High Orbital Eccentricities of Extrasolar Planets Induced by the Kozai Mechanism

One of the most remarkable properties of extrasolar planets revealed by the on-going radial-velocity surveys is their high orbital eccentricities, which are difficult to explain within our current theoretical paradigm for planet formation. Observations have shown that at least ∼ 20% of these planets, including some with particularly high eccentricities, are orbiting a component of a wide binary star system. The presence of a distant binary companion can cause significant secular perturbations to the orbit of a planet. In particular, at high relative inclinations, a planet can undergo a large-amplitude eccentricity oscillation. This so-called “Kozai mechanism” is effective at a very long range, and its amplitude is purely dependent on the relative orbital inclination. In this paper, we address the following simple question: assuming that every host star with a detected giant planet also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, how well could secular perturbations reproduce the observed eccentricity distribution of planets? Our calculations show that the Kozai mechanism consistently produces an excess of planets with very high (e & 0.6) and very low (e . 0.1) eccentricities. Assuming an isotropic distribution of relative orbital inclination, we would expect that 23% of planets do not have sufficiently high inclination angles to experience the eccentricity oscillation. By a remarkable coincidence, only 23% of currently known extrasolar planets have eccentricities e < 0.1. However, this paucity of near-circular orbits in the observed sample cannot be explained solely by the Kozai mechanism. This is because, even with high enough inclinations, the Kozai mechanism often fails to produce significant eccentricity perturbations when there are other competing sources of orbital perturbations on secular timescales, such as general relativity. On the other hand, the Kozai mechanism can produce many highly eccentric orbits. Indeed the overproduction of high eccentricities observed in our models could be combined with plausible circularizing mechanisms (e.g., friction from residual gas) to create more intermediate eccentricities (e ≃ 0.1− 0.6).