Binary YORP and Evolution of Binary Asteroids

The rotation states of kilometer sized near earth asteroids are known to be affected by the YORP effect. In a related effect, Binary YORP (BYORP) the orbital properties of a binary asteroid evolves under a radiation effect mostly acting on a tidally locked secondary. The BYORP effect can alter the orbital elements in $\sim 10^{4-5}$ years for a $D_{p}=2\;km$ primary with a $D_{s}=0.4\; km$ secondary at $1\; AU$. It can either separate the binary components or cause them to collide. In this paper we devise a simple approach to calculate the YORP effect on asteroids and BYORP effect on binaries including $J_2$ effects due to primary oblateness and the sun. We apply this to asteroids with known shapes as well as a set of randomly generated bodies with various degrees of smoothness. We find a strong correlation between the strengths of an asteroid's YORP and BYORP effects. Therefore, a statistical knowledge on one, could be used to estimate the effect of the other. We show that the action of BYORP preferentially shrinks rather than expands the binary orbit and that YORP preferentially slows down asteroids. This conclusion holds for the two extremes of thermal conductivities studied in this work and assuming the asteroid reaches a stable point, but may break down for moderate thermal conductivity. The YORP and BYORP effects are shown to be smaller than what could be naively expected due to near cancellation of the effects on small scales. Taking this near cancellation into account, a simple order of magnitude estimate of the YORP and BYORP effects as function of the sizes and smoothness of the bodies is calculated. Finally, we provide a simple proof showing that there is no secular effect due to absorption of radiation in BYORP.