On the pressure of collisionless particle fluids. The case of solids settling in disks

TL;DR

This paper rigorously evaluates when dust and particle fluids in disks can be considered pressureless, revealing that for Stokes numbers above 1/2, pressure effects are significant, impacting models of disk dynamics.

Contribution

It provides an exact calculation of particle fluid pressure in disk settling, challenging the common assumption of pressureless dust for Stokes numbers greater than 1/2.

Findings

Pressureless assumption fails for Stokes number > 1/2

Pressure becomes significant in particle settling in disks

Results likely extend to turbulent disk flows

Abstract

Aims. Collections of dust, grains, and planetesimals are often treated as a pressureless fluid. We study the validity of neglecting the pressure of such a fluid by computing it exactly for the case of particles settling in a disk. Methods. We solve a modified collisionless Boltzmann equation for the particles and compute the corresponding moments of the phase space distribution: density, momentum, and pressure. Results. We find that whenever the Stokes number, defined as the ratio of the gas drag timescale to the orbital timescale, is more than 1/2, the particle fluid cannot be considered as pressureless. While we show it only in the simple case of particles settling in a laminar disk, this property is likely to remain true for most flows, including turbulent flows.