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Planet formation occurs within the gas and dust rich environments ofprotoplanetary disks. Observations of these objects show that the growth ofprimordial sub micron sized particles into larger aggregates occurs at theearliest stages of the disks. However, theoretical models of particle growththat use the Smoluchowski equation to describe collisional coagulation andfragmentation have so far failed to produce large particles while maintaining asignificant populations of small grains. This has been generally attributed tothe existence of two barriers impeding growth due to bouncing and fragmentationof colliding particles. In this paper, we demonstrate that the importance ofthese barriers has been artificially inflated through the use of simplifiedmodels that do not take into account the stochastic nature of the particlemotions within the gas disk. We present a new approach in which the relativevelocities between two particles is described by a probability distributionfunction that models both deterministic motion and stochastic motion. Takingboth into account can give quite different results to what has been consideredrecently in other studies. We demonstrate the vital effect of two "ingredients"for particle growth: the proper implementation of a velocity distributionfunction that overcomes the bouncing barrier and, in combination with masstransfer in high-mass-ratio collisions, boosts the growth of larger particlesbeyond the fragmentation barrier. A robust result of our simulations is theemergence of two particle populations (small and large), potentially explainingsimultaneously a number of long-standing problems in protoplanetary disks,including planetesimal formation close to the central star, the presence of mmto cm size particles far out in the disk, and the persistence of micron-sizegrains for millions of years.

From dust to planetesimals: an improved model for collisional growth in protoplanetary disks