The dynamics of self-gravity wakes in the Mimas 5:3 bending wave: modifying the linear theory

Abstract

The satellite Mimas launches a bending wave -- a warping of the rings that propagates radially through self-gravity -- at the 5:3 inner vertical resonance with Saturn's rings. We present a modification of the linear bending wave theory which includes the effects of satellite self-gravity wakes on the particles in the wave. We show that, when treated as rigid, these wakes generate an extra layer of particles whose number density is proportional to the magnitude of the slope of the warped ring. Using a ray-tracing code we compare our predictions with those of linear bending wave theory and with 60 stellar occultations observed by the Cassini Ultraviolet Imaging Spectrograph (UVIS) and find that the extra layer of particles of our perturbed bending wave model has a considerable explanatory power for the UVIS dataset. Our best model explains the most discrepant and surprising features of the Mimas 5:3 bending wave; the enhancement of the signal for the cases of occultations with high ring opening angle and the bigger-than-expected viscosity, $\nu = 576 \, \mathrm{cm^2/s}$, which is more than double the viscosity computed from density waves. This shows that self-gravity wakes can be effective at transporting angular momentum in a vertically perturbed disk. Relative to neighboring density waves, we find a lower-than-expected value for the surface mass density, $\sigma = 36.7 \, \mathrm{g/cm^2}$, which suggests that the enhanced viscous interactions may be transporting material into the surrounding regions.