Formation of Kuiper belt binaries by recoil

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Recent observations have discovered that over one percent of the known Kuiper belt objects are binaries. Besides this high population, these binaries are formed by comparable mass components with large separations between them. Such systems have defied models to account for their formation based on restricted three-body interactions. Among current theories, some consider that they could be produced by collisions of planetesimals within the Hill sphere of a hosting body during the low velocity accretion of the solar nebula. The collision of the two bodies results in their accretion. This and the hosting body then forms a binary. Others believe the usual projectile-target formation mechanism which is believed to have formed the Moon-Earth system. Some others ponder close gravitational interactions, not collisions, of two bodies to form a transient binary which could be stabilized through dynamic friction from the surrounding medium or through scattering of a third large body (planet) that happens to be there. To account for the unique features of Kuiper belt binaries, we consider the gravitational interactions of two comparable masses s and G under the field of the central Sun S. Since the two masses are comparable, they will react on each other and generate recoil on their orbits, contrary to the restricted three-body interactions. By considering angular momentum and energy conservations, it is shown that part of the S-centered relative angular momentum between s and G before encounter can be transferred to the orbital angular momentum of the sG pair leaving a small enough S-centered angular momentum to be converted into a stable G-centered mutual angular momentum of the sG binary. The energy of this binary system measured with respect to its orbital energy is so close to zero that the separation between the components is large which is consistent with observations. This recoil mechanism operates under a constraint that links the mass ratio of the components to their S-centered relative angular momentum before encounter. Nevertheless, this mechanism falls short in accounting for the Charon-Pluto pair.

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