjectures that such systems, with their non-intuitive dynamical structures, could be leveraged as signaling beacons, framing an alternative means by which intelligent life might signal its presence across interstellar distances.

Future Prospects

The exploration of co-orbital architectures opens new avenues in the study of planetary dynamics and SETI, raising questions about the natural occurrence of such systems and the potential for intelligent design. Future work may explore:

• The role of planetary formation processes and migration in naturally placing planets in stable co-orbital arrangements.
• The interaction of tidal forces with co-orbital planets, particularly around low-mass stars where tides could play a more significant role.
• Comprehensive surveys of potential TTV signals using both current and upcoming observational platforms, optimizing strategies to identify and characterize these unique astronomical systems.

This study's findings embrace both the realms of theoretical astrophysics and the speculative boundaries of astrobiology, proposing a captivating intersection between celestial mechanics and the search for life beyond Earth.