Difficulty in Formation of Counter-orbiting Hot Jupiters from Near-coplanar Hierarchical Triple Systems: A Sub-stellar Perturber

Among a hundred transiting planets with a measured projected spin-orbit angle {\lambda}, several systems are suggested to be counter-orbiting. While they may be due to the projection effect, the mechanism to produce a counter-orbiting planet is not established. A promising scenario for the counter-orbiting planets is the extreme eccentricity evolution in near-coplanar hierarchical triple systems with eccentric inner and outer or- bits. We examine this scenario in detail by performing a series of systematic numerical simulations, and consider the possibility of forming hot Jupiters, especially counter- orbiting one under this mechanism with a distant sub-stellar perturber. We incorporate quadrupole and octupole secular gravitational interaction between the two orbits, and also short-range forces (correction for general relativity, star and inner planetary tide and rotational distortion) simultaneously. We find that most of systems are tidally disrupted and that a small fraction of survived planets turns out to be prograde. The formation of counter-orbiting hot Jupiters in this scenario is possible only in a very restricted parameter region, and thus very unlikely in practice.