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Circumbinary planets are thought to form far from the central binary and migrate inwards by interactions with the circumbinary disk, ultimately stopping near their present location either by a planetary trap near the disk inner edge or by resonance capture. Here, we analyze the second possibility, presenting a detailed numerical study on the capture process, resonant dynamics and tidal evolution of circumbinary planets in high-order mean-motion resonances (MMRs). Planetary migration was modeled as an external acceleration in an N-body code, while tidal effects were incorporated with a weak-friction equilibrium tide model. As a working example we chose Kepler-38, a highly evolved system with a planet in the vicinity of the 5/1 MMR. Our simulations show that resonance capture is a high-probability event under a large range of system parameters, although several different resonant configuration are possible. We identified three possible outcomes: aligned librations, anti-aligned librations and chaotic solutions. All were found to be dynamically stable, even after the dissipation of the disk, for time-spans of the order of the system’s age. We found that while tidal evolution decreases the binary’s separation, the semimajor axis of the planet is driven outwards. Although the net effect is a secular increase in the mean-motion ratio, the system requires a planetary tidal parameter of the order of unity to reproduce the observed orbital configuration. The results presented here open an interesting outlook into the complex dynamics of high-order resonances in circumbinary systems.

Resonant capture and tidal evolution in circumbinary systems: testing the case of Kepler-38