TRAPPIST-1

Long-term Tidal Evolution Of The TRAPPIST-1 System

By Keith Cowing
astro-ph.EP
July 12, 2022
Filed under
Long-term Tidal Evolution Of The TRAPPIST-1 System
Tidal parameters for plants b to f obtained from interior modelling as a function of eccentricity (coloured diagonal bands). The results from the dynamical analyses are overplotted as small circles with error bars. The colour of the circle matches the colour of the band for each planet for easy comparison . Horizontal error b

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∼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 k2/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.

R. Brasser, G. Pichierri, V. Dobos, A. C. Barr

Comments: Accepted in Monthly Notices of the Royal Astronomical Society
Subjects: Earth and Planetary Astrophysics (astro-ph.EP)
Cite as: arXiv:2207.05336 [astro-ph.EP] (or arXiv:2207.05336v1 [astro-ph.EP] for this version)
https://doi.org/10.48550/arXiv.2207.05336
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Submission history
From: Ramon Brasser
[v1] Tue, 12 Jul 2022 06:29:33 UTC (4,599 KB)
https://arxiv.org/abs/2207.05336
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