Hydrodynamic Simulations of Moonlet-induced Propellers in Saturn’s Rings: Application to Blériot

Martin Seiß,Holger Hoffmann,Jürgen Schmidt,Nicole Albers,Miodrag Sremčević,Frank Spahn,Heikki Salo,Michael Seiler

doi:10.3847/1538-3881/aaed44

Abstract

Abstract 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 ν 0 = 340 cm2 s−1, a dispersion velocity in the range of 0.3 cm s−1 < c 0 < 1.5 cm s−1, and a fairly high bulk viscosity 7 < ξ 0/ν 0 < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.

Highlights

Saturn’s dense rings consist of icy particles with sizes of centimeters up to tens of meters
We find excellent agreement between these new hydrodynamic and corresponding N-body simulations
The hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. 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

Summary

Introduction

Saturn’s dense rings consist of icy particles with sizes of centimeters up to tens of meters. Pan and Daphnis are massive enough to open and maintain a circumferential gap around their orbit (Henon 1981; Lissauer et al 1981; Petit & Henon 1988; Spahn & Sponholz 1989; Spahn & Wiebicke 1989) They further cause wavy gap edges and corresponding wakes (Cuzzi & Scargle 1985; Showalter et al 1986; Borderies et al 1989; Spahn et al 1994; Hertzsch et al 1997; Lewis & Stewart 2000; Weiss et al 2009; Seiß et al 2010). Pan maintains a central ringlet on its orbit (Dermott et al 1980; Dermott & Murray 1981; Spahn & Sponholz 1989)

Methods

Results

Conclusion