Deciphering the embedded wave in Saturn’s Maxwell ringlet

• Published in: Icarus (New York, N.Y. 1962) N.Y. 1962), 2016-11, Vol.279, p.62-77
• Main Authors: French, Richard G., Nicholson, Philip D., Hedman, Mathew M., Hahn, Joseph M., McGhee-French, Colleen A., Colwell, Joshua E., Marouf, Essam A., Rappaport, Nicole J.
• Format: Article
• Language: English
• Subjects: Amplitudes; Cassini mission; Computer simulation; Density; Dispersion (wave); Eccentricity; Lindblad resonance; Occultations; Planetary rings; Resonances, rings; Saturn (planet); Saturn, interior; Saturn, rings
• ISSN: 0019-1035; 1090-2643
• DOI: 10.1016/j.icarus.2015.08.020

•Saturn’s Maxwell ringlet is home to a density wave.•Cassini occultation observations reveal complex structure of the wave.•The wave is identified as an m=2 outer Lindblad resonance.•The likely origin of the wave is from Saturn internal oscillations.•N-body simulations reproduce complex structure seen in the wave. The eccentric Maxwell ringlet in Saturn’s C ring is home to a prominent wavelike structure that varies strongly and systematically with true anomaly, as revealed by nearly a decade of high-SNR Cassini occultation observations. Using a simple linear “accordion” model to compensate for the compression and expansion of the ringlet and the wave, we derive a mean optical depth profile for the ringlet and a set of rescaled, background-subtracted radial wave profiles. We use wavelet analysis to identify the wave as a 2-armed trailing spiral, consistent with a density wave driven by an m=2 outer Lindblad resonance (OLR), with a pattern speed Ωp=1769.17°d−1 and a corresponding resonance radius ares=87530.0km. Estimates of the surface mass density of the Maxwell ringlet range from a mean value of 110.25em0exg0.25em0excm−2 derived from the self-gravity model to 5−12gcm−2, as inferred from the wave’s phase profile and a theoretical dispersion relation. The corresponding opacity is about 0.120.25em0excm20.25em0exg−1, comparable to several plateaus in the outer C ring (Hedman, M.N., Nicholson, P.D. [2014]. Mont. Not. Roy. Astron. Soc. 444, 1369–1388). A linear density wave model using the derived wave phase profile nicely matches the wave’s amplitude, wavelength, and phase in most of our observations, confirming the accuracy of the pattern speed and demonstrating the wave’s coherence over a period of 8years. However, the linear model fails to reproduce the narrow, spike-like structures that are prominent in the observed optical depth profiles. Using a symplectic N-body streamline-based dynamical code (Hahn, J.M., Spitale, J.N. [2013]. Astrophys. J. 772, 122), we simulate analogs of the Maxwell ringlet, modeled as an eccentric ringlet with an embedded wave driven by a fictitious satellite with an OLR located within the ring. The simulations reproduce many of the features of the actual observations, including strongly asymmetric peaks and troughs in the inward-propagating density wave. We argue that the Maxwell ringlet wave is generated by a sectoral normal-mode oscillation inside Saturn with ℓ=m=2, similar to other planetary internal modes that have been inferr