EDP Sciences
Free access
Volume 502, Number 1, July IV 2009
Page(s) 385 - 389
Section Planets and planetary systems
DOI http://dx.doi.org/10.1051/0004-6361/200911865
Published online 15 June 2009
A&A 502, 385-389 (2009)
DOI: 10.1051/0004-6361/200911865

Research Note

On the pressure of collisionless particle fluids

The case of solids settling in disks
F. Hersant1, 2

1  Université de Bordeaux, Laboratoire d'Astrophysique de Bordeaux (LAB), 2 rue de l'Observatoire, BP 89, 33271 Floirac Cedex, France
2  CNRS/INSU - UMR5804, BP 89, 33271 Floirac Cedex, France
    e-mail: Franck.Hersant@obs.u-bordeaux1.fr

Received 17 February 2009 / Accepted 4 May 2009

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.

Key words: hydrodynamics -- methods: analytical -- planetary systems: formation

© ESO 2009