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.

We present 3D smoothed particle hydrodynamics simulations of the collapse of clumps formed through gravitational instability in the outer part of a protoplanetary disc. The initial conditions are taken directly from a global disc simulation, and a realistic equation of state is used to follow the clumps as they contract over several orders of magnitude in density, approaching the molecular hydrogen dissociation stage. The effects of clump rotation, asymmetries and radiative cooling are studied. Rotation provides support against fast collapse, but non‐axisymmetric modes develop and efficiently transport angular momentum outwards, forming a circumplanetary disc. This transport helps the clump reach the dynamical collapse phase, resulting from molecular hydrogen dissociation, on a thousand‐year time‐scale, which is smaller than time‐scales predicted by some previous spherical 1D collapse models. Extrapolation to the threshold of the runaway hydrogen dissociation indicates that the collapse time‐scales can be shorter than inward migration time‐scales, suggesting that clumps could survive tidal disruption and deliver a protogas giant to distances of even a few au from the central star.

Although it is fairly established that Gravitational Instability (GI) should occur in the early phases of the evolution of a protoplanetary disk, the fate of the clumps resulting from disk fragmentation and their role in planet formation is still unclear.In the present study we investigate semi-analytically their evolution following the contraction of a synthetic population of clumps with varied initial structure and orbits coupled with the surrounding disk and the central star. Our model is based on recently published state-of-the-art 3D collapse simulations of clumps with varied thermodynamics. Various evolutionary mechanisms are taken into account, and their effect is explored both individually and in combination with others: migration and tidal disruption, mass accretion, gap opening and disk viscosity. It is found that, in general, at least 50% of the initial clumps survive tides, leaving behind potential gas giant progenitors after ∼ 10 5 yr of evolution in the disk. The rest might be either disrupted or produce super-Earths and other low mass planets provided that a solid core can be assembled on a sufficiently short timescale, a possibility that we do not address in this paper. Extrapolating to million year timescales, all our surviving protoplanets would lead to close-in gas giants. This outcome might in part reflect the limitations of the migration model adopted, and is reminiscent of the analogous result found in core-accretion models in absence of fine-tuning of the migration rate. Yet it suggests that a significant fraction of the clumps formed by gravitational instability could be the precursors of Hot Jupiters.

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We perform coagulation & fragmentation simulations to understand grain growth in T Tauri & brown dwarf discs. We present a physically-motivated approach using a probability distribution function for the collision velocities and separating the deterministic & stochastic velocities. We find growth to larger sizes compared to other models. Furthermore, if brown dwarf discs are scaled-down versions of T Tauri discs (in terms of stellar & disc mass, and disc radius), growth at the same location with respect to the outer edge occurs to similar sizes in both discs.