We have investigated i ) the formation of gravitationally bounded pairs of gas-giant planets ( which we call ” binary planets ” ) from capturing each other through planet-planet dynamical tide during their close encounters and ii ) the following long-term orbital evolution due to planet-planet and planet-star quasi-static tides .
For the initial evolution in phase i ) , we carried out N-body simulations of the systems consisting of three jupiter-mass planets taking into account the dynamical tide .
The formation rate of the binary planets is as much as 10 % of the systems that undergo orbital crossing and this fraction is almost independent of the initial stellarcentric semi-major axes of the planets , while ejection and merging rates sensitively depend on the semi-major axes .
As a result of circularization by the planet-planet dynamical tide , typical binary separations are a few times the sum of the physical radii of the planets .
After the orbital circularization , the evolution of the binary system is governed by long-term quasi-static tide .
We analytically calculated the quasi-static tidal evolution in later phase ii ) .
The binary planets first enter the spin-orbit synchronous state by the planet-planet tide .
The planet-star tide removes angular momentum of the binary motion , eventually resulting in a collision between the planets .
However , we found that the binary planets survive the tidal decay for main-sequence life time of solar-type stars ( \sim 10 Gyrs ) , if the binary planets are beyond \sim 0.3 AU from the central stars .
These results suggest that the binary planets can be detected by transit observations at \gtrsim 0.3 AU .