Perturbed particle disks

Abstract

ABSTRACTWe solve the Boltzmann moment equations to determine the disk particle velocity ellipsoid near an isolated satellite resonance. In a coordinate frame which rotates with the pattern speed of the perturbation potential the solutions are stationary functions of the azimuthal angle. From the velocity ellipsoid we obtain the stress tensor due to particle collisions and consequently, the viscous angular momentum flux. We find that in sufficiently perturbed regions there are ranges of azimuthal angle within which the radial component of the angular momentum flux is negative. It is even possible for the angular momentum luminosity, the radial flux integrated over azimuth, to be negative. We also show that the magnitude of the rate of deformation tensor in a perturbed particle disk is bounded from above by Ω(1 + τ2)½, where Ω is the orbital angular velocity and τ Is the optical depth. These results are applied to sharp edges of planetary rings, the decay of density waves, and the damping of differential precession and eccentricity in narrow ringlets.