Orbital evolution of circumbinary planets due to creep tides

Abstract

Most confirmed circumbinary planets are located very close to their host binary where the tidal forces are expected to play an important role in their dynamics. Here we consider the orbital evolution of a circumbinary planet with arbitrary viscosity, subjected to tides due to both central stars. We adopt the creep tide theory and assume that the planet is the only extended body in the system and that its orbital evolution occurs after acquiring its pseudo-synchronous stationary rotational state. With this aim, we first performed a set of numerical integrations of the tidal equations, using a Kepler-38-type system as a working example. For this case we find that the amount of planetary tidal migration and also, curiously, its direction both depend on the viscosity. However, the effect of tides on its eccentricity and pericenter evolutions is simply a move toward pure gravitational secular solutions. Then we present a secular analytical model for the planetary semimajor axis and eccentricity evolution that reproduces very well the mean behavior of the full tidal equations and provides a simple criterion to determine the migration directions of the circumbinary planets. This criterion predicts that some of the confirmed circumbinary planets are tidally migrating inward, but others are migrating outward. However, the typical timescales are predicted to be very long, and not much orbital tidal evolution is expected to have taken place in these systems. Finally, we revisit the orbital evolution of a circumbinary planet in the framework of the constant time lag model. We find that the results predicted with this formalism are identical to those obtained with creep theory in the limit of gaseous bodies.