Rotation Rates of Particles in Saturn's Rings

Abstract

Rotational states of particles in Saturn's rings are not directly observable but have been inferred from spacecraft and ground-based observations of their thermal emission. A temperature contrast between night- and daysides of particles in Saturn's C ring during crossing of the planetary shadow has been detected and interpreted as indicating the particles' having spin rates comparable to or less than their orbital frequency. Previous numerical simulations showed such slow rotation when the particles' size distribution was not taken into account. Faster rotation of smaller particles has been suggested, but rotation of ring particles with a broad size distribution has been poorly understood. Here we derive an evolution equation for the rotational energy of ring particles with an arbitrary size distribution and show the results of calculations of rotation rates of particles with a broad size distribution, from centimeters to 10 m. Numerical results show that 10 cm-sized or smaller particles would spin several tens to hundreds of times in one orbital period, while large ones spin slowly. The spin axes of slowly rotating large particles have a tendency to be nearly aligned in the direction normal to the ring plane, while rapidly rotating small particles have random spin orientations. In optically thin rings such as Saturn's C ring, small particles with a spin axis pointing nearly toward the Sun are likely responsible for the observed temperature contrast, as recently pointed out by Morishima & Salo. Rapidly rotating small particles have larger orbital inclinations than slowly rotating large particles; thus, ring particles' rotational states have vertical heterogeneity.