Tidal effects on extrasolar resonant chains

During the late-stage formation of planetary systems, the planets migrate within a gaseous disk. This migration process can reduce the period ratio between the planets until they become trapped in mean-motion resonances (MMRs) with resonant angles oscillating around a fixed value. Once the gas in the disk is depleted, tidal forces from the host star take over, pushing the planets away from exact MMRs, while the resonant angles continue to oscillate. In systems with more than two planets, resonant chains can form, i.e., each pair of planets is in an MMR with its neighbors. A couple of exoplanetary systems have been found to exhibit resonant chains. Several works have recently studied the possible equilibrium configurations of the resonant angles after the disk-induced or the tidal migration process of resonant chains, with the aim of identifying the preferred libration centers. In this work we carry out N-body simulations with disk-induced migration and tidal effects as well as analytical computations of the equilibria with the aim to understand how tidal forces affect the behavior of resonant chains. In particular, we will investigate the possible modifications of libration centers under the action of tides for Kepler-80, a system with four low-mass planets interlinked in a resonant chain.