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

Abstract

One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings which cause S-shaped density structures in their close vicinity, called propellers (Spahn & Sremčević 2000;Tiscareno et al. 2006;Sremčević et al. 2007). Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn's A ring which denote a further development of the original model (Spahn & Sremčević 2000). We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws (Spahn & Sremčević 2000) and the analytical solution for the density in the propeller gaps (Sremčević et al. 2002). 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), that 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 favours a kinematic shear viscosity of the surrounding ring material of ν 0 = 340 cm 2 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.

Hydrodynamic Simulations of Asymmetric Propeller Structures in Saturn's Rings

“…A more detailed overview of the implementation of the integration routine and the used numerical methods is given in Section 3 in Seiß et al (2017). The simulation scheme uses following scaled values:…”

“…Here, we will focus on the asymmetry formation for the giant trans-Encke propellers. For this reason, we will consider a Blériot-sized moonlet with 400 m Hill radius (Hoffmann et al 2016;Seiß et al 2017), allowing us to predict the asymmetry of its propeller. Therefore, we will simulate the moonlet at a radial location close to its observed orbital position and we will adopt the viscosity accordingly (Seiß et al 2017).…”

“…The largest propeller structure is called Blériot and is created by a moonlet of about 400 m in Hill radius (Hoffmann et al 2016;Seiß et al 2017). Its excess motion can be reconstructed by a superposition of three sinusoidal harmonics with periods of 11.1, 3.7 and 2.2 years and amplitudes of 1845, 152 and 58 km with a standard deviation of about 17 km of the remaining residual (Seiler et al 2017;Spahn et al 2018).…”

“…Our hydrodynamic simulation routine bases on the code, developed by Seiß et al (2017). This integration routine will be modified so that the moonlet can librate around its mean orbital position within the simulation grid.…”

The radial density profile of Saturn's A ring

“…Numerical and theoretical studies over the last decades have shown, that bodies embedded in protoplanetary disks E-mail: fgraetz@uni-potsdam.de or planetary rings create a) S-shaped density modulations, dubbed propellers, if their masses are below a certain threshold or b) cause a gap around the entire circumference of the disk if the embedded bodies mass exceeds the threshold (see Spahn & Wiebicke (1989), Spahn & Sremčević (2000); Sremčević et al (2002) for theoretical and Seiß et al (2005); Sremčević et al (2007); Lewis & Stewart (2009); Seiß et al (2019) for numerical studies). The gravitational disturber exerts a torque on nearby disk particles, especially where resonances overlap, pushing them away from their original radial location, thus depleting the disk's density in its vicinity and trying to sweep free a gap.…”