Evolution of an Asteroid Family under YORP, Yarkovsky, and Collisions

Any population of asteroids, like asteroid families, will disperse in semimajor axis due to the Yarkovsky effect. The amount of drift is modulated by the asteroid spin state evolution, which determines the balance between the diurnal and seasonal Yarkovsky forces. The asteroid's spin state is, in turn, controlled in part by the Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect. The otherwise smooth evolution of an asteroid can be abruptly altered by collisions, which can cause impulsive changes in the spin state and can move the asteroid onto a different YORP track. In addition, collisions may also alter the YORP parameters by changing the superficial features and overall shape of the asteroid. Thus, the coupling between YORP and Yarkovsky is also strongly affected by the impact history of each body. To investigate this coupling, we developed a statistical code modeling the time evolution of semimajor axis under YORP–Yarkovsky coupling. It includes the contributions of NYORP (normal YORP), TYORP (tangential YORP), and collisions whose effects are deterministically calculated and not added in a statistical way. We find that both collisions and TYORP increase the dispersion of a family in semimajor axis by making the spin axis evolution less smooth and regular. We show that the evolution of a family's structure with time is complex and collisions randomize the YORP evolution. In our test families, we do not observe the formation of a "YORP-eye" in the semimajor axis versus diameter distribution, even after a long period of time. If present, the "YORP-eye" might be a relic of an initial ejection velocity pattern of the collisional fragments.