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[19.01] Simulations of Dense Planetary Rings: Rotating Self-gravitating particles with size distribution

R. Morishima, H. Salo (University of Oulu)

Spin state of ring particles is investigated using N-body simulations. Through mutual collisions, some of random kinetic energy is transferred to rotation. For optically thin disks, we confirm that the equilibrium ratio of the rotational energy to the kinetic energy is consistent with the analytic prediction E_rot/E_kin = 2(1-e_t)/(14-5(1-e_t)), where e_t represents the tangential restitution coefficient. For optically thick disks, gravitational wakes add large systematic motions to random velocities whereas spin velocities are less enhanced, formally leading to reduced E_rot/E_kin. However, the local random velocities measured by using only the nearest neighbours remain small and the locally measured E_rot/E_kin is in fact larger than the above analytical prediction. In such closely packed systems, spin velocities are enhanced by multiple collisions occurring in same particle pairs with very small time intervals (or one particle hits two other particles alternately). Most importantly, we find that E_rot/E_kin depends quite weakly on particle size for a size distribution case.

Particle spin frequency is one of the important factors determining the temperature difference between lit and unlit faces of Saturn rings, which will be systematically monitored by Cassini space craft. Our results suggest that spin frequencies of largest particles are comparable to the orbital frequency. Since E_rot/E_kin is practically independent of particle radius r, and since the random velocities of the smallest particles are only a few times larger than those of the largest particles, the typical spin frequency is proportional to 1/r. Thus, as long as disk particles possess an extended size distribution, the effective spin frequency (average weighted with particle cross section) is much larger than the orbital frequency. This looks contradictory to the notion of ``slow rotation'' (spin frequency is comparable to the orbital frequency), suggested by previous analyses of thermal infrared observations.

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Bulletin of the American Astronomical Society, 36 #4
© 2004. The American Astronomical Soceity.