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Fig. 3

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Collapse time as a function of solid planetesimal radius for clouds with initially monodisperse mm-, cm-, or dm-sized pebbles. Power-law fits to the data and the free-fall time of the initial cloud (tff ~ 25.1 yrs) are added to the plot. For small planetesimals (50 km) the collapse time is inversely proportional to the planetesimal radius and increases linearly with the pebble size. This is the same relation as we find in Appendix A where we assume bouncing as the only collisional outcome. For larger planetesimals (Rsolid ≳ 50 km) the collapse time drops rapidly as pebbles fragment and the number density and collision rates increases. The collapse time is, however, limited downwards by free-fall, so for even larger planetesimals with Rsolid ≳ 70 km the collapse time is equal to the free-fall time of the initial cloud.

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