Orbital stability of compact three-planet systems, II: Post-instability impact behaviour

Abstract

Recent observational missions have uncovered a significant number of compact multi-exoplanet systems. The tight orbital spacing of these systems has led to much effort being applied to the understanding of their stability; however, a key limitation of the majority of these studies is the termination of simulations as soon as the orbits of two planets cross. In this work we explore the stability of compact, three-planet systems and continue our simulations all the way to the first collision of planets to yield a better understanding of the lifetime of these systems. We perform over $25,000$ integrations of a Sun-like star orbited by three Earth-like secondaries for up to a billion orbits to explore a wide parameter space of initial conditions in both the co-planar and inclined cases, with a focus on the initial orbital spacing. We calculate the probability of collision over time and determine the probability of collision between specific pairs of planets. We find systems that persist for over $10^8$ orbits after an orbital crossing and show how the post-instability survival time of systems depends upon the initial orbital separation, mutual inclination, planetary radius, and the closest encounter experienced. Additionally, we examine the effects of very small changes in the initial positions of the planets upon the time to collision and show the effect that the choice of integrator can have upon simulation results. We generalise our results throughout to show both the behaviour of systems with an inner planet initially located at $1$ AU and $0.25$ AU.

References in corpus (19)

• Statistical applications of the multivariate skew-normal distribution
• REBOUND: An open-source multi-purpose N-body code for collisional dynamics
• Architecture of Kepler's Multi-transiting Systems: II. New investigations with twice as many candidates
• IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits
• A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11
• Validation of Kepler's Multiple Planet Candidates. III: Light Curve Analysis & Announcement of Hundreds of New Multi-planet Systems
• The HARPS search for southern extra-solar planets XXXIV. Occurrence, mass distribution and orbital properties of super-Earths and Neptune-mass planets
• Exoplanet Orbital Eccentricities Derived From LAMOST-Kepler Analysis
• Validation of Kepler's Multiple Planet Candidates. II: Refined Statistical Framework and Descriptions of Systems of Special Interest
• Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
• Predicting the long-term stability of compact multiplanet systems
• The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star
• A Machine Learns to Predict the Stability of Tightly Packed Planetary Systems
• The path to instability in compact multi-planetary systems
• Survival of non-coplanar, closely-packed planetary systems after a close encounter
• Dynamical instability and its implications for planetary system architecture
• Fundamental limits from chaos on instability time predictions in compact planetary systems
• Formation of Close-in Super-Earths by Giant Impacts: Effects of Initial Eccentricities and Inclinations of Protoplanets
• Terrestrial Exoplanet Simulator (TES): an error optimal planetary systems integrator that permits close encounters

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• Updated Catalog of Kepler Planet Candidates: Focus on Accuracy and Orbital Periods
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• Dynamical Instability of Multi-planet Systems and Free-floating Planets
• Moon-packing around an Earth-mass Planet
• Orbital Stability of Closely-Spaced Four-planet Systems
• Orbital stability of compact three-planet systems III. The role of three-body resonances