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The size distribution in the cold classical Kuiper belt can be approximatedby two idealized power laws: one with steep slope for radii R>R* and one withshallow slope for R<R*, where R*~25-50 km. Previous works suggested that theSFD roll-over at R* can be the result of extensive collisional grinding in theKuiper belt that led to the catastrophic disruption of most bodies with R<R*.Here we use a new code to test the effect of collisions in the Kuiper belt. Wefind that the observed roll-over could indeed be explained by collisionalgrinding provided that the initial mass in large bodies was much larger thanthe one in the present Kuiper belt, and was dynamically depleted. In additionto the size distribution changes, our code also tracks the effects ofcollisions on binary systems. We find that it is generally easier to dissolvewide binary systems, such as the ones existing in the cold Kuiper belt today,than to catastrophically disrupt objects with R~R*. Thus, the binary survivalsets important limits on the extent of collisional grinding in the Kuiper belt.We find that the extensive collisional grinding required to produce the SFDroll-over at R* would imply a strong gradient of the binary fraction with R andseparation, because it is generally easier to dissolve binaries with smallcomponents and/or those with wide orbits. The expected binary fraction for R<R*is <0.1. The present observational data do not show such a gradient. Instead,they suggest a large binary fraction of ~0.4 for R=30-40 km. This may indicatethat the roll-over was not produced by disruptive collisions, but is instead afossil remnant of the KBO formation process.

Observed Binary Fraction Sets Limits on the Extent of Collisional Grinding in the Kuiper Belt