Why dust pressure matters in debris discs

There is a common assumption in the particulate disc community that the pressure in particulate discs is essentially zero and that the disc streamlines follow Keplerian orbits, in the absence of self-gravity or external perturbations. It is also often assumed that the fluid description of particulate discs is not valid in the presence of crossing orbits (e.g. from nonzero free eccentricities). These stem from the misconception that fluid pressure arises due to the (typically rare) collisions between particles and that the velocity of particles in fluids are single-valued in space. In reality, pressure is a statistical property of the particle distribution function which arises precisely because there is a distribution of velocities at a given position. In this letter we demonstrate, with simple examples, that pressure in particulate discs is non-zero and is related to the inclination and free eccentricity distributions of the constituent particles in the discs. This means many common models of debris discs implicitly assume a nonzero, and potentially quite significant, dust pressure. We shall also demonstrate that the bulk motion of the dust is not the same as the particle motion and that the presence of pressure gradients can lead to strong departures from Keplerian motion.