Andrew Shannon, Yanqin Wu, Yoram Lithwick
We study the efficiency of growing large bodies, starting from a sea of equal-sized planetesimal seeds. This is likely one of the earlier steps of planet formation and is related to the origin of the asteroid belt, the Kuiper belt and extra-solar debris disks. Here we study the case that the seeds do not collide frequently enough for dynamical cooling to be important (the collisionless limit), using a newly constructed conglomeration code, and by carefully comparing numerical results with analytical scalings. We find that large bodies grow primarily by accreting small seeds (and not by accreting each other). As the velocity dispersion of the small bodies (u) is increasingly excited by the growing big bodies, growth passes from the well-known run-away stage (when u is higher than the big bodies' hill velocity) to the newly discovered trans-hill stage (when u and big bodies both grow, but u remains at the big bodies' hill velocity). We find, concurring with analytical understandings developed in Lithwick (2013), as well as previous numerical studies, that a size spectrum dn/dR ~ R^{-4} results, and the formation efficiency, defined as mass fraction in bodies much greater than the seed sizes, is ~ a few times R_sun/a, or ~10^{-3} at the distance of the Kuiper belt. This extreme inefficiency argues against the collisionless limit for the formation of the Kuiper belt and extra-solar debris disks. To conglomerate large bodies in those regions, the initial planetesimals may have to be small and highly collisional.
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http://arxiv.org/abs/1303.3888
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