Conglomeration of kilometre-sized planetesimals

This is the accepted manuscript for a paper published in The Astrophysical Journal, 801:15 (12pp), 2015 March 1, doi:10.1088/0004-637X/801/1/15We study the efficiency of forming large bodies, starting from a sea of equal-sized planetesimals. This is likely one of the earlier steps of planet formation and relevant for the formation of the asteroid belt, the Kuiper Belt, and extrasolar debris disks. Here we consider the case that the seed planetesimals do not collide frequently enough for collisions to be dynamically important (the collisionless limit), using a newly constructed conglomeration code, and by carefully comparing numerical results with analytical scalings. In the absence of collisional cooling, as large bodies grow by accreting small bodies, the velocity dispersion of the small bodies (u) is increasingly excited. Growth passes from the well-known runaway 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 the analytical understandings developed by Lithwick, as well as previous numerical studies, that a size spectrum dn/dR R^_4 results, and that the formation efficiency, defined as the mass fraction in bodies much larger than the initial size, is ~ x a few R ʘ a , or ~ 10^_3 at the distance of the Kuiper Belt. We argue that this extreme inefficiency invalidates the conventional conglomeration model for the formation of both our Kuiper Belt and extrasolar debris disks. New theories, possibly involving direct gravitational collapse, or strong collisional cooling of small planetesimals, are required.We thank the first referee, Chris Ormel, and a second anonymous referee for a knowledgeable critique of our numerical procedure. We substantially revamped our numerical procedures following these comments. YW acknowledges grants from NSERC and the government of Ontario. YL acknowledges grants AST-1109776 and AST-1352369 from NSF, and NNX14AD21G from NASA. AS was supported by the government of Ontario by a Ontario Graduate Scholarship in Science and Technology; and is supported by the European Union through ERC grant number 279973