Revised Description of Dust Diffusion and a New Instability Creating Multiple Rings in Protoplanetary Disks

Abstract

Abstract Various instabilities have been proposed as a promising mechanism for accumulating dust. Moreover, some of them are expected to lead to multiple-ring structure formation and planetesimal formation in protoplanetary disks. In a turbulent gaseous disk, the growth of the instabilities and the dust accumulation are quenched by the turbulent diffusion of dust grains. The diffusion process has often been modeled by a diffusion term in the continuity equation for the dust density. The dust diffusion model, however, does not guarantee conservation of angular momentum in a disk. In this study, we first formulate equations that describe dust diffusion and also conserve the total angular momentum of a disk. Second, we perform a linear perturbation analysis on the secular gravitational instability (GI) using the equations. The results show that the secular GI is a monotonically growing mode, contrary to the result of previous analyses that found it overstable. We find that the overstability is caused by the nonconservation of the angular momentum. Third, we find a new axisymmetric instability due to the combination of dust–gas friction and turbulent gas viscosity, which we refer to as two-component viscous gravitational instability (TVGI). The most unstable wavelength of TVGI is comparable to or smaller than the gas scale height. TVGI accumulates dust grains efficiently, which indicates that TVGI is a promising mechanism for the formation of multiple-ring-like structures and planetesimals. Finally, we examine the validity of the ring formation via the secular GI and TVGI in the HL Tau disk and find both instabilities can create multiple rings whose width is about 10 au at orbital radii larger than 50 au.