Evidence for Random Walk Transport of Small Asteroids from the Main Belt to the Inner Solar System

The transport of some main-belt asteroids to the inner solar system depends on Yarkovsky radiation forces changing the orbits of those asteroids. However, these forces depend on the rotational states of the asteroids, and YORP radiation forces act to change the rotational states. In addition, impacts by other asteroids change both the rotation periods and the spin directions with the result that the transport rates are uncertain. Here we show, using observations of the distributions of the rotation periods, sizes, and semimajor axes of the asteroids in the Eunomia, Hungaria, and Vesta families, that the semimajor axis distributions of the asteroids in these families with diameters less than 2 or 3 km are consistent with Gaussian distributions characteristic of a random walk. This implies that their spin directions experience random changes and that their rate of transport to the inner solar system is considerably less than estimates that assume a fixed rotational state, including those used to determine family ages from V shapes. In addition, the transport process is selective, and we must expect the characteristics of the near-Earth asteroid (NEA) population to differ from those of the main belt. In particular, the transport of some family asteroids is likely only for a narrow band of asteroid sizes, and this could result in a deficit of subkilometer asteroids in the NEA population if the main-belt supply of those asteroids is dominated by a few families.