The ratio of retrograde to prograde orbits: A test for Kuiper Belt binary formation theories

With the discovery of Kuiper Belt binaries that have wide separations and roughly equal masses, new theories were proposed to explain their formation. Two formation scenarios were suggested by Goldreich and collaborators. In the first, dynamical friction generated by a sea of small bodies enables a transient binary to become bound (the L(2)s mechanism); in the second, a transient binary gets bound by an encounter with a third body (the L-3 mechanism). We show that these different binary formation scenarios leave their own unique signatures in the relative abundance of prograde to retrograde binary orbits. This signature is due to the fact that stable retrograde orbits can exist much further out in the Hill sphere than prograde orbits. This provides an excellent opportunity to distinguish between the different binary formation scenarios observationally. We predict that if binary formation proceeded while sub-Hill velocities prevailed, the vast majority of all binaries with comparable masses would have retrograde orbits. This dominance of retrograde binary orbits is a result of binary formation via the L(2)s mechanism, or any other mechanism that dissipates energy in a smooth and gradual manner. For super-Hill velocities, binary formation proceeds via the L-3 mechanism, which produces a roughly equal number of prograde and retrograde binaries. These predictions assume that subsequent orbital evolution due to dynamical friction and dynamical stirring of the Kuiper Belt did not alter the sense of the binary orbit after formation.