Gravitational instability of a dust layer composed of porous silicate dust aggregates in a protoplanetary disk

TL;DR

This study investigates the gravitational stability of porous silicate dust layers in protoplanetary disks, considering various physical factors, and identifies conditions under which such layers become gravitationally unstable, aiding planetesimal formation understanding.

Contribution

It provides a detailed analysis of the gravitational instability conditions for porous dust aggregates, incorporating effects of turbulence, gas drag, and collisions, which was not previously explored.

Findings

Dust layer becomes unstable at low turbulence levels (α≲10^{-5} at 1 au).

Higher dust-to-gas ratios promote gravitational instability.

Larger disk mass, dust-to-gas ratio, and monomer size increase instability likelihood.

Abstract

Planetesimal formation is one of the most important unsolved problems in planet formation theory. In particular, rocky planetesimal formation is difficult because silicate dust grains are easily broken when they collide. Recently, it has been proposed that they can grow as porous aggregates when their monomer radius is smaller than $\sim$ 10 nm, which can also avoid the radial drift toward the central star. However, the stability of a layer composed of such porous silicate dust aggregates has not been investigated. Therefore, we investigate the gravitational instability of this dust layer. To evaluate the disk stability, we calculate Toomre's stability parameter $Q$, for which we need to evaluate the equilibrium random velocity of dust aggregates. We calculate the equilibrium random velocity considering gravitational scattering and collisions between dust aggregates, drag by mean flow of gas, stirring by gas turbulence, and gravitational scattering by gas density fluctuation due to turbulence. We derive the condition of the gravitational instability using the disk mass, dust-to-gas ratio, turbulent strength, orbital radius, and dust monomer radius. We find that, for the minimum mass solar nebula model at 1 au, the dust layer becomes gravitationally unstable when the turbulent strength $\alpha\lesssim10^{-5}$. If the dust-to-gas ratio is increased twice, the gravitational instability occurs for $\alpha\lesssim10^{-4}$. We also find that the dust layer is more unstable in disks with larger mass, higher dust-to-gas ratio, and weaker turbulent strength, at larger orbital radius, and with a larger monomer radius.