Dynamics of self-gravity wakes within a bending wave: the case of the Mimas 5:3 vertical resonance

Elongated aggregates of the order of a Toomre wavelength have been known to exist in the denser rings of Saturn. They occur in the A and B rings at distances from Saturn where the average particles are not big enough to fill their Hill sphere, and they are usually understood in the framework non-axisymmetric disk responses to density irregularities in a Keplerian disk that have a pitch-angle of about 20°. To study their motion under the influence of a bending wave (launched by a vertical resonance with the moon Mimas), we model them as rigid bodies subjected to the influences of tidal forces, both due to Saturn and the vertical gravitational field caused by the bent ring, and collisions. We find that the rigid-body model can predict the observed pitch-angle outside of the bending wave region, together with the shear-rate v. pitch-angle relationship we know from n-body shearbox simulations (Salo et al. Icarus 180:36-50, 2004). Within the bending wave, we find that the rigid-body model predicts collisions that can create the thus-far-unexplained normal optical depth increase in the bending wave region.