1. Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
2. Department of Astrophysics, American Museum of Natural History, 79th Street at Central Park West, New York, New York 10024-5192, USA
3. Department of Astronomy, University of Virginia, Charlottesville, Virginia 22904, USA
4. Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 3H8, Canada

Correspondence to: Anders Johansen¹ Correspondence and requests for materials should be addressed to A.J. (Email: johansen@mpia.de).

During the initial stages of planet formation in circumstellar gas disks, dust grains collide and build up larger and larger bodies¹. How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem²: boulders are expected to stick together poorly³, and to spiral into the protostar in a few hundred orbits owing to a 'headwind' from the slower rotating gas⁴. Gravitational collapse of the solid component has been suggested to overcome this barrier^{1, 5, 6}. But even low levels of turbulence will inhibit sedimentation of solids to a sufficiently dense midplane layer^{2, 7}, and turbulence must be present to explain observed gas accretion in protostellar disks⁸. Here we report that boulders can undergo efficient gravitational collapse in locally overdense regions in the midplane of the disk. The boulders concentrate initially in transient high pressure regions in the turbulent gas⁹, and these concentrations are augmented a further order of magnitude by a streaming instability^{10, 11, 12} driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar disks.

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