ar X iv : a st ro - p h / 06 12 75 7 v 1 2 8 D ec 2 00 6 Dynamics of Planetary Systems in Star Clusters

Stars are generally formed in clusters. Prior to the the dispersal of small clusters, which occurs on the time scale of 10 8 yr, dynamical interaction between young stars may also affect the stability and dynamical evolution of their companion planetary systems. Through a series of numerical simulations, we show that distant stellar encounters generally do not strongly modify the compact and nearly circular orbits of those planetary systems formed with kinematic properties similar to the solar system. But, the stellar encounters can strongly perturb the dynamical structure of planetary systems with extended and eccentric orbits. Close stellar encounters can also excite modest eccentricity for all planets including those with relatively short periods and small eccentricities and induce dynamical instability in systems which are closely packed with multiple planets. The highly eccentric planets are much more prone to be detached from their host stars by the stellar encounters. We explore the possibility that this process may have led to the formation of " freely floating planets " in young stellar clusters such as σ Orionis. We also discuss the differential cross section for the eccentricity and the relative binding energy changes, which are in a good agreement with analytical formulae. The results of numerical simulations, both N-body and Hybrid Monte Carlo, are in a reasonable agreement with analytical predictions for a tidal adiabatic and an impulsive limits.