Poster title: Resonant Capture and Tidal Evolution in Circumbinary Systems: The Case of Kepler-38

Poster abstract: 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 introduced in an N-body code through an ad-hoc external acceleration that mimics the 
results of hydrodynamical simulations. Tidal effects were incorporated with a weak-friction equilibrium tide model, where 
we included the post-main-sequence change in the stellar radii as predicted by the stellar evolution models.
We used Kepler-38 as an example and focused on the dynamics of the 5/1 MMR. Kepler-38 is a highly evolved stellar 
system with an estimated age of 12 Gyrs and an inflated central star that has undergone significant changes in its 
physical radius during the last few Gyrs, making it an excellent case to evaluate long-term tidal evolution. The present-day 
mean-motion ratio between planet and secondary star is ∼ 5.6, close to but significantly displaced from the nominal 
resonant value. 
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 
by a mechanism that may involve the perturbation of near-resonant terms on the secular modes. 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 (resonance offset and planet eccentricity). The results presented here open 
an interesting outlook into the complex dynamics of high-order resonances in circumbinary systems.