Tidal decay and orbital circularization in close-in two-planet systems
The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the exact equations of motion through the numerical simulation of the system evolution. In addition to the orbital decay and circularization, we show that the final configuration of the system is affected by the shrink of the inner orbit. Our second approach consist in the analysis of the stationary solutions of mean equations of motion based on a Hamiltonian formalism. We consider the case of a hot super-Earth planet with a more massive outer companion. As a real example, the CoRoT-7 system is analyzed solving the exact and mean equations of motion. The star-planet tidal interaction produces orbital decay and circularization of the orbit of CoRoT-7b. In addition, the long-term tidal evolution is such that the eccentricity of CoRoT-7c is also circularized and a pair of final circular orbits is obtained. A curve in the space of eccentricities can be constructed through the computation of stationary solutions of mean equations including dissipation. The application to CoRoT-7 system shows that the stationary curve agrees with the result of numerical simulations of exact equations. A similar investigation performed in a super-Earth-Jupiter two-planet system shows that the doubly circular state is accelerated when there is a significant orbital migration of the inner planet, in comparison with previous results were migration is neglected.