Planet formation occurs within the gas-and dust-rich environments of protoplanetary disks. Observations of these objects show that the growth of primordial submicronsized 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 been generally 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 is 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 arXiv:1209.0013v3 [astro-ph.EP] 15 Dec 2012 number of long-standing problems in protoplanetary disks, including planetesimal formation close to the central star, the presence of mm-to cm-size particles far out in the disk, and the persistence of micron-size grains for millions of years.
The relevance of encounters on the destruction of protoplanetary discs in the Orion Nebula Cluster (ONC) is investigated by combining two different types of numerical simulation. First, star-cluster simulations are performed to model the stellar dynamics of the ONC, the results of which are used to investigate the frequency of encounters, the mass ratio and separation of the stars involved, and the eccentricity of the encounter orbits. The results show that interactions that could influence the star-surrounding disc are more frequent than previously assumed in the core of the ONC, the so-called Trapezium cluster. Second, a parameter study of star-disc encounters is performed to determine the upper limits of the mass loss of the discs in encounters. For simulation times of ∼ 1-2 Myr (the likely age of the ONC) the results show that gravitational interaction might account for a significant disc mass loss in dense clusters. Disc destruction is dominated by encounters with high-mass stars, especially in the Trapezium cluster, where the fraction of discs destroyed due to stellar encounters can reach 10-15%. These estimates are in accord with observations of Lada et al. (2000) who determined a stellar disc fraction of 80-85%. Thus, it is shown that in the ONC -a typical star-forming region -stellar encounters do have a significant effect on the mass of protoplanetary discs and thus affect the formation of planetary systems.
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