Stability of Planetary Motion in Binary Star Systems
We considered the problem of stability for planets of finite mass in binary star systems. We selected a huge set of initial conditions for planetary orbits of the S-type, to perform high precision and very extended in time integrations. For our numerical integrations, we resorted to the use of a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term time integrations. We estimated the probability of different types of instability: planet collisions with the primary or secondary star or planet ejected away from the binary star system. We confirm and generalize to massive planets the dependence of the critical semi-major axis on eccentricity and mass ratio of the binary already found by Holman and Wiegert (1999). We were also able to pick a significant number of orbits that are only `marginally' stable, according to the classification introduced by Musielak et al. (2005). A, natural, extension of this work has been the study of the effect of perturbations induced to circumbinary planet motion by a passing-by star, like it often happens in a star cluster. One of the targets of this analysis is the investigation of the possibility that a planet, formerly on a stable S-type orbit around one of the two stars, could transit to a stable P-type orbit (or viceversa). We performed a series of more than 4500 scattering experiments with different initial conditions typical of encounters in small star clusters. We found some interesting behaviors of the systems after perturbation and showed how a transition from an inner (S-type) stable orbit to a circumbinary (P-type) (and vice-versa) has a very low (but non null) probability.