Formation of Kuiper Belt Binaries

It appears that at least several percent of large Kuiper belt objects are members of wide binaries. Physical collisions are too infrequent to account for their formation. Collisionless gravitational interactions are more promising. These provide two channels for binary formation. In each, the initial step is the formation of a transient binary when two large bodies penetrate each other's Hill spheres. Stabilization of a transient binary requires that it lose energy. Either dynamical friction due to small bodies or the scattering of a third large body can be responsible. Our estimates favor the former, albeit by a small margin. We predict that most objects of size comparable to those currently observed in the Kuiper belt are members of multiple systems. More specifically, we derive the probability that a large body is a member of a binary with semi-major axis of order a. The probability depends upon sigma, the total surface density, Sigma, the surface density of large bodies having radius R, and theta=10^-4, the angle subtended by the solar radius as seen from the Kuiper belt. For (sigma/Sigma)R<a< R/theta, the probability is just (Sigma/rho R)theta^-2, the optical depth of the large bodies divided by the solid angle subtended by the Sun. For R<a<r_u=(sigma/Sigma)R, it varies inversely with semimajor axis and reaches (sigma/rho R)theta^-2 at a=R. Based on current surveys of the Kuiper belt, we estimate Sigma/rho=3 10^-4cm and R=100km. We obtain sigma/rho=0.3cm by extrapolating the surface density deduced for the minimum mass solar nebula. Rough predictions are: outside of the critical separation r_u/a_odot=3'', the binary probability is 0.3%; at separations of 0.2'', comparable to current resolving capabilities, it reaches 5%, in agreement with results from the HST binary survey by Brown.