Binary Asteroid Orbit Expansion due to Continued YORP Spin-up of the Primary and Primary Surface Particle Motion

We examine the hypothesis that within any member of a significant class of close binary asteroid systems with super-synchronously rotating, roughly spheroidal primary and synchronous elongated secondary, continued YORP angular acceleration of the primary causes it to spin at rates where loose material near its equator is lofted from the surface. Subsequent interaction of the material with the secondary causes that material to lose angular momentum and re-impact alpha, but in the process angular momentum is transferred to the orbit causing it to expand. We confirm this hypothesis through precise dynamic and approximate statistical simulation, using the well-characterized 1999 KW4 system model, as KW4 typifies the class of binaries of interest. Our results visibly demonstrate the transfer of angular momentum and our orbit evolution mechanism. In particular, we observe regulation of Alpha spin rate at the rate for which material lofting begins on the same side of Alpha as Beta, but not yet on the opposite side, and nearly constant Alpha angular momentum while the orbit angular momentum grows steadily. The linear fit to that growth is consistent with the YORP torque angular acceleration applied. Lofting occurs in fast transient episodes separated by long periods of slow spin-up under that acceleration. The average amount of material aloft and rate of mass lofting are interesting metrics for the system’s lofting activity level contained in our results, but aren’t physically descriptive at any particular instant given episodic lofting. We translate the orbit angular momentum growth to average semi-major axis change rate with a simple formula, whose integration also leads to time scales for the system evolution several times faster than standard tidal evolution (such as present orbit size doubling time of 2.46 Myr for KW4). The observationally-supported end state of the system’s evolution is likely separation into two asteroids on closely-related heliocentric orbits, with possible shedding of sufficiently more material from the still YORP-torqued, but at that point solitary, primary to form a new secondary and repeat the overall system evolution.