Normal modes and their librations at the outer edge of Saturn's B Ring, as observed in Cassini stellar and radio occultation data

• Published in: Icarus (New York, N.Y. 1962) Vol. 405
• Main Authors: French, Richard G, Nicholson, Philip D, Mcghee-French, Colleen A, Longaretti, Pierre-Yves, Hedman, Matthew M, Colwell, Joshua, Marouf, Essam A, Rappaport, Nicole, Flury, Sophia, Fong, Jolene, Maguire, Ryan, Steranka, Glen
• Format: Journal Article
• Language: English
• Published: Elsevier 15.11.2023
• Subjects: Astrophysics; Earth and Planetary Astrophysics; Sciences of the Universe
• ISSN: 0019-1035; 1090-2643
• DOI: 10.1016/j.icarus.2023.115678

We redetermine 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 the End-of-Mission in late 2017, considerably expanding the range and number of individual ring edge measurements used in our previous analysis (Nicholson, P. D. et al. [2014] Icarus 227,152-175). During this 12-year interval, the dominant m = 2 pattern driven by the Mimas 2:1 inner Lindblad resonance completed just over two slow prograde circulations relative to Mimas, at an angular frequency of Ω L = 0.1838 ± 0.0006 • d −1 (corresponding to a period of 5.362 ± 0.017 yr). At the same time, the radial amplitude of this pattern varied from a minimum of ∼ 4 km to a maximum of ∼ 71 km, due to beating between the forced and free m = 2 components originally identified by Spitale, J. and Porco, C. [2010] (Astron. J. 140, 1747-1757). This circulation pattern has remained essentially unchanged when compared with previous studies based on Cassini imaging and occultation data sets acquired prior to 2012 (Spitale and Porco 2010; Nicholson et al. 2014a). On the other hand, we find strong evidence for significant time variability in the four additional perturbations seen at the B ring edge with azimuthal wavenumbers m = 1, 3, 4 and 5. These nonresonant perturbations have previously been interpreted as normal (or edge) modes that exist in relatively narrow cavities adjacent to the ring edge, perhaps triggered by viscous overstabilities (see reviews by Longaretti (2018) and Nicholson et al. (2018)). The m = 1 perturbation, which rotates at the local apsidal precession rate, decreased in radial amplitude from ∼25 km in 2005 to ∼20 km in 2008/09, but subsequently increased to ∼30 km in 2013, before falling back to ∼17 km in 2016/17. These variations can be modeled as a libration in the eccentricity of the ring’s streamlines involving two independent modes with periods of 8.6 and 5.9 yr and amplitudes of 4.4 and 2.8 km, respectively. Similar variability in the amplitude of the m = 3 perturbation from a minimum of ∼ 6 km to a minimum of ∼ 20 km can be modeled in terms of librations with periods of 19.7 and 7.3 yr and amplitudes of 7.4 and 2.2 km, respectively. Smaller but still significant variations are seen in the amplitudes of the m = 4 and m = 5 modes, with periods of 2.3 – 5.9 yr and amplitudes of 1.6 – 2.8 km. We present libration models for all four non-resonant perturbations, fitted to the Cassini occultation data, but the physical interpretation of these models is uncertain. Theoretical modeling by ? suggests that the observed amplitude variations could represent (1) interference between multiple normal modes with the same value of the azimuthal wavenumber m but different numbers of radial nodes nr, (2) a periodic oscillation in the amplitude of a single normal mode with nr = 0 (known as the ‘nodeless mode’), or (3) nonlinear coupling between normal modes with different values of m, leading to long-term aperiodic variatiuions in the mode amplitudes. On the assumption that model (1) is correct, we use the observed oscillation and libration frequencies of the modes to estimate the surface mass density in the outer ∼ 1200 km of the B ring, finding values ranging from 50 g cm^−2 to ∼ 250 g cm^−2.