Orbital stability of compact three-planet systems

Context . Observational surveys show that at least ∼30% of short-period multi-planet systems contain planets in tightly packed orbits. Some of these systems are locked in stable chains of mean-motion resonances. Although significant advances have been made in recent years, our understanding of the dynamical stability of these systems remains incomplete. Overall, numerical simulations show that the general trend is an exponential increase in a system’s lifetime with increasing orbital separation, with mean motion resonances being a key mechanism that modulates stability. Tightly packed three-planet systems exhibit a specific dynamical behavior that is not yet found in systems with more planets: a small yet significant fraction of the phase space of very compact three-planet systems is anomalously stable. Aims . This study investigates the dynamics of extremely compact three-planet systems, focusing on those that are anomalously long-lived, and explores their connection to resonant chains observed in exoplanetary systems. Methods . We used numerical integrators to explore the dynamics of coplanar, initially circular, tightly packed, and equal-mass three-planet systems over timescales on the order of the star’s lifetime, with a very high resolution in orbital separation. We analyzed the results in light of recent analytical studies. Results . We identify the fraction of phase space with anomalously stable, very tightly packed orbits, including systems that are orders of magnitude longer-lived than expected from the exponential trend. We show an unambiguous link between the stability of these systems and isolated three-body mean-motion resonances. Conclusions . We find that very tightly packed three-planet systems can remain stable when captured in a small subset of isolated zeroth-order three-body resonances. Stability critically depends on the initial orbital longitudes and on the interplay between the three-body mean-motion resonance network and the two-body mean-motion resonance network.