TIDAL EVOLUTION OF RUBBLE PILES

Abstract

Many small bodies in the solar system are believed to be rubble piles, a collection of smaller elements separated by voids.We propose a model for the structure of a self-gravitating rubble pile. Static friction prevents its elements from sliding relative to each other. Stresses are concentrated around points of contact between individual elements. The effective dimensionless rigidity, μ˜ rubble, is related to that of a monolithic body of similar composition and size, μ˜ by μ˜ rubble ∼ μ˜^1/2 eY^−1/2, where eY ∼ 10^−2 is the yield strain. This represents a reduction in effective rigidity below the maximum radius, Rmax ∼ [μeY /(Gρ^2)]^1/2 ∼ 10^3 km, at which a rubble pile can exist. Our model for the rigidity of rubble piles is compatible with laboratory experiments on the speed of shear waves in sand. Densities derived for binary asteroids imply that they are rubble piles. Thus their tidal evolution proceeds faster than it would if they were monoliths. Binary orbit evolution is also driven by torques resulting from the asymmetrical scattering and reradiation of sunlight (YORP and BYORP effects). The tidal torque probably overcomes the radiative (YORP) torque and synchronizes the spins of secondaries in near-Earth binary asteroids and it definitely does so for secondaries of main-belt binary asteroids. Synchronization is a requirement for the radiative (BYORP) torque to act on the binary orbit. This torque clearly dominates the tidal torque for all near-Earth binary asteroids and for some binaries in the main belt. For other main-belt binaries, the tidal torque appears to be at least comparable in strength to the BYORP torque. An exciting possibility is that in these systems the angular momentum added to the orbit by the tidal torque might be removed by the radiative torque.