Evolution of MU69 from a binary planetesimal into contact by Kozai-Lidov oscillations and nebular drag

The New Horizons flyby of the cold classical Kuiper Belt object MU69 showed it to be a contact binary. The existence of other contact binaries in the 1-10 km range raises the question of how common these bodies are and how they evolved into contact. Here we consider that the pre-contact lobes of MU69 formed as a binary embedded in the Solar nebula, and calculate its subsequent orbital evolution in the presence of gas drag. We find that the sub-Keplerian wind of the disk brings the drag timescales for 10 km bodies to under 1 Myr for quadratic-velocity drag, which is valid in the asteroid belt. In the Kuiper belt, however, the drag is linear with velocity and the effect of the wind cancels out as the angular momentum gained in half an orbit is exactly lost in the other half; the drag timescales for 10 km bodies remain ≳10 Myr. In this situation we find that a combination of nebular drag and Kozai-Lidov oscillations is a promising channel for collapse. We analytically solve the hierarchical three-body problem with nebular drag and implement it into a Kozai cycles plus tidal friction model. The permanent quadrupoles of the pre-merger lobes make the Kozai oscillations stochastic, and we find that when gas drag is included the shrinking of the semimajor axis more easily allows the stochastic fluctuations to bring the system into contact. Evolution to contact happens very rapidly (within 10⁴ yr) in the pure, double-average quadrupole, Kozai region between ≈85 - 95^∘, and within 3 Myr in the drag-assisted region beyond it. The synergy between J₂ and gas drag widens the window of contact to 80^∘ - 100^∘ initial inclination, over a larger range of semimajor axes than Kozai and J₂ alone. As such, the model predicts a low initial occurrence of binaries in the asteroid belt, and an initial contact binary fraction of about 10% for the cold classicals in the Kuiper belt. The speed at contact is the orbital velocity; if contact happens at pericenter at high eccentricity, it deviates from the escape velocity only because of the oblateness, independently of the semimajor axis. For MU69, the oblateness leads to a 30% decrease in contact velocity with respect to the escape velocity, the latter scaling with the square root of the density. For mean densities in the range 0.3-0.5 g cm^-3, the contact velocity should be 3.3 - 4.2 m s^-1, in line with the observational evidence from the lack of deformation features and estimate of the tensile strength.