Scale-Free Dynamics of Monopole-Quadrupole Binaries Applied to the Morphogenesis of Bi-lobed KBOs

A significant fraction of Kuiper Belt Objects (KBOs) are observed to have strongly asymmetric, particularly bi-lobed, shapes. Arrokoth, recently imaged by the New Horizons space probe, is one example of a KBO with such shape. Such morphologies suggest an origin from a gentle collision between two smaller bodies that were in a binary. A recent study by Grishin et al. (Nature, 2020) suggested that chaotic Kozai-Lidov (KL) oscillations might be responsible for causing the orbiting binary to collide and produce a highly irregular, bi-lobed object. Another possibility, which can also be extended to systems with a broad range of scales, is an orbital eccentricity evolution due to spin-orbit coupling that may also bring two bodies to a merger. Here we present a new code for evolving perturbed binaries in which the shape of the secondary is taken into account by approximating it as a gravitating quadrupole. We use quaternion algebra for representing orientation of the secondary and derive equations of motion based on MacCullagh's formula. We present several tests of the code and discuss possible pathways for the morphogenesis of bi-lobed objects from such systems. Indeed, in a system with strong spin-orbit coupling, one might expect eccentricity oscillations similar to those produced by KL mechanism when the spin of the secondary is not aligned with orbital angular momentum. It is also important to take into account spin-orbit coupling at the periapsis of the KL cycle, as it might strongly alter the outcome of KL-triggered encounters.