Wide-orbit exoplanets are starting to be detected, and planetary formation models are under development to understand their properties. We propose a population of Oort planets around other stars, forming by a mechanism analogous to how the Solar Systems Oort cloud of comets was populated. Gravitational scattering among planets is inferred from the eccentricity distribution of gas-giant exoplanets measured by the Doppler technique. This scattering is thought to commence while the protoplanetary disk is dissipating, $10^6-10^7$ yr after formation of the star, or perhaps soon thereafter, when the majority of stars are expected to be part of a natal cluster. Previous calculations of planet-planet scattering around isolated stars have one or more planets spending $10^4-10^7$ yr at distances >100 AU before ultimately being ejected. During that time, a close flyby of another star in the cluster may dynamically lift the periastron of the planet, ending further scattering with the inner planets. We present numerical simulations demonstrating this mechanism as well as an analysis of the efficiency. We estimate an occurrence of planets between 100 and 5000 AU by this mechanism to be <1% for gas giants and up to a few percent for Neptunes and super-Earths.
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