Long-term tidal evolution of the TRAPPIST-1 system

TL;DR

This study uses numerical simulations to explore the long-term tidal evolution of the TRAPPIST-1 planetary system, explaining current orbital eccentricities and resonances through coupled tidal damping and resonant interactions.

Contribution

It demonstrates that the current orbital configuration results from coupled tidal evolution and constrains the planets' tidal parameters based on simulation outcomes.

Findings

Current eccentricities are consistent with coupled tidal damping.

Resonant configurations cannot be reproduced from primordial resonances by tides alone.

Tidal parameters $k_2/Q$ are estimated to be between 10^-3 and 10^-2.

Abstract

The ultracool M-dwarf star TRAPPIST-1 is surrounded by seven planets configured in a resonant chain. Transit-timing variations have shown that the planets are caught in multiple three-body resonances and that their orbits are slightly eccentric, probably caused by resonant forcing. The current values of the eccentricities could be a remnant from their formation. Here we run numerical simulations using fictitious forces of trapping the fully-grown planets in resonances as they migrated in the gas disc, followed by numerical simulations detailing their tidal evolution. For a reduced disc scale height $h\sim 0.03$--0.05, the eccentricities of the planets upon capture in resonance are higher than their current values by factors of a few. We show that the current eccentricities and spacing of planets d to h are natural outcomes of coupled tidal evolution wherein the planets simultaneously damp their eccentricities and separate due to their resonant interaction. We further show that the planets evolve along a set of equilibrium curves in semimajor axis--eccentricity phase space that are defined by the resonances, and that conserve angular momentum. As such, the current 8:5--5:3--(3:2)$^2$--4:3--3:2 resonant configuration cannot be reproduced from a primordial (3:2)$^4$--4:3--3:2 resonant configuration from tidal dissipation in the planets alone. We use our simulations to constrain the long-term tidal parameters $k_2/Q$ for planets b to e, which are in the range $10^{-3}$ to $10^{-2}$, and show that these are mostly consistent with those obtained from interior modelling following reasonable assumptions.