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

¹ Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180, Vienna, Austria
e-mail: eduard.vorobiev@univie.ac.at
² Research Institute of Physics, Southern Federal University, Rostov-on-Don 344090, Russia
³ School of Physics, University of Leicester, Leicester LE1 7RH, UK
⁴ Centre for Star and Planet Formation, Globe Institute, University of Copenhagen, Øster Voldgade 5 – 7, 1350 Copenhagen, Denmark
⁵ Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden
⁶ Lavrentyev Institute of Hydrodynamics SB RAS, 15 Lavrentyev Ave., 630090 Novosibirsk, Russia
⁷ Mechanics and Mathematics Department, Novosibirsk State University, 2 Pirogov str., 630090 Novosibirsk, Russia

Received: 14 July 2022
Accepted: 28 November 2022

Abstract

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 α parameter, while the effects of gravitational instability on dust growth were accounted for by calculating the effective parameter α_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 α = 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 α = 10⁻³ model and, especially, the α = 10⁻⁴ model are dominated by gravitational instability. The effective parameter α + α_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.