An Instability in Planetary Rings Due to Ballistic Transport

Abstract

Ballistic transport in planetary rings is the net radial transport of mass and angular momentum due to exchanges of meteoroid impact ejecta between neighboring ring regions. The detailed linear stability analysis in this paper demonstrates that ballistic transport causes wavelike disturbances to grow and propagate in an otherwise uniform ring. The growth is strongest for intermediate values of the normal ring optical depth τ = 0.1 to 1.0 and goes to zero as τ → 0 and τ → ∞. For nominal values of various physical parameters, the minimum e-folding time is ∼ 105 years for τ ∼ 0.4. The direction of propagation is opposite to the sense of any asymmetry that may exist in the ejecta direction distribution (inward for prograde ejecta and outward for retrograde ejecta). The additional effect of viscous transport tends to damp wavelike perturbations strongly at short wavelengths and at high values of τ. The quantitative agreement between this analytic work and numerical simulations reported elsewhere is generally quite good.As applied to Saturn's rings, the results in this paper strengthen the earlier conclusion from numerical calculations that the 100-km structure in the inner B Ring is caused by ballistic transport. However, it is also clear that ballistic transport cannot produce the complex structure seen in the outer two-thirds of the B Ring where τ ≤ 1.5. Wavelike structures in the C Ring might also be attributed to ballistic transport; but this requires further study.