The ballistic transport instability in Saturn's rings I: formalism and linear theory

Abstract

Planetary rings sustain a continual bombardment of hypervelocity meteoroids that erode the surfaces of ring particles on time scales of 10^5 - 10^7 years. The debris ejected from such impacts re-accretes on to the ring, though often at a slightly different orbital radius from the point of emission. This `ballistic transport' leads to a rearrangement of the disk's mass and angular momentum, and gives rise to a linear instability that generates structure on relatively large scales. It is likely that the 100-km undulations in Saturn's inner B-ring and the plateaus and 1000-km waves in Saturn's C-ring are connected to the nonlinear saturation of the instability. In this paper the physical problem is reformulated so as to apply to a local patch of disk (the shearing sheet). This new streamlined model helps facilitate our physical understanding of the instability, and also makes more tractable the analysis of its nonlinear dynamics. We concentrate on the linear theory in this paper, showing that the instability is restricted to a preferred range of intermediate wavenumbers and optical depths. We subsequently apply these general results to the inner B-ring and the C-ring and find that in both regions the ballistic transport instability should be near marginality, a fact that may have important consequences for its prevalence and nonlinear development. Owing to damping via self-gravity wakes, the instability should not be present in the A-ring. A following paper will explore the instability's nonlinear saturation and how it connects to the observed large-scale structure.

14 pages, 7 figures, MNRAS accepted

References in corpus (3)

• Cassini Imaging of Saturn's Rings II: A Wavelet Technique for Analysis of Density Waves and Other Radial Structure in the Rings
• The linear stability of dilute particulate rings
• Dense planetary rings and the viscous overstability

Cited by in corpus (6)

• Large-scale N-body simulations of the viscous overstability in Saturn's rings
• Constraints on the initial mass, age and lifetime of Saturn's rings from viscous evolutions that include pollution and transport due to micrometeoroid bombardment
• Large mass inflow rates in Saturn's rings due to ballistic transport and mass loading
• The Structure and Stability of Extended, Inclined Circumplanetary Disk or Ring Systems
• The ballistic transport instability in Saturn's rings II: nonlinear wave dynamics
• The ballistic transport instability in Saturn's rings III: numerical simulations