# Revised description of dust diffusion and a new instability creating multiple rings in protoplanetary disks

**Authors:** Ryosuke T. Tominaga, Sanemichi Z. Takahashi, Shu-ichiro Inutsuka  
**arXiv:** [1905.12899](https://arxiv.org/abs/1905.12899)  
**Date:** 2019-05-30  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1905.12899v1/

## Key points

- Protoplanetary disks contain instabilities that can lead to the formation of multiple-ring structures and planetesimals
- Turbulent diffusion of dust grains hinders these instabilities and dust accumulation in a turbulent gaseous disk
- Equations were formulated to describe dust diffusion while conserving total angular momentum in a disk
- Linear perturbation analysis on secular gravitational instability (GI) using these equations found it to be a monotonically growing mode, contrary to previous analyses that found it overstable
- A new axisymmetric instability called two-component viscous gravitational instability (TVGI) was discovered, caused by the combination of dust-gas friction and turbulent gas viscosity, which efficiently accumulates dust grains and is promising for forming multiple-ring-like structures and planetesimals
- TVGI's most unstable wavelength is comparable to or smaller than the gas scale height
- Both secular GI and TVGI were found capable of creating multiple rings with widths around 10 au at orbital radii larger than 50 au in HL Tau disk
- This refined understanding of dust diffusion and instabilities in protoplanetary disks could provide insights into how planets form around young stars.

## Summary

Protoplanetary disks are known to contain various instabilities that can accumulate dust and lead to the formation of multiple-ring structures and planetesimals. However, in a turbulent gaseous disk, these instabilities and dust accumulation are hindered by the turbulent diffusion of dust grains. To model this diffusion process, a diffusion term is often added to the continuity equation for the dust density. In a recent study led by Ryosuke T. Tominaga from Kyoto University, equations were formulated that describe dust diffusion while conserving total angular momentum in a disk. The team then performed linear perturbation analysis on secular gravitational instability (GI) using these equations and found that it is a monotonically growing mode, contrary to previous analyses that found it overstable. The overstability was attributed to non-conservation of angular momentum. The team also discovered a new axisymmetric instability called two-component viscous gravitational instability (TVGI), caused by the combination of dust-gas friction and turbulent gas viscosity. TVGI accumulates dust grains efficiently, making it a promising mechanism for forming multiple-ring-like structures and planetesimals. The most unstable wavelength of TVGI is comparable to or smaller than the gas scale height. Finally, the validity of ring formation via secular GI and TVGI was examined in HL Tau disk. Both instabilities were found capable of creating multiple rings with widths around 10 au at orbital radii larger than 50 au. This refined understanding of dust diffusion and instabilities in protoplanetary disks could provide insights into how planets form around young stars.