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 ≪ νH) 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 ≪ νH) 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.
- Kuiper belt
- Planets and satellites: formation