The formation of systems with closely spaced low-mass planets and the application to Kepler-36

The Kepler-36 system consists of two planets that are spaced unusually close together, near the 7:6 mean motion resonance. While it is known that mean motion resonances can easily form by convergent migration, Kepler-36 is an extreme case due to the close spacing and the relatively high planet masses of four and eight times that of the Earth. In this paper, we investigate whether such a system can be obtained by interactions with the protoplanetary disc. These discs are thought to be turbulent and exhibit density fluctuations which might originate from the magnetorotational instability. We adopt a realistic description for stochastic forces due to these density fluctuations and perform both long-term hydrodynamical and N-body simulations. Our results show that planets in the Kepler-36 mass range can be naturally assembled into a closely spaced planetary system for a wide range of migration parameters in a turbulent disc similar to the minimum-mass solar nebula. The final orbits of our formation scenarios tend to be Lagrange stable, even though large parts of the parameter space are chaotic and unstable.