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Collisional Evolution of Ultra-Wide Trans-Neptunian Binaries

The widely-separated, near-equal mass binaries hosted by the cold Classical Kuiper Belt are delicately bound and subject to disruption by many perturbing processes. We use analytical arguments and numerical simulations to determine their collisional lifetimes given various impactor size distributions, and include the effects of mass-loss and multiple impacts over the lifetime of each system. These collisional lifetimes constrain the population of small (R > ~1 km) objects currently residing in the Kuiper Belt, and confirm that the size distribution slope at small size cannot be excessively steep - likely q < ~3.5. We track mutual semi-major axis, inclination, and eccentricity evolution through our simulations, and show that it is unlikely that the wide binary population represents an evolved tail of the primordially-tight binary population. We find that if the wide binaries are a collisionally-eroded population, their primordial mutual orbit planes must have preferred to lie in the plane of the solar system. Finally, we find that current limits on the size distribution at small radii remain high enough that the prospect of detecting dust-producing collisions in real-time in the Kuiper Belt with future optical surveys is feasible.