Formation of Kuiper Belt Binaries

TL;DR

This paper calculates formation rates of Kuiper Belt binaries via two mechanisms, revealing their relative importance across different velocity regimes and clarifying the role of transient binaries in their formation.

Contribution

It provides accurate calculations of L^2s and L^3 formation rates for Kuiper Belt binaries, refining previous estimates and analyzing their dependence on velocity and dynamical friction.

Findings

L^2s formation rate is similar to previous estimates.

L^3 formation rate is about four times smaller than prior estimates.

L^3 mechanism dominates at super-Hill velocities.

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 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 (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/v_H) 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 et al. (2007). For the L^2s 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 only becomes important for very weak dynamical friction (i.e. D \lesssim 0.002) and is most likely not crucial for KBB formation.