Formation of pebbles in (gravito-)viscous protoplanetary disks with various turbulent strengths

Aims. Dust plays a crucial role in the evolution of protoplanetary disks. We study the dynamics and growth of initially submicron dust particles in self-gravitating young protoplanetary disks with various strengths of turbulent viscosity. We aim to understand the physical conditions that determine the formation and spatial distribution of pebbles when both disk self-gravity and turbulent viscosity are at work.Methods. We performed thin-disk hydrodynamics simulations of self-gravitating protoplanetary disks over an initial time period of 0.5 Myr using the FEOSAD code. Turbulent viscosity was parameterized in terms of the spatially and temporally constant alpha parameter, while the effects of gravitational instability on dust growth were accounted for by calculating the effective parameter alpha(GI). We considered the evolution of the dust component, including the momentum exchange with gas, dust self-gravity, and a simplified model of dust growth.Results. We find that the level of turbulent viscosity strongly affects the spatial distribution and total mass of pebbles in the disk. The alpha = 10(-2) model is viscosity-dominated, pebbles are completely absent, and the dust-to-gas mass ratio deviates from the reference 1:100 value by no more than 30% throughout the extent of the disk. On the contrary, the alpha = 10(-3) model and, especially, the alpha = 10(-4) model are dominated by gravitational instability. The effective parameter alpha + alpha(GI) is now a strongly varying function of radial distance. As a consequence, a bottleneck effect develops in the innermost disk regions, which makes gas and dust accumulate in a ring-like structure. Pebbles are abundant in these models, although their total mass and spatial extent is sensitive to the dust fragmentation velocity and to the strength of gravitoturbulence. The use of the standard dust-to-gas mass conversion is not suitable for estimating the mass of pebbles.Conclusions. Our numerical experiments demonstrate that pebbles can already be abundant in protoplanetary disks at the initial stages of disk evolution. Dust growth models that consider disk self-gravity and ice mantles may be important for studying planet formation via pebble accretion.