Measuring the amplitudes of bending waves in Saturn’s rings

A bending wave (henceforth BW) in a planetary ring is a tightly-wrapped spiral waveform that involves periodic vertical displacement of the ring material as the wave propagates radially. Like density waves, BWs are driven at orbital resonances with external satellites or internal planetary oscillations. The most prominent BWs in Saturn’s rings are driven by the satellites Mimas and Titan, whose orbits are inclined wrt the planet’s equatorial plane. Although first studied in Voyager imaging [Shu et al. (1983) Icarus 53:185; Lissauer (1985) Icarus 62:433] and radio occultation data [Gresh et al. (1986) Icarus 68:481; Rosen & Lissauer (1988) Science 241:690], their vertical amplitudes remain poorly known.

Based on the theoretical formalism developed by Gresh et al. (and used more recently by Hedman et al. (2015) [Icarus 248:137] to model impact-induced vertical corrugations in the D ring) we have developed a simple analytical model that enables the apparent optical depth profile in a BW to be converted into estimates of the local surface slope, which can then be integrated to determine the wave’s radial profile of vertical displacement. Previous studies of BWs employed numerical ray-tracing or light-scattering models based on theoretical models of linear waves. Our approach allows us to avoid the assumption of linearity. Our objective is to analyze a representative sample of the several hundred profiles of BWs in Saturn’s rings that are recorded in stellar and radio occultation data collected by Cassini’s Visual & Infrared Mapping Spectrometer (VIMS) and Radio Science Subsystem (RSS), exploiting their wide range of observing geometries to resolve model ambiguities.

Our work to date has concentrated on the two strongest (and nonlinear) waves: the Mimas 5:3 BW in the outer A ring, and the Titan nodal BW in the inner C ring (also known as the -1:0 wave). Preliminary results indicate that the Titan wave is characterized by local slopes of up to 45^o and corresponding vertical amplitudes A_V ~ 500-1500 m at distances of 15-45 km from the resonance, consistent with previous estimates [Nicholson & Hedman (2016) Icarus 279:78]. The Mimas 5:3 wave is less extreme, with maximum slopes of ~10^o in the VIMS data and an A_V that peaks at ~400 m. Variations in the background optical depth of the rings across this wave as a function of opening angle suggest that self-gravity wakes may also be playing an important role here [Sega (2021) BAAS 53:406.05].