The tidal parameters of TRAPPIST-1 b and c

Abstract

The TRAPPIST-1 planetary system consists of seven planets within 0.05 au of each other, five of which are in a multi-resonant chain. {These resonances suggest the system formed via planet migration; subsequent tidal evolution has damped away most of the initial eccentricities. We used dynamical N-body simulations to estimate how long it takes for the multi-resonant configuration that arises during planet formation to break. From there we use secular theory to pose limits on the tidal parameters of planets b and c. We calibrate our results against multi-layered interior models constructed to fit the masses and radii of the planets, from which the tidal parameters are computed independently.} The dynamical simulations show that the planets typically go unstable 30 Myr after their formation. {Assuming synchronous rotation throughout} we compute $\frac{k_2}{Q}\gtrsim 2\times 10^{-4}$ for planet b and $\frac{k_2}{Q}\gtrsim 10^{-3}$ for planet c. Interior models yield $(0.075-0.37)\times 10^{-4}$ for TRAPPIST-1 b and $(0.4-2)\times 10^{-4}$ for TRAPPIST-1 c. The agreement between the {dynamical and interior} models is not too strong, but is still useful to constrain the dynamical history of the system. We suggest that this two-pronged approach could be of further use in other multi-resonant systems if the planet's orbital and interior parameters are sufficiently well known.

arXiv commentAccepted for publication in Monthly Notices of the Royal Astronomical Society

References in corpus (35)

• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• New evolutionary models for pre-main sequence and main sequence low-mass stars down to the hydrogen-burning limit
• A torque formula for non-isothermal Type I planetary migration - II. Effects of diffusion
• Separating gas-giant and ice-giant planets by halting pebble accretion
• Breaking the Chains: Hot Super-Earth systems from migration and disruption of compact resonant chains
• A seven-planet resonant chain in TRAPPIST-1
• The nature of the TRAPPIST-1 exoplanets
• Analytical protostellar disk models 1: the effect of internal dissipation and surface irradiation on the structure of disks and the location of the snow line around Sun-like stars
• Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc
• Overstable Librations can account for the Paucity of Mean Motion Resonances among Exoplanet Pairs
• Tidally Heated Terrestrial Exoplanets: Viscoelastic Response Models
• Evolution of Snow Line in Optically Thick Protoplanetary Disks: Effects of Water Ice Opacity and Dust Grain Size
• Formation of TRAPPIST-1 and other compact systems
• Tidal dissipation compared to seismic dissipation: in small bodies, in earths, and in superearths
• The radial dependence of pebble accretion rates: A source of diversity in planetary systems I. Analytical formulation
• Planets Near Mean-Motion Resonances
• Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
• The HARPS search for southern extra-solar planets. XXVII. Up to seven planets orbiting HD 10180: probing the architecture of low-mass planetary systems
• On the Age of the TRAPPIST-1 System
• Giant Planet Formation, Evolution, and Internal Structure
• Convergent Migration Renders TRAPPIST-1 Long-lived
• Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology
• Early 2017 observations of TRAPPIST-1 with $\text{Spitzer}$
• Dynamical rearrangement of super-Earths during disk dispersal I. Outline of the magnetospheric rebound model
• Mercury-T: A new code to study tidally evolving multi-planet systems. Applications to Kepler-62
• Interior Structures and Tidal Heating in the TRAPPIST-1 Planets
• X-Shooter study of accretion in $\rho$-Ophiucus: very low-mass stars and brown dwarfs
• On the equilibrium figure of close-in planets and satellites
• Interior characterization in multiplanetary systems: TRAPPIST-1
• Equilibrium rotation of semiliquid exoplanets and satellites
• Spin-orbital tidal dynamics and tidal heating in the TRAPPIST-1 multi-planet system
• Tidal Heating and the Habitability of the TRAPPIST-1 Exoplanets
• Resonant Chains and Three-body Resonances in the Closely-Packed Inner Uranian Satellite System
• Updated Masses for the TRAPPIST-1 Planets
• Resolving the Sin(I) degeneracy in Low-Mass Multi-Planet Systems

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