A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets
arXiv:1803.08510 · doi:10.3847/1538-3881/aad32c
Abstract
We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets' masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos occurs where mean motion resonances overlap, as in Wisdom (1980)'s pioneering work. But whereas Wisdom considered only nearly circular planets, and hence examined only first order resonances, we extend his results to arbitrarily eccentric planets (up to crossing orbits) by examining resonances of all orders. We thereby arrive at a simple expression for the critical eccentricity. We do this first for a test particle in the presence of a planet, and then generalize to the case of two massive planets, based on a new approximation to the Hamiltonian (Hadden, in prep). We then confirm our results with detailed numerical simulations. Finally, we explore the extent to which chaotic two-planet systems eventually result in planetary collisions.
17 pages, 13 figures. Accepted for publication in AJ. Revised in response to community and referee comments
References in corpus (4)
Cited by in corpus (51)
- Exoplanet Statistics and Theoretical Implications
- Predicting the long-term stability of compact multiplanet systems
- The path to instability in compact multi-planetary systems
- A Tale of Planet Formation: From Dust to Planets
- An upper limit on late accretion and water delivery in the Trappist-1 exoplanet system
- An Integrable Model for the Dynamics of Planetary Mean Motion Resonances
- Dynamical instability and its implications for planetary system architecture
- A Criterion for the Stability of Planets in Chains of Resonances
- Mean motion resonance capture in the context of type-I migration
- Eccentricity Driven Climate Effects in the Kepler-1649 System
- Fundamental limits from chaos on instability time predictions in compact planetary systems
- Effects of non-Kozai mutual inclinations on two-planet system stability through all phases of stellar evolution
- Prospects for TTV Detection and Dynamical Constraints with TESS
- How Close are Compact Multi-Planet Systems to the Stability Limit?
- celmech: A Python package for celestial mechanics
- The Criterion for Chaos in Three-Planet Systems
- Are long-term -body simulations reliable?
- GJ 3090 b: one of the most favourable mini-Neptune for atmospheric characterisation
- Predicting multiple planet stability and habitable zone companions in the TESS era
- An integrable model for first-order three-planet mean motion resonances
- The LHS 1678 System: Two Earth-Sized Transiting Planets and an Astrometric Companion Orbiting an M Dwarf Near the Convective Boundary at 20 pc
- Orbital stability of compact three-planet systems, I: Dependence of system lifetimes on initial orbital separations and longitudes
- Stability Constrained Characterization of Multiplanet Systems
- The instability mechanism of compact multiplanet systems
- Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems
- On the Divergence of First Order Resonance Widths at Low Eccentricities
- On the Degree of Dynamical Packing in the Kepler Multi-planet Systems
- Resilient habitability of nearby exoplanet systems
- Orbital Dynamics and the Evolution of Planetary Habitability in the AU Mic System
- TOI-712: a system of adolescent mini-Neptunes extending to the habitable zone
- Period Ratio Sculpting Near Second-Order Mean-Motion Resonances
- A Pair of Planets Likely in Mean-motion Resonance From Gravitational Microlensing
- Multi-harmonic Hamiltonian models with applications to first-order resonances
- Can metal-rich worlds form by giant impacts?
- High-resolution resonant portraits of a single-planet white dwarf system
- Fear the Shadows of the Giants: On Secular Perturbations in Circumstellar Habitable Zones of Double Stars
- Relative Habitability of Exoplanet Systems with Two Giant Planets
- Planet Mass Function around M stars at 1-10 au: A Plethora of sub-Earth mass objects
- Extended planetary chaotic zones
- Constraints on Evolutionary Timescales for M Dwarf Planets from Dynamical Stability Arguments
- A Bayesian neural network predicts the dissolution of compact planetary systems
- The Perturbation Theory Approach to Stability in the Scattered Disk
- Higher-Order Mean-Motion Resonances Can Form in Type-I Disk Migration
- Moon-packing around an Earth-mass Planet
- Secular Dynamics of Compact Three-Planet Systems
- New results on orbital resonances
- A Criterion for the Onset of Chaos in Compact, Eccentric Multiplanet Systems
- Dynamical Evolution of Planetary Systems
- Orbital stability of compact three-planet systems III. The role of three-body resonances
- Instability from high-order resonant chains in wide-separation massive planet systems
- Dynamics of Two Planets near a 2:1 Resonance: Case Studies of Known and Synthetic Exosystems on a Grid of Initial Configurations