Formation of the Laplace resonance around GJ 876 through migration in an eccentric disk

Orbital mean motion resonances in planetary systems originate from dissipative processes in disk-planet interactions that lead to orbital migration. In multi-planet systems that host giant planets, the perturbation of the protoplanetary disk strongly affects the migration of companion planets. By studying the well-characterized resonant planetary system around GJ 876 we aim to explore which effects shape disk-driven migration in a multi-planet system. We model the orbital migration of three planets in a protoplanetary disk using two-dimensional locally isothermal hydrodynamical simulations. A parameter study is performed by varying the disk thickness, α viscosity, mass as well as the initial position of the planets. Moreover, we carefully compare simulations with various boundary conditions at the disk’s inner rim.

Due to the high masses of the giant planets in this system, substantial eccentricity is excited in the disk. This results in large variations of the torque acting on the outer lower-mass planet, which we attribute to a shift of Lindblad and corotation resonances at the eccentric gap edge.

Depending on disk parameters, the migration of the outer planet can be stopped at the gap edge in a non-resonant state. In other models, the outer planet is able to open a partial gap and to  circularize the disk again, later entering resonance with the most massive planet in the system, completing the observed 4:2:1 Laplace resonance. Disk-mediated interactions between planets due to spiral waves and excitation of disk eccentricity by massive planets cause deviations from smooth inward migration of exterior lower mass planets.

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