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