Growing and trapping pebbles with fragile collisions of particles in protoplanetary disks

Recent laboratory experiments indicate that destructive collisions of icy dust particles occur with much lower velocities than previously thought. These fragmentation velocities play a crucial role in planet formation because they set the maximum grain size in collisional growth models. When these new velocities are considered from laboratory experiments in dust evolution models, a growth to pebble sizes (typically millimeter- to decimeter-sized particles) in protoplanetary disks is difficult. This may contradict (sub-) millimeter observations and challenge the formation of planetesimals and planets. We investigate the conditions that are required in dust evolution models for growing and trapping pebbles in protoplanetary disks when the fragmentation speed is 1 m s(-1) in the entire disk. In particular, we distinguish the parameters controlling the effects of turbulent velocities (delta (t)), vertical stirring (delta (z)), radial diffusion (delta (r)), and gas viscous evolution (alpha), always assuming that particles cannot diffuse faster (radially or vertically) than the gas (i.e., delta (r,z,t) <= alpha). We compare our models with observations of protoplanetary disks at both the near-infrared and millimeter regimes. To form pebbles and produce effective particle trapping, the parameter that controls the particle turbulent velocities must be small (delta (t) less than or similar to 10(-4)). In these cases, the vertical settling can limit the formation of pebbles, which also prevents particle trapping. Therefore the parameter that sets the vertical settling and stirring of the grains must be delta (z) < 10(-3). Our results suggest that different combinations of the particle and gas diffusion parameters can lead to a large diversity of millimeter fluxes and dust-disk radii. When pebble formation occurs and trapping is efficient, gaps and rings have higher contrast at millimeter emission than in the near-infrared. In the case of inefficient trapping, structures are also formed at the two wavelengths, producing deeper and wider gaps in the near-infrared. Our results highlight the importance of obtaining observational constraints of gas and particle diffusion parameters and the properties of gaps at short and long wavelengths to better understand basic features of protoplanetary disks and the origin of the structures that are observed in these objects.