A Criterion for the Stability of Planets in Chains of Resonances

Abstract

Uncovering the formation process that reproduces the distinct properties of compact super-Earth exoplanet systems is a major goal of planet formation theory. The most successful model argues that non-resonant systems begin as resonant chains of planets that later experience a dynamical instability. However, both the boundary of stability in resonant chains and the mechanism of the instability itself are poorly understood. Previous work postulated that a secondary resonance between the fastest libration frequency and a difference in synodic frequencies destabilizes the system. Here, we use that hypothesis to produce a simple and general criterion for resonant chain stability that depends only on planet orbital periods and masses. We show that the criterion accurately predicts the maximum mass of planets in synthetic resonant chains up to six planets. More complicated resonant chains produced in population synthesis simulations are found to be less stable than expected, although our criterion remains useful and superior to machine learning models.

8 pages, 4 figures; accepted to Icarus

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• Scaling K2. VI. Reduced Small Planet Occurrence in High Galactic Amplitude Stars
• Monitoring the young planet host V1298 Tau with SPIRou: planetary system and evolving large-scale magnetic field
• The GAPS program at TNG XLVII: The unusual formation history of V1298 Tau
• Dissipative Capture of Planets Into First-Order Mean-Motion Resonances
• Stable Orbits in the Feeding Zone of the Planet Proxima Centauri c
• Forming rocky exoplanets around K-dwarf stars