A new equilibrium state for singly synchronous binary asteroids

The evolution of rotation states of small asteroids is governed by the YORP effect, nonetheless some asteroids can stop their YORP evolution by attaining a stable equilibrium. The same is true for binary asteroids subjected to the BYORP effect. Here we discuss a new type of equilibrium that combines these two, which is possible in a singly synchronous binary system. This equilibrium occurs when the normal YORP, the tangential YORP and the binary YORP compensate each other, and tidal torques distribute the angular momentum between the components of the system and dissipate energy. Such a system if unperturbed would remain singly synchronous in perpetuity with constant spin and orbit rates, as the tidal torques dissipate the incoming energy from impinging sunlight at the same rate. The probability of the existence of this kind of equilibrium in a binary system is found to be on the order of a few percent.