Planetary Migration and Eccentricity and Inclination Resonances in Extrasolar Planetary Systems

The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration due to planet-disk interaction. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee (2004). This new family has outer orbital eccentricity e2 & 0.4–0.5, asymmetric librations of both eccentricity resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m1/m2 & 0.2, it is possible to evolve into this family by fast migration only for m1/m2 & 2. Thommes & Lissauer (2003) have found that a capture into the 4:2 inclination resonances is possible only for m1/m2 . 2. We show that this capture is also possible for m1/m2 & 2 if the migration rate is slightly slower than that adopted by Thommes & Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale comparable to or shorter than the migration timescale, e2 may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the 4:2 inclination resonances. Thus, if future observations of extrasolar planetary systems were to reveal certain combinations of mass ratio and resonant configuration, they would place a constraint on the strength of eccentricity damping during migration, as well as on the rate of the migration itself.