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 et al. (2002) 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 (Ls mechanism); in the second, a binary is formed by three body gravitational deflection (L mechanism). Here, we accurately calculate the Ls and L formation rates for sub-Hill velocities. While the Ls formation rate is close to previous order of magnitude estimates, the L formation rate is about a factor of 4 smaller. For sub-Hill KBO velocities (v ≪ vH) the ratio of the L 3 to the Ls formation rate is 0.05(v/vH) independent of the small bodies’ velocity dispersion, their surface density or their mutual collisions. For Super-Hill velocities (v ≫ vH) the L mechanism dominates over the Ls mechanism. Binary formation via the L 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 L mechanism, contrary to Lee et al. (2007). For the Ls mechanism we find that the typical time, 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 as suggested by Astakhov et al. (2005)) only becomes important for very weak dynamical friction (i.e. D . 0.002) and is most likely not crucial for KBB formation. Subject headings: Kuiper Belt — planets and satellites: formation