Shaping the Kuiper belt size distribution by shattering large but strengthless bodies

The observed size distribution of Kuiper belt objects (KBOs)—small icy and rocky Solar System bodies orbiting beyond Neptune—is well described by a power law at large KBO sizes. However, recent work by Bernstein et al. (2004, Astron. J. 128, 1364–1390) indicates that the size distribution breaks and becomes shallower for KBOs smaller than about 70 km in size. Here we show that we expect such a break at KBO radius ∼40km since destructive collisions are frequent for smaller KBOs. Specifically, we assume that KBOs are gravity-dominated bodies with negligible material strength. This gives a power-law slope q ≃ 3 where the number N_(>r) of KBOs larger than a size r is given by N_(>r)∝r^(1−q); the break location follows from this slope through a self-consistent calculation. The existence of this break, the break's location, and the power-law slope we expect below the break are consistent with the findings of Bernstein et al. (2004, Astron. J. 128, 1364–1390). The agreement with observations indicates that KBOs as small as ∼40km are effectively strengthless