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Dust in the arcs of Methone and Anthe

Methone and Anthe are two tiny moons (with diameter $<3$ km) in the inner part of Saturn's E ring. Both moons are embedded in an arc of dust particles. To understand the amount of micron-sized dust and their spatial distribution in these arcs, we model the source, dynamical evolution, and sinks of these dust in the arc. We assume hypervelocity impacts of micrometeoroids on the moons as source of these dust (Hedman et al., 2009), the so called impact-ejecta process (Krivov et al., 2003; Spahn et al., 2006). After ejecting and escaping from the moons, these micron-sized particles are subject to several perturbing forces, including gravitational perturbation from Mimas, oblateness of Saturn, Lorentz force, solar radiation pressure, and plasma drag. Particles can be either confined in the arcs due to corotational resonance with Mimas, as their source moons (Spitale et al., 2006; Cooper et al., 2008; Hedman et al., 2009), or pushed outward by plasma drag. Particle sinks are recollisions with the source moon, collision with other moons, or migrate out of the radial zone of interest. In addition to that, the upper limit of the particle lifetimes are controlled by plasma sputtering, which decreases the particle size in a rate of order 1$μ$m radius every 100 years (Johnson et al., 2008). Our simulation results show that ejecta from both moons can form the arcs of maximal optical depths $τ$ in the order of $10^{-8} - 10^{-6}$, although the absolute amount of dust have uncertainties. We also find out the longitudinal extension of the arcs in our simulation are consistent with observation and the theory. Smaller particles are more likely to escape the arc because of the stronger influence of plasma drag. On the other hand, large particles can stay in arcs for longer time and therefore are more likely to collide with the source moon.