Analysis of bending waves in Saturn’s rings.

Bending waves (henceforth BWs) in a planetary ring are tightly-wrapped spiral waveforms that involve periodic vertical displacements of the ring material as the waves propagate radially. Like their better-known cousins, density waves, BWs are driven at orbital resonances with external satellites or with internal nonradial planetary oscillations. The most prominent BWs in Saturn’s rings are driven by the satellites Mimas and Titan, whose orbits are inclined relative to the planet’s equatorial plane. We have begun a systematic study of these waves, using a simple analytical model to convert the apparent optical depth profile in a wave, as observed in stellar and radio occultation profiles, into estimates of the local surface slope θ. This can then be integrated to determine the wave’s radial profile of vertical displacement z(r) [Koh et al. (2022) BAAS 54:301.07]. Our model is based on previous studies of Voyager occultation data [Gresh et al. (1986) Icarus 68:481] and Cassini imaging observations of vertical corrugations in the D ring [Hedman et al. (2015) Icarus 248:137]. Our work to date has concentrated on the two strongest BWs: the Mimas 5:3 wave in the A ring and the Titan nodal wave in the C ring.

We have analyzed data for the Mimas 5:3 wave from over 80 Cassini stellar (VIMS) occultations, covering a wide range of effective ring opening angles¹ down to B_eff = 13.4^o. As expected, the wave is more prominent at lower values of B_eff, but remains visible up to ~60^o. However, its maximum vertical amplitude appears to decrease from ~450m to ~250m at values of B_eff < 25^o. Data from ~50 Cassini radio science (RSS) occultations allow us to extend our opening angle coverage down to B_eff = 4.5^o, and again we see an apparent decrease in amplitude of the wave at low effective opening angles, and especially for B_eff < 7.5^o. This trend may indicate an unrecognized limitation in our inversion algorithm, a failure in the simple model of a many-particle-thick ring that underlies it, or perhaps an unexpected consequence of the 100m-scale self-gravity wakes that are ubiquitous in the A ring. The latter have recently been invoked to account for several other peculiarities in the Mimas 5:3 BW [Sega & Stewart (2022) BAAS 54:317.02]. Multi-path effects are only likely for B_eff < 10^o.

¹The visibility of a BW is determined by the effective opening angle of the rings B_eff, defined by the expression tan (B_eff) = tan (B) / cos (φ), where B is the inclination of the line of sight to the ring plane and φ is the difference in azimuth between the radial direction and the line of sight, as projected into the ring plane.