Tidal dissipation in rubble-pile asteroids

We develop a simple scaling argument for frictional dissipation in rubble-pile asteroids, parameterized as an effective dissipation factor Q. This scaling is combined with a prediction (Goldreich, P., Sari, R., 2009. Tidal evolution of rubble piles. Astrophys. J. 691, 54–60) for the tidal response amplitude, parameterized by the Love number k₂. We compare the combined scaling with k₂/Q values inferred from asteroid binaries in which the semi-major axis is determined by a balance between tidal dissipation and the binary YORP (or BYORP) effect (Jacobson, S.A., Scheeres, D.J., 2011. Long-term stable equilibria for synchronous binary asteroids. Astrophys. J. Lett. 736, L19). The k₂/Q scaling matches the inferred values if dissipation is confined to a regolith layer of thickness ∼ 30 m, similar to the available asteroid regolith thickness estimates. The scaling suggests a regolith thickness that is independent of (or decreases slightly with) increasing asteroid radius; this result is consistent with at least one model of regolith generation via impacts.