The dynamics of particle disks III. Dense and spinning particle disks
Abstract
Thermal steady states of differentially rotating axisymmetric disks composed of identical hardsphere particles which have both spin and translational degrees of freedom are investigated when there are substantial effects due to the finite size of disk particles: nonlocal collisions and finite filling factors. In order to take these effects into account, a kinetic theory of dense gases with Enskog's collision term is employed. Major results are: (i) When the finite particle size effects are included, a thermal steady state becomes possible at any point in the (τ, ∊_{n}, ∊_{t}) space lying below the thermal balance surface obtained by neglecting these effects. (ii) At finite optical depths the nonlocal collision effect tends to vanish as the filling factor FF decreases. However, if the optical depth is low, the effect can remain substantial even at low filling factors. (iii) A nonGaussian vertical density profile has been determined by solving the momentum equation. Unlike the particle systems in thermodynamic equilibrium which undergo a phase transition into the zeroshear phase above FF ∼ 0.50, the particle disks under Keplerian shear develop a peculiar layered structure at high filling factors. (iv) It is necessary to introduce the finite particle size effects once the particle spin is taken into consideration. Then the mean spin is found to have the same sense as the mean orbital angular velocity and about 30% of its magnitude at all optical depths regardless of the choice of other model parameters. (v) The thermal balance surface for spinning particle disks determined in Araki (1988) must be shifted when the finite particle size effects are included. (vi) Addition of the overall selfgravity also tends to shift the stability boundary upward. (vii) Viscous instability is not present in any models considered. The present numerical analysis will serve to better understand the structure and stability of the low as well as moderately high optical depth regions in planetary rings where the finite particle size effects are not negligible, including Saturn's B ring.
 Publication:

Icarus
 Pub Date:
 March 1991
 DOI:
 10.1016/00191035(91)900766
 Bibcode:
 1991Icar...90..139A
 Keywords:

 Inelastic Collisions;
 Kinetic Theory;
 Particle Collisions;
 Planetary Rings;
 Rotating Environments;
 Degrees Of Freedom;
 Particle Size Distribution;
 Planetary Structure;
 Vertical Distribution;
 PLANETS;
 PARTICLES;
 DYNAMICS;
 DENSITY;
 SPIN;
 THERMAL PROPERTIES;
 SIZE;
 COLLISIONS;
 THEORETICAL STUDIES;
 KINETICS;
 OPTICAL PROPERTIES;
 DEPTH;
 NUMERICAL METHODS;
 STRUCTURE;
 STABILITY;
 RINGS;
 PARAMETERS;
 VELOCITY;
 CALCULATIONS;
 GRAVITY EFFECTS;
 VISCOSITY;
 MODELS;
 MOMENTUM;
 ELASTICITY;
 Lunar and Planetary Exploration; Planets