2013ApJ...764..146G

Planet formation occurs within the gas- and dust-rich environments of protoplanetary disks. Observations of these objects show that the growth of primordial submicron-sized particles into larger aggregates occurs at the earliest evolutionary stages of the disks. However, theoretical models of particle growth that use the Smoluchowski equation to describe collisional coagulation and fragmentation have so far failed to produce large particles while maintaining a significant population of small grains. This has generally been attributed to the existence of two barriers impeding growth due to bouncing and fragmentation of colliding particles. In this paper, we demonstrate that the importance of these barriers has been artificially inflated through the use of simplified models that do not take into account the stochastic nature of the particle motions within the gas disk. We present a new approach in which the relative velocities between two particles are described by a probability distribution function that models both deterministic motion (from the vertical settling, radial drift, and azimuthal drift) and stochastic motion (from Brownian motion and turbulence). Taking both into account can give quite different results to what has been considered recently in other studies. We demonstrate the vital effect of two "ingredients" for particle growth: the proper implementation of a velocity distribution function that overcomes the bouncing barrier and, in combination with mass transfer in high-mass-ratio collisions, boosts the growth of larger particles beyond the fragmentation barrier. A robust result of our simulations is the emergence of two particle populations (small and large), potentially explaining simultaneously a number of longstanding problems in protoplanetary disks, including planetesimal formation close to the central star, the presence of millimeter- to centimeter-sized particles far out in the disk, and the persistence of µm-sized grains for millions of years.