Size Distribution of Main-Belt Asteroids with High Inclination

We investigated the size distribution of high-inclination main-belt asteroids (MBAs) to explore asteroid collisional evolution under hypervelocity collisions of around 10 km/s. We performed a wide-field survey for high-inclination sub-km MBAs using the 8.2-m Subaru Telescope with the Subaru Prime Focus Camera (Suprime-Cam). Suprime-Cam archival data were also used. A total of 616 MBA candidates were detected in an area of 9.0 deg^2 with a limiting magnitude of 24.0 mag in the SDSS r filter. Most of candidate diameters were estimated to be smaller than 1 km. We found a scarcity of sub-km MBAs with high inclination. Cumulative size distributions (CSDs) were constructed using Subaru data and published asteroid catalogs. The power-law indexes of the CSDs were 2.17 +/- 0.02 for low-inclination (< 15 deg) MBAs and 2.02 +/- 0.03 for high-inclination (> 15 deg) MBAs in the 0.7-50 km diameter range. The high-inclination MBAs had a shallower CSD. We also found that the CSD of S-like MBAs had a small slope with high inclination, whereas the slope did not vary with inclination in the C-like group. The most probable cause of the shallow CSD of the high-inclination S-like MBAs is the large power-law index in the diameter-impact strength curve in hypervelocity collisions. The collisional evolution of MBAs may have advanced with oligopolistic survival during the dynamical excitation phase in the final stage of planet formation.