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One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings that cause S-shaped density structures in their close vicinity, called propellers. Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn's A ring that denote a further development of the original model. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. Finally, this mean field approach allows us to simulate the pattern of the giant propeller Blériot, which is too large to be modeled by direct N-body simulations. Our results are compared to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS), which intersect the propeller Blériot. Best fits to the UVIS optical depth profiles are achieved for a Hill radius of 590 m, which implies a moonlet diameter of about 860 m. Furthermore, the model favors a kinematic shear viscosity of the surrounding ring material of ν0 = 340 cm2 s−1, a dispersion velocity in the range of 0.3 cm s−1 < c0 < 1.5 cm s−1, and a fairly high bulk viscosity 7 < ξ0/ν0 < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.
Saturn’s main rings are composed of >95% water ice, and the nature of the remaining few percent has remained unclear. The Cassini spacecraft’s traversals between Saturn and its innermost D ring allowed its cosmic dust analyzer (CDA) to collect material released from the main rings and to characterize the ring material infall into Saturn. We report the direct in situ detection of material from Saturn’s dense rings by the CDA impact mass spectrometer. Most detected grains are a few tens of nanometers in size and dynamically associated with the previously inferred “ring rain.” Silicate and water-ice grains were identified, in proportions that vary with latitude. Silicate grains constitute up to 30% of infalling grains, a higher percentage than the bulk silicate content of the rings.
Saturn's rings host two known moons, Pan and Daphnis, which are massive enough to clear circumferential gaps in the ring around their orbits. Both moons create wake patterns at the gap edges by gravitational deflection of the ring material (Cuzzi, J.N., Scargle, J.D. [1985]. Astrophys. J. 292, 276-290; Showalter, MR., Cuzzi, J.N., Marouf, E.A., Esposito, LW. [1986]. Icarus 66, 297-323). New Cassini observations revealed that these wavy edges deviate from the sinusoidal waveform, which one would expect from a theory that assumes a circular orbit of the perturbing moon and neglects particle interactions. Resonant perturbations of the edges by moons outside the ring system, as well as an eccentric orbit of the embedded moon, may partly explain this behavior (Porco, CC., and 34 colleagues [2005]. Science 307, 1226-1236; Tiscareno, M.S., Burns, J.A., Hedman, MM., Spitale, J.N., Porco, CC., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, CC., Tiscareno, M.S., Burns, J.A., Dones, L [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, CC., Tiscareno, M.S. [2009]. Astron. J. 138, 272-286). Here we present an extended non-collisional streamline model which accounts for both effects. We describe the resulting variations of the density structure and the modification of the nonlinearity parameter q. Furthermore, an estimate is given for the applicability of the model. We use the streamwire model introduced by Stewart (Stewart, G.R. [1991]. Icarus 94, 436-450) to plot the perturbed ring density at the gap edges. We apply our model to the Keeler gap edges undulated by Daphnis and to a faint ringlet in the Encke gap close to the orbit of Pan. The modulations of the latter ringlet, induced by the perturbations of Pan (Burns, J.A., Hedman, M.M., Tiscareno, M.S., Nicholson, P.D., Streetman, B.J., Colwell, J.E., Showalter, M.R., Murray, C.D., Cuzzi, J.N., Porco, CC., and the Cassini ISS team [2005]. Bull. Am. Astron. Soc. 37, 766), can be well described by our analytical model. Our analysis yields a Hill radius of Pan of 17.5 km, which is 9% smaller than the value presented by Porco (Porco, CC., and 34 colleagues [2005]. Science 307, 1226- 1236), but fits well to the radial semi-axis of Pan of 17.4 km. This supports the idea that Pan has filled its Hill sphere with accreted material (Porco, C.C., Thomas, P.C., Weiss, J.W., Richardson, D.C. [2007]. Science 318, 1602-1607). A numerical solution of a streamline is used to estimate the parameters of the Daphnis-Keeler gap system, since the close proximity of the gap edge to the moon induces strong perturbations, not allowing an application of the analytic streamline model. We obtain a Hill radius of 5.1 km for Daphnis, an inner edge variation of 8 km, and an eccentricity for Daphnis of 1.5 x 10(-5). The latter two quantities deviate by a factor of two from values gained by direct observations (Jacobson, R.A., Spitale, J., Porco, C.C., Beurle, K., Cooper, N.J., Evans, M.W., Murray, C.D. [2008]. Astron. J. 135, 261-263; Tiscareno, M.S., Burns, J.A., Hedman, M.M., Spitale, J.N., Porco, C.C., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767), which might be attributed to the neglect of particle interactions and vertical motion in our model.
One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. model using a granular flow model to define the shear and bulk viscosities, ν and ζ, and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings. Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps