Why Dust Pressure Matters in Debris Discs

There is a common assumption in the particulate disc community that thepressure in particulate discs is essentially zero and that the disc streamlinesfollow Keplerian orbits, in the absence of self-gravity or externalperturbations. It is also often assumed that the fluid description ofparticulate discs is not valid in the presence of crossing orbits (e.g. fromnonzero free eccentricities). These stem from the misconception that fluidpressure arises due to the (typically rare) collisions between particles andthat the velocity of particles in fluids are single-valued in space. Inreality, pressure is a statistical property of the particle distributionfunction which arises precisely because there is a distribution of velocitiesat a given position. In this letter we demonstrate, with simple examples, thatpressure in particulate discs is non-zero and is related to the inclination andfree eccentricity distributions of the constituent particles in the discs. Thismeans many common models of debris discs implicitly assume a nonzero, andpotentially quite significant, dust pressure. We shall also demonstrate thatthe bulk motion of the dust is not the same as the particle motion and that thepresence of pressure gradients can lead to strong departures from Keplerianmotion.