A Criterion for the Stability of Planets in Chains of Resonances

TL;DR

This paper introduces a simple, general criterion for the stability of planetary resonant chains based on orbital periods and masses, improving predictions of system stability and surpassing machine learning methods.

Contribution

It proposes a new, analytically derived stability criterion for resonant planetary chains that is simple, accurate, and applicable to systems with up to six planets.

Findings

The criterion accurately predicts maximum planetary masses in synthetic chains.

More complex chains are less stable than the criterion suggests, but it remains useful.

The criterion outperforms machine learning models in stability prediction.

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.