Formation of Kuiper Belt binaries

The discovery that a substantial fraction of Kuiper Belt objects (KBOs) exists in binaries with wide separations and roughly equal masses has motivated a variety of new theories explaining their formation. Goldreich and colleagues proposed two formation scenarios: In the first, a transient binary is formed, which becomes bound with the aid of dynamical friction from the sea of small bodies (L²S mechanism); in the second, a binary is formed by three-body gravitational deflection (L³ mechanism). Here, we accurately calculate the L²s and L³ formation rates for sub-Hill velocities. While the L²S formation rate is close to previous order of magnitude estimates, the L³ formation rate is about a factor of 4 smaller. For sub-Hill KBO velocities (ν ≪ ν^H) the ratio of the L³ to the L²S formation rate is 0.05(ν/νH), independent of the small bodies' velocity dispersion, their surface density, or their mutual collisions. For super-Hill velocities (ν ≪ ν^H) the L³ mechanism dominates over the L ²s mechanism. Binary formation via the L³ mechanism competes with binary destruction by passing bodies. Given sufficient time, a statistical equilibrium abundance of binaries forms. We show that the frequency of long-lived transient binaries drops exponentially with the system's lifetime and that such transient binaries are not important for binary formation via the L³ mechanism, contrary to Lee and colleagues. For the L²S mechanism we find that the typical time that transient binaries must last to form Kuiper Belt binaries (KBBs) for a given strength of dynamical friction, D, increases only logarithmically with D. Longevity of transient binaries (with lifetimes 15Ω^-1 as suggested by Astakhov and colleagues) only becomes important for very weak dynamical friction (i.e., D ≳ 0.002) and is most likely not crucial for KBB formation.