Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks

TL;DR

This study investigates how turbulence in protoplanetary disks affects dust particle collisions with planetesimals, revealing that turbulence can significantly increase collision rates especially for smaller dust particles, impacting planet formation theories.

Contribution

The paper provides the first detailed numerical analysis of turbulence effects on dust-planetesimal collision rates, extending previous laminar flow studies to turbulent conditions.

Findings

Turbulence can double the collision rate for small dust particles.

Collision probabilities remain high or increase with turbulence, even for smaller dust sizes.

Derived formulas relate impact probabilities to turbulence intensity, dust, and planetesimal sizes.

Abstract

Planetesimals in gaseous protoplanetary disks may grow by collecting dust particles. Hydrodynamical studies show that small particles generally avoid collisions with the planetesimals because they are entrained by the flow around them. This occurs when $St$, the Stokes number, defined as the ratio of the dust stopping time to the planetesimal crossing time, becomes much smaller than unity. However, these studies have been limited to the laminar case, whereas these disks are believed to be turbulent. We want to estimate the influence of gas turbulence on the dust-planetesimal collision rate and on the impact speeds. We used three-dimensional direct numerical simulations of a fixed sphere (planetesimal) facing a laminar and turbulent flow seeded with small inertial particles (dust) subject to a Stokes drag. A no-slip boundary condition on the planetesimal surface is modeled via a penalty method. We find that turbulence can significantly increase the collision rate of dust particles with planetesimals. For a high turbulence case (when the amplitude of turbulent fluctuations is similar to the headwind velocity), we find that the collision probability remains equal to the geometrical rate or even higher for $St\geq 0.1$, i.e., for dust sizes an order of magnitude smaller than in the laminar case. We derive expressions to calculate impact probabilities as a function of dust and planetesimal size and turbulent intensity.