DYNAMICS OF PLANETARY SYSTEMS IN STAR CLUSTERS

At least 10%–15% of nearby Sunlike stars have known Jupiter-mass planets. In contrast, very few planets are found in mature open and globular clusters such as the Hyades and 47 Tuc. We explore here the possibility that this dichotomy is due to the postformation disruption of planetary systems associated with the stellar encounters in long-lived clusters. One supporting piece of evidence for this scenario is the discovery of freely floating low-mass objects in star forming regions. We use two independent numerical approaches, a hybrid Monte Carlo and a direct N-body method, to simulate the impact of the encounters. We show that the results of numerical simulations are in reasonable agreement with analytical determinations in the adiabatic and impulsive limits. They indicate that distant stellar encounters generally do not significantly modify the compact and nearly circular orbits. However, moderately close stellar encounters, which are likely to occur in dense clusters, can excite planets' orbital eccentricity and induce dynamical instability in systems that are closely packed with multiple planets. The disruption of planetary systems occurs primarily through occasional nearly parabolic, nonadiabatic encounters, though eccentricity of the planets evolves through repeated hyperbolic adiabatic encounters that accumulate small-amplitude changes. The detached planets are generally retained by the potential of their host clusters as free floaters in young stellar clusters such as σ Orionis. We compute effective cross sections for the dissolution of planetary systems and show that, for all initial eccentricities, dissolution occurs on timescales that are longer than the dispersion of small stellar associations, but shorter than the age of typical open and globular clusters. Although it is much more difficult to disrupt short-period planets, close encounters can excite modest eccentricity among them, such that subsequent tidal dissipation leads to orbital decay, tidal inflation, and even disruption of the close-in planets.