Size Distribution of Main-Belt Asteroids with High Inclination

Abstract

We investigated the size distribution of high-inclination main-belt asteroids (MBAs) so as to explore asteroid collisional evolution under hypervelocity collisions of around 10 km s$^{-1}$. 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 the 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$\ \pm\ $0.02 for low-inclination ($\lt\ $15$^{\circ}$) MBAs and 2.02$\ \pm\ $0.03 for high-inclination ($\gt\ $15$^{\circ}$) 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 the 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.