Various instabilities have been proposed as a promising mechanism to accumulate dust. Moreover, some of them are expected to lead to the multiple-ring structure formation and the planetesimal formation in protoplanetary disks. In a turbulent gaseous disk, the growth of the instabilities and the dust accumulation are quenched by turbulent diffusion of dust grains. The diffusion process has been often modeled by a diffusion term in the continuity equation for the dust density. The dust diffusion model, however, does not guarantee the angular momentum conservation in a disk. In this study, we first formulate equations that describe the dust diffusion and also conserve the total angular momentum of a disk. Second, we perform the 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 non-conservation of the angular momentum. Third, we find a new axisymmetric instability due to the combination of the dust-gas friction and the 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.

We present a new instability driven by a combination of coagulation and radial drift of dust particles. We refer to this instability as “coagulation instability” and regard it as a promising mechanism to concentrate dust particles and assist planetesimal formation in the very early stages of disk evolution. Because of dust-density dependence of collisional coagulation efficiency, dust particles efficiently (inefficiently) grow in a region of positive (negative) dust density perturbations, leading to a small radial variation of dust sizes and as a result radial velocity perturbations. The resultant velocity perturbations lead to dust concentration and amplify dust density perturbations. This positive feedback makes a disk unstable. The growth timescale of coagulation instability is a few tens of orbital periods even when dust-to-gas mass ratio is on the order of 10−3. In a protoplanetary disk, radial drift and coagulation of dust particles tend to result in dust depletion. The present instability locally concentrates dust particles even in such a dust-depleted region. The resulting concentration provides preferable sites for dust–gas instabilities to develop, which leads to further concentration. Dust diffusion and aerodynamical feedback tend to stabilize short-wavelength modes, but do not completely suppress the growth of coagulation instability. Therefore, coagulation instability is expected to play an important role in setting up the next stage for other instabilities, such as streaming instability or secular gravitational instability, to further develop toward planetesimal formation.

Secular gravitational instability (GI) is one promising mechanism for creating annular substructures and planetesimals in protoplanetary disks. We perform numerical simulations of secular GI in a radially extended disk with inwardly drifting dust grains. The results show that, even in the presence of dust diffusion, dust rings form via secular GI while the dust grains are moving inward, and the dust surface density increases by a factor of 10. Once secular GI develops into a nonlinear regime, the total mass of the resultant rings can be a significant fraction of the dust disk mass. In this way, a large amount of drifting dust grains can be collected in the dusty rings and stored for planetesimal formation. In contrast to the emergence of remarkable dust substructures, secular GI does not create significant gas substructures. This result indicates that observations of a gas density profile near the disk midplane enable us to distinguish the mechanisms for creating the annular substructures in the observed disks. The resultant rings start decaying once they enter the inner region stable to secular GI. Because the ring-gap contrast smoothly decreases, it seems possible that the rings are observed even in the stable region. We also discuss the likely outcome of the nonlinear growth and indicate the possibility that a significantly developed region of secular GI may appear as a gap-like substructure in dust continuum emission as dust growth into larger solid bodies and planetesimal formation reduce the total emissivity.