The tidal parameters of TRAPPIST-1b and c

The TRAPPIST-1 planetary system consists of seven planets within 0.05 au of each other, five of which are in a multiresonant 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 multiresonant 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 multilayered 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 k_2/Q ≳ 2× 10^{-4} for planet b and k_2/Q ≳ 10^{-3} for planet c. Interior models yield (0.075-0.37) × 10^-4 for TRAPPIST-1b and (0.4-2) × 10^-4 for TRAPPIST-1c. 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 multiresonant systems if the planet's orbital and interior parameters are sufficiently well known.