Migration of Two Massive Planets Into (And Out Of) First Order Mean Motion Resonances

We consider the dynamical evolution of two planets with nearly circular and nearly coplanar orbits undergoing eccentricity damping and convergent migration in the vicinity of a first order mean motion resonance. Following Goldreich & Schlichting, we include a coupling between the dissipative semimajor axis evolution and the damping of the eccentricities. In agreement with past studies, we find that this coupling can lead to instability of the resonance and that for a certain range of parameters capture into resonance is only temporary. Using a more general model, we show that whether escape from resonance can occur depends in a characteristic way on the mass ratio between the two planets as well as their relative eccentricity damping timescales. In particular, systems undergoing Type I migration with a more massive inner planet typically result in permanent capture. Additionally, we show that even when escape from resonance does occur, the timescale for escape is long enough such at any given time a pair of planets is more likely to be found in a low-order resonance rather than migrating between them. Thus, we argue that intrinsic instability of resonances cannot singlehandedly reconcile convergent migration with the observed lack of Kepler planet pairs found near resonances.