Moonlet induced wakes in planetary rings: Analytical model including eccentric orbits of moon and ring particles

Abstract

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 and Scargle (1985), Showalter et al. (1986)). 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. (2005)), which might be attributed to the neglect of particle interactions and vertical motion in our model.

Sharp Gap Edges in Dense Planetary Rings: An Axisymmetric Diffusion Model

“…and A 1 = 6.7187 Seiß et al 2010). Ω is the Kepler frequency and M s and M p denote the masses of the moon and the planet, respectively.…”

“…The ring moons Pan and Daphnis were found in the Encke and Keeler division, where their gravity is strong enough to sweep free a complete gap (Showalter 1991;Porco 2005). Stewart (1991) and Seiß et al (2010) theoretically analyze collisionless edge dynamics and show that a moonlet can open a gap by collisionless gravitational interaction alone through clearing of the chaotic zone in the moonlet vicinity (Longaretti 2017). In Grätz et al (2018) we derived an axisymmetric diffusion model, that describes the radial density profile of a gap an embedded moon creates.…”

“…Stewart (1991) introduced the streamwire model, that was later used inSeiß et al (2010) to avoid the singularity when the streamlines cross or merge.…”

The radial density profile of Saturn's A ring

“…with A 1 = 6.7187 (see Seiß et al 2010). Equations ( 22) and ( 23) are used to describe the drift of the ring material caused by the perturbing moons in Equation (5).…”

Planetary Ring Dynamics -- The Streamline Formalism -- 2. Theory of Narrow Rings and Sharp Edges

“…No amount of phase synchronization can suppress the velocity dispersion and ensuing collisional spreading continuously driven by the ring particles' mutual gravitational stirring if nothing else. Some papers have also been devoted to the theoretical analysis of a collisionless edge dynamics, e.g., Stewart (1991) and Seiß et al (2010). A moonlet can open a gap by collisionless gravitational interaction alone, but through a different process as the one studied here, i.e., through clearing of the chaotic zone in the moonlet vicinity (Wisdom, 1980;Duncan et al, 1989); the resulting gap width scales as (M m /M p ) 2/7 according to the famous result of Wisdom (1980) (M m is the moonlet mass).…”