The path to instability in compact multi-planetary systems

Abstract

The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience instability on timescales up to billions of years. Moreover, an exponential trend between the planet orbital separation measured in units of Hill radii and the survival time has been reported. While these findings have been observed in numerous numerical simulations, little is known of the actual mechanism leading to instability. Contrary to a constant diffusion process, planetary systems seem to remain dynamically quiescent for most of their lifetime before a very short unstable phase. In this work, we show how the slow chaotic diffusion due to the overlap of three-body resonances dominates the timescale leading to the instability for initially coplanar and circular orbits. While the last instability phase is related to scattering due to two-planet mean motion resonances (MMR), for circular orbits the two-planets MMR are too far separated to destabilize systems initially away from them. We develop an analytical model to generalize the empirical trend obtained for equal mass and equally-spaced planets to general systems. We obtain an analytical estimate of the survival time consistent with simulations over four orders of magnitude for the planet to star mass ratio $\epsilon$, and 6 to 8 orders of magnitude for the instability time. We also confirm that measuring the orbital spacing in terms of Hill radii is not adapted and that the right spacing unit scales as ${\epsilon }^{1/4}$. We predict that beyond a certain spacing, the three-planet resonances are not overlapped, which results in an increase of the survival time. We finally discuss the extension of our result to more general systems, containing more planets on initially non circular orbits.

Accepted in A&A. Added numerical tests with test particles and non uniform systems. A notebook as well as python scripts to reproduce the article figure are available at https://github.com/acpetit/PlanetSysSurvivalTime

References in corpus (38)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The NumPy array: a structure for efficient numerical computation
• The false positive rate of Kepler and the occurrence of planets
• REBOUND: An open-source multi-purpose N-body code for collisional dynamics
• Characteristics of planetary candidates observed by Kepler, II: Analysis of the first four months of data
• Prevalence of Earth-size planets orbiting Sun-like stars
• Architecture and Dynamics of Kepler's Candidate Multiple Transiting Planet Systems
• Architecture of Kepler's Multi-transiting Systems: II. New investigations with twice as many candidates
• A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11
• WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
• The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced
• Exoplanet Orbital Eccentricities Derived From LAMOST-Kepler Analysis
• Architecture of Planetary Systems Based on Kepler Data: Number of Planets and Coplanarity
• First order resonance overlap and the stability of close two planet systems
• Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems
• Hybrid Symplectic Integrators for Planetary Dynamics
• AMD-stability and the classification of planetary systems
• Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
• Can planetary instability explain the Kepler dichotomy?
• Bounds on the Lambert function and their application to the outage analysis of user cooperation
• The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star
• A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets
• Chaotic Disintegration of the Inner Solar System
• A Machine Learns to Predict the Stability of Tightly Packed Planetary Systems
• Hill stability in the AMD framework
• Analytical model of multi-planetary resonant chains and constraints on migration scenarios
• AMD-stability in presence of first order Mean Motion Resonances
• The onset of instability in resonant chains
• Survival of non-coplanar, closely-packed planetary systems after a close encounter
• Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river
• Resonance Capture and Dynamics of 3-Planet Systems
• On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems
• Chirikov Diffusion in the Asteroidal Three-Body Resonance (5,-2,-2)
• Dynamical instabilities in systems of multiple short-period planets are likely driven by secular chaos: a case study of Kepler-102
• The role of dissipative evolution for three-planet, near-resonant extrasolar systems
• Fundamental limits from chaos on instability time predictions in compact planetary systems
• Resonant Laplace-Lagrange theory for extrasolar systems in mean-motion resonance
• Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems

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