Further reverberations of the 1983 impact with Saturn’s C ring

Abstract

A pattern of $\sim$1 km wavelength ripples exhibiting a periodic beating pattern in Saturn’s inner C ring (74,500–77,765 km) was detected in low-inclination Cassini Radio Science Subsystem (RSS) occultation observations made in 2010 (Marouf et al., 2011). Initially interpreted as analogous to the $\sim$30 km wavelength vertical corrugations with $m=1$ discovered in the C and D rings in near-equinox Cassini Imaging Science Subsystem (ISS) images by Hedman et al. (2007, 2011), the shorter wavelength of these features suggested that they had evolved from a pair of impacts several centuries ago. However, important inconsistencies with this model prevented a secure identification of their origin. A comprehensive search has revealed additional detections of this pattern in Cassini RSS, Visual and Infrared Mapping Spectrometer (VIMS) and Ultraviolet Imaging Spectrograph (UVIS) occultations observed between 2008 and 2017 that show a significant decrease in the wavelength of the ripples over time, suggesting a much more recent origin than centuries ago. We identify the conspicuous beat pattern visible in the ripple structure as the interference of $m=0$ and $m=2$ vertical modes of similar amplitudes but slightly different frequencies, evolving over time and winding up at a rate governed by the mean motion of ring particles, rather than by the much slower node rate that is applicable to the $m=1$ corrugations. From empirical fits to the observed time-dependent wavelengths of the two modes and power spectral analysis of individual optical depth profiles, we demonstrate that the short-wavelength vertical corrugations originated from the same event that produced the longer-wavelength $m=1$ periodic structure in the rings. We infer an impact date of UTC 1983 Sep 19.25 ± 5.5 d, taking into account a plausibly small contribution of ring self-gravity to the windup rates of the corrugations. No convincing signatures of counterpart $m=0$ or $m=2$ radial modes, or of vertical modes with $m\ge 3$, are present in the occultation data, and no evidence of ripple structure is detectable beyond an orbital radius of 77,765 km. The measured amplitudes $A_z^0$ and $A_z^2$ of the newly-identified modes are anti-correlated with the ring optical depth. We detect a significant decrease in the amplitudes of both modes between 2008 and 2017. N-body numerical collisional simulations provide constraints on the vertical and radial ring viscosity that are compatible with the observed radial trend of mode amplitudes $A_z^0$ and $A_z^2$ and their variation with time. Assuming an effective particle size $R$=1 m, the inferred coefficient of restitution ${ϵ}_n\sim 0.5$, with corresponding vertical and radial viscosities ν_z = 1.6 ${{\mathrm{cm}}^{2}s}^{-1}$and ν_r = 2.2 ${{\mathrm{cm}}^{2}s}^{-1}$at a radius of 75,500 km. The initial amplitudes of the $m=0$ and $m=2$ vertical modes are estimated to be $\sim$4 to 7 times their observed values in 2017 in this region.