Formation of Kuiper Belt binaries

Abstract

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 (L^2s mechanism); in the second, a binary is formed by three-body gravitational deflection (L^3 mechanism). Here, we accurately calculate the L^2s and L^3 formation rates for sub-Hill velocities. While the L^2s formation rate is close to previous order of magnitude estimates, the L^3 formation rate is about a factor of 4 smaller. For sub-Hill KBO velocities (v >> v_H) the ratio of the L^3 to the L^2s 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>>v_H) the L^3 mechanism dominates over the L^2s mechanism. Binary formation via the L^3 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^3 mechanism, contrary to Lee and colleagues. For the L^2s 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.

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