Migration of planets into and out of mean motion resonances in protoplanetary discs: overstability of capture and non-linear eccentricity damping

A number of multiplanet systems are observed to contain planets very close to mean motion resonances (MMRs), although there is no significant pile-up of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture into first-order MMRs using a parametrized planet migration model that takes into account non-linear eccentricity damping due to planet-disc interaction. This parametrization is based on numerical hydrodynamical simulations and is more realistic than the simple linear parametrization widely used in previous analytic studies. We find that non-linear eccentricity damping can significantly influence the stability and outcome of resonance capture. In particular, the equilibrium eccentricity of the planet captured into MMRs becomes larger, and the captured MMR state tends to be more stable compared to the prediction based on the simple migration model. In addition, when the migration is sufficiently fast or/and the planet mass ratio is sufficiently small, we observe a novel phenomenon of eccentricity overshoot, where the planet's eccentricity becomes very large before settling down to the lower equilibrium value. This can lead to the ejection of the smaller planet if its eccentricity becomes too large during the overshoot. This may help explain the intra-system mass uniformity observed in compact multiplanet systems and the lack of a low-mass planet companion of hot Jupiters when compared to warm Jupiters.