The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier

Context. The sticking of micron-sized dust particles caused by surface forces within circumstellar disks is the first stage in the production of asteroids and planets. The key components describing this process are the relative velocity between the dust particles in this environment and the complex physics of dust aggregate collisions. Aims. We present the results of a collision model based on laboratory experiments of these aggregates. We investigate the maximum aggregate size and mass that can be reached by coagulation in protoplanetary disks. Methods. We use the results of laboratory experiments to establish the collision model previously published by Guttler et al. The collision model is based on the assumptions that we model the aggregates as spheres with compact and porous phases and that there is a continuous transition between these two. We apply this collision model to the Monte Carlo method developed previously by Zsom & Dullemond and include Brownian motion, radial drift, and turbulence as contributors of relative velocity between dust particles. Results. We model the growth of dust aggregates at 1 AU in the midplane for three different gas densities. We find that the evolution of the dust does not follow the previously assumed growth-fragmentation cycles. Catastrophic fragmentation hardly occurs in the three disk models. Furthermore, we see long-lived, quasi-steady states in the distribution function of the aggregates caused by bouncing. We explore how the mass and the porosity depend on both the turbulence parameter and the critical mass ratio of dust particles. Upon varying the turbulence parameter, the system behaves in a non-linear way, and we find that the critical mass ratio has a strong effect on the particle sizes and masses. Particles reach Stokes numbers of roughly 10(-4) during the simulations. Conclusions. The particle growth is stopped by bouncing rather than fragmentation in these models. The final Stokes number of the aggregates is rather insensitive to the variations in the gas density and the strength of turbulence. The maximum mass of the particles is limited to approximate to 1 g (chondrule-sized particles). Planetesimal formation can proceed by the means of the turbulent concentration of these aerodynamically size-sorted, chondrule-sized particles.