Trapping in high-order orbital resonances and inclination excitation in extrasolar systems

Exoplanetary systems in mean motion resonance (MMR) are thought to have been captured as a result of gas-induced (Type II) orbital migration, during their early evolution phases. Using three-dimensional numerical simulations, Thommes & Lissauer showed that resonant inclination excitation can occur, for a system of two planets that evolves into a 2/1 MMR by Type II migration. In this paper, we examine whether capture in higher order resonances can also result in inclination excitation. We undertake a parametric study, varying the masses and orbital parameters of the planets, as well as the migration rate and eccentricity damping rate. We show that captures in high-order resonances (such as the 3/1, 4/1 and 5/1) are also able to produce inclination excitation. The maximal mutual inclination between the two orbital planes reaches values between 20° and 70° during a simulation, depending on the masses of the planets. Inclination excitation is observed for all configurations as long as (i) the inner planet is not very massive and (ii) at least one of the planets develops an eccentricity e > 0.4. Thus, our simulations imply that inclination excitation is a common outcome, as long as eccentricity damping is not too strong. On the other hand, our results suggest that planets in the exosystems HD 60532 (3/1 MMR), HD 108874 (4/1 MMR) and HD 102272 (4/1 MMR) are most probably in coplanar orbits, since they do not meet the above two constraints. Indeed, this result was verified by a series of dedicated numerical simulations.