Secular Evolution of Planetary Systems in Binaries

The orbital eccentricity of a single planet in a stellar binary system with a sufficiently large mutual inclination angle is known to oscillate on a secular timescale through the Kozai mechanism. We have investigated the effects of the Kozai mechanism on double-planet systems in binaries. The evolutionary sequence of a pair of planets under the influence of a binary companion is fairly complex. Various dynamical outcomes are seen in numerical simulations. One interesting outcome is the rigid rotation of the planetary orbits in which the planetary orbital planes secularly precess in concert, while the orbital eccentricities oscillate synchronously. In such cases the outer planet acts as a propagator of the perturbation from the binary companion to the inner planet and drives the inner planetary orbit to precess at a rate faster than what is predicted by the Kozai mechanism. 1. The Kozai Mechanism The first decade of radial-velocity and photometric surveys has revealed that planetary systems commonly form among stellar binary systems. As of July 2007, at least 37 planetary systems (∼ 20% of all the known systems) are members of multiple-stellar systems (Raghavan et al. 2006; Desidera & Barbieri 2007). The true stellar multiplicity among planetary systems may be higher than 20% since the photometric surveys in search for stellar companions around currently known planetary systems are not yet complete. Because most of these stellar companions are in wide orbits (typically a = 10 AU or greater), their orbital inclinations are not correlated with the invariable plane of the planetary systems, implying that many binary companions orbit around planetary systems in largely inclined orbits . It has been known in celestial mechanics that in a hierarchical triple-body system with sufficiently large mutual inclination angle (I > Icrit = 39.2 ) between the inner and outer binaries, the inner binary’s orbital eccentricity and inclination undergo large-amplitude oscillations on a secular timescale through the “Kozai mechanism” (Kozai 1962). When adopted to planetary systems, the inner binary orbit can be replaced by the osculating orbit of a planet around the primary star. The Kozai mechanism has following unique properties (see also Figure 1): (1) the orbital eccentricity of the planet oscillates with an amplitude If the distribution of the mutual inclination angle is completely isotropic, the probability of the mutual inclination angle being greater than the critical Kozai angle (39.2◦) is 77%