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Summary

In this review we have studied possible formation scenarios of the observed mean-motion resonances in extrasolar planetary systems. As the majority of resonant systems are locked in a 2:1 resonance we concentrate in particular on these systems.

We have shown that planet-disk interaction between young embedded protoplanets and the protoplanetary disk may usually lead to a differential migration where the outer planet approaches the inner one. To analyze the outcome of the convergent migration we first perform full hydrodynamical simulations with two embedded planets and then compare these to forced three-body simulations where additional forces mimicking the planet-disk interaction have been added. We find that resonant capture into the 2:1 resonance indeed occurs frequently and that continued driving of the disk will move the system deep into the resonance with significant growth of the eccentricity of the two planets. Additionally, the final configuration of the orbits is symmetric where the periapses are aligned with only small libration. We refer to this state as apsidal co-rotation.

The well observed system GJ 876 is, in fact, in this symmetric configuration with only small libration of the two resonant angles. The relatively small planetary eccentricities in this system can only be explained if one assumes that after resonant capture occurred the length of migration was limited by disk dispersal. Alternatively, it may be possible that an additional damping mechanism has operated on the eccentricities during their migration process.

In the other two systems analyzed (HD 128311 and HD 73526) the eccentricities in the current observed state vary much more strongly and vanish peri odically for one planet. We demonstrate that the dynamical structure of these two systems may be the results of the mixed evolutionary scenario, melting together inward migration and a sudden perturbation.

In summary, the complex dynamical behavior of the observed resonant planetary systems can be understood in the framework of their formation process. Interaction with the protoplanetary disk and possibly more sudden planet-planet scattering events are important ingredients in shaping planetary systems.

Acknowledgments

Part of this work has been supported by the Hungarian Scientific Research Fund (OTKA) under the grants D048424, T043739 and by the German Science Foundation (DFG) under grant 436 UNG 17/1/07.

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