TRAPPIST-1: Dynamical analysis of the transit-timing variations and origin of the resonant chain

Abstract

We analyze solutions drawn from the recently published posterior distribution of the TRAPPIST-1 system, which consists of seven Earth-size planets appearing to be in a resonant chain around a red dwarf. We show that all the planets are simultaneously in two-planet and three-planet resonances, apart from the innermost pair for which the two-planet resonant angles circulate. By means of a frequency analysis, we highlight that the transit-timing variation (TTV) signals possess a series of common periods varying from days to decades, which are also present in the variations of the dynamical variables of the system. Shorter periods (e.g., the TTVs characteristic timescale of 1.3 yr) are associated with two-planet mean-motion resonances, while longer periods arise from three-planet resonances. By use of $N$-body simulations with migration forces, we explore the origin of the resonant chain of TRAPPIST-1 and find that for particular disc conditions, a chain of resonances - similar to the observed one - can be formed which accurately reproduces the observed TTVs. Our analysis suggests that while the 4-yr collected data of observations hold key information on the two-planet resonant dynamics, further monitoring of TRAPPIST-1 will soon provide signatures of three-body resonances, in particular the 3.3 and 5.1 yr periodicities expected for the current best-fit solution. dditional observations would help to assess whether the innermost pair of planets is indeed resonant (its proximity to the 8:5 resonance being challenging to explain), and therefore give additional constraints on formation scenarios.

arXiv comment11 pages, 14 figures, accepted for publication in A&A

References in corpus (47)

• Astropy: A Community Python Package for Astronomy
• Binary companions of evolved stars in APOGEE DR14: Search method and catalog of ~5,000 companions
• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• REBOUND: An open-source multi-purpose N-body code for collisional dynamics
• DHP Framework: Digital Health Passports Using Blockchain -- Use case on international tourism during the COVID-19 pandemic
• On detecting terrestrial planets with timing of giant planet transits
• Architecture of Kepler's Multi-transiting Systems: II. New investigations with twice as many candidates
• Temperate Earth-sized planets transiting a nearby ultracool dwarf star
• WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
• Migration and the formation of systems of hot super-Earths and Neptunes
• A seven-planet resonant chain in TRAPPIST-1
• How to Constrain Your M dwarf II: the mass-luminosity-metallicity relation from 0.075 to 0.70$M_{\odot }$
• Extracting Planet Mass and Eccentricity From TTV data
• The Lick-Carnegie Exoplanet Survey: A Uranus-mass Fourth Planet for GJ 876 in an Extrasolar Laplace Configuration
• Orbital perturbations on transiting planets: A possible method to measure stellar quadrupoles and to detect Earth-mass planets
• Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc
• REBOUNDx: A Library for Adding Conservative and Dissipative Forces to Otherwise Symplectic N-body Integrations
• Toward a Deterministic Model of Planetary Formation VI: Dynamical Interaction and Coagulation of Multiple Rocky Embryos and Super-Earth Systems around Solar Type Stars
• A resonant chain of four transiting, sub-Neptune planets
• Kepler Planet Masses and Eccentricities from TTV Analysis
• Resonant Repulsion of Kepler Planet Pairs
• Kepler 18-b, c, and d: A System Of Three Planets Confirmed by Transit Timing Variations, Lightcurve Validation, Spitzer Photometry and Radial Velocity Measurements
• Six transiting planets and a chain of Laplace resonances in TOI-178
• Transit Timing Observations from Kepler: III. Confirmation of 4 Multiple Planet Systems by a Fourier-Domain Study of Anti-correlated Transit Timing Variations
• N-body simulations of planetary accretion around M dwarf stars
• On disc driven inward migration of resonantly coupled planets with application to the system around GJ876
• Formation of TRAPPIST-1 and other compact systems
• A Dynamical Analysis of the Kepler-80 System of Five Transiting Planets
• Convergent Migration Renders TRAPPIST-1 Long-lived
• Transit Timing Observations from Kepler: II. Confirmation of Two Multiplanet Systems via a Non-parametric Correlation Analysis
• Early 2017 observations of TRAPPIST-1 with $\text{Spitzer}$
• Formation of close-in super-Earths in evolving protoplanetary disks due to disk winds
• Stellar parameters for TRAPPIST-1
• Effects of Type I Migration on Terrestrial Planet Formation
• The Importance of Disk Structure in Stalling Type I Migration
• Pebble-driven planet formation for TRAPPIST-1 and other compact systems
• Pebbles versus Planetesimals: The case of Trappist-1
• The TRAPPIST-1 system: Orbital evolution, tidal dissipation, formation and habitability
• The Laplace resonance in the Kepler-60 system
• The K2-138 System: A Near-Resonant Chain of Five Sub-Neptune Planets Discovered by Citizen Scientists
• TRAPPIST-1: Global Results of the Spitzer Exploration Science Program {\it Red Worlds}
• The 0.8-4.5$\mu$m broadband transmission spectra of TRAPPIST-1 planets
• Resonance Capture and Dynamics of 3-Planet Systems
• Modal Decomposition of TTV - Inferring Planet Masses and Eccentricities
• The tidal parameters of TRAPPIST-1 b and c
• Transit-Timing Variation Signature of Planet Migration: The Case of K2-24
• Detection of Laplace-resonant three-planet systems from transit timing variations

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• Stability of a cluster-disrupted mean-motion resonance (chain) in HR 8799 and PDS 70
• Particle dynamics in TOI-178 planetary system