Normal modes at the outer edge of Saturn’s B ring

We have re-determined the time-variable shape of the outer edge of Saturn’s B ring using the complete set of Cassini radio and stellar occultation data obtained between mid-2005 and late 2017, considerably expanding the range and number of individual ring edge measurements used in previous analyses (Spitale & Porco 2010; Nicholson et al 2014). During this period, the dominant m=2 pattern driven by the Mimas 2:1 inner Lindblad resonance (ILR) completed just over two rotations relative to Mimas, with a circulation period of 5.36 yr, while its radial amplitude varied from a minimum of ~4 km to a maximum of ~71 km. We also confirm the existence of four additional perturbations with azimuthal wavenumbers m=1, 3, 4 and 5 and mean amplitudes ranging from 5 to 24 km, which we interpret as normal or edge modes, possibly triggered by viscous overstabilities in the dense B ring (Borderies et al 1985; Longaretti 2018). Fits of a numerical multi-streamline model to the observed pattern speeds and amplitudes of the edge modes suggest a surface mass density in the outer 30 km of the B ring of ~200 g/cm², considerably greater than the 50-70 g/cm² inferred from density and bending waves in most other regions of this ring (Hedman & Nicholson 2016). However, mode interactions may reduce this estimate by a factor of ~2. Surprisingly, all four of these modes exhibit significant librations in their amplitudes and phases, with periods between 2.3 and 8.6 yr and amplitudes of 1.6 to 7.4 km. The origin of these librations is unknown, but their frequencies do not match those expected for edge modes with varying numbers of radial nodes. They may instead reflect nonlinear, non-resonant coupling between normal modes with different values of m, leading to long-term aperiodic variations in the mode amplitudes, or periodic oscillations in the amplitudes of individual normal modes.