Statistical evaluation of boulder spatial patterns on asteroids and application to Eros, Itokawa and Ryugu

In planetary science, the statistical properties of spatial distributions are frequently examined to understand the formation and evolution of a body's surface. The surfaces of the asteroids directly explored by spacecraft are covered with numerous boulders and/or regolith particles. However, the spatial distribution of these boulders has not been statistically studied, although much statistical research has been done on the spatial distributions of craters. Thus, it is not known whether the spatial distribution of boulders on asteroids explored by spacecraft is random or not. Squyres et al. (1997) developed a simple model of crater formation and obliteration based on several assumptions, but some of their assumptions do not hold for boulders. In this study, we construct a simple model of the spatial distribution of boulders by verifying some assumptions, and investigate the effect of various assumptions and parameter variations on the model results. From these quantitative calculations, we investigate the spatial distribution of boulders on the asteroids Eros, Ryugu, and Itokawa. Our quantitative results show that boulders on Eros are spatially clustered at the 95 % confidence level. On the other hand, on Ryugu and Itokawa, decameter-sized boulders are spatially less clustered, while meter-sized small boulders are spatially clustered, all at the 95 % confidence level. This suggests that the clustered spatial distribution of small boulders on Ryugu and Itokawa can be explained by their migration.