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∝r1−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.