The Modification of Planetary Orbits in Dense Open Clusters

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Abstract
We show that Jovian planets will frequently experience orbital disruption due to interactions with binary stars in their birth clusters. We attack the problem using a Monte Carlo approach and estimate the effective cross section for severe orbital disruption: σ=(230 AU)2. Combining the numerically determined cross section with typical cluster densities n and velocity dispersions v, we find a typical interaction rate of Γ=n σv ≈ 0.13 disruptive encounters per star per 100 million years. This scattering mechanism naturally accounts for extrasolar systems such as 14 Her or 16 Cyg B, in which a Jovian planet is found in an eccentric and reasonably close orbit. This mechanism can also produce systems with extremely small orbits, such as 51 Peg. However, the efficiency is too low to account for the observed frequency of such close systems, and hence some other mechanism for orbital migration is almost certainly at work. Because of mass segregation within the birth cluster, we predict that higher mass stars will have a larger fraction of planets with eccentric orbits than the low-mass stars that comprise the bulk of the stellar population.