Boom and Bust Cycles in Saturn’s rings? Larry W. Esposito LASP / University of Colorado Cassini Science Highlight PSG Munich, 10 June 2010 Revised 30 June 2010.

Features in F ring UVIS occultations initially identified 13 statistically significant features Interpreted as temporary clumps and a possible moonlet, ‘Mittens’ Meinke etal (2010) now catalog 25 features from the first 102 stellar occultations For every feature, we have a location, width, maximum optical depth (opacity), nickname

F Ring Search Method Search was tuned for 1 VIMS-confirmed event: Optimal data-bin size  threshold VIMS UVIS Pywacket -15 km 0 15 km

Fluffy Butterball

New Features

We identify our ‘kittens’ as temporary clumps

Features Lag Prometheus 12 of 25 features have =180º ± 20º The maximum optical depth is at =161º Sinusoidal fit gives Δλ=191º

Sub-km structure seen in wavelet analysis varies with longitude Wavelet analysis from multiple occultations is co-added to give a significance estimate For the B ring edge, the significance of features with sizes 200-2000m shows maxima at 90 and 270 degrees ahead of Mimas For density waves, significance correlated to resonance torque from the perturbing moon

We identify this structure as temporary clumps

Observational Findings F ring kittens more opaque trailing Prom by π Sub-km structure, which is seen by wavelet analysis at strongest density waves and at B ring edge, is correlated with torque (for density waves) and longitude (B ring edge) Structure leads Mimas by π/2, equivalent to π in the m=2 forcing frame The largest structures could be visible to ISS: we thought they might be the equinox objects

Rings resemble a system of foxes and hares In absence of interaction between size and velocity, prey (mean mass) grows; predator (velocity) decays When they interact, a stable equilibrium exists with an equilibrium for the size distribution and a thermal equilibrium

Model Approach We model accretion/fragmentation balance as a predator-prey model Prey: Mean aggregate mass Predator: Mean random velocity (it ‘feeds’ off the mean mass) Calculate the system dynamics Compare to UVIS HSP data: wavelet analysis (B-ring), kittens (F-ring) Relate to Equinox aggregate images

Predator-Prey Model Simplify accretion/fragmentation balance equations, similar to approach used for plasma instabilities Include accretional aggregate growth, collisional disruption, dissipation, viscous stirring Different from Showalter & Burns (1982) moons perturb the system, not just the orbits

Lotka-Volterra Equations M= ∫ n(m) m dm; Vrel2= ∫ n(m) Vrel2 dm dM/dt= M/Tacc – Vrel2/vth2 * M/Tcoll dVrel2/dt= (1-ε2)Vrel2/Tcoll + M2/M02 *Vrel2/Tstir M: mean mass; Vrel2: velocity dispersion; Vth: fragmentation threshold; ε: restitution coeff; M0: reference mass (10m); Tacc: accretion; Tcoll: collision; Tstir: viscous stirring timescales

Lotka-Volterra equations describe a predator-prey system This system is neutrally stable around the non-trivial fixed point Near the fixed point, the level curves are ellipses, same as for pendulum The size and shape of the level curves depend on size of the initial impulse The system limit cycles with fixed period Predators lag prey by π/2

F ring Predator-Prey model, forced by Prometheus

Better Ring Model A more realistic ring model is modified from the Lotka-Volterra equations Now the fixed point is a spiral stable point; Stability analysis is the same as for a forced damped pendulum at origin: The system spirals to the stable point Driving this system at low amplitude gives a steady state solution at the forcing frequency in the synodic frame with mass max trailing velocity min by roughly π/2

Better Model dM/dt= M/Tacc – Vrel2/vth2 * M/Tcoll dVrel2/dt= (1-ε2)Vrel2/Tcoll + M2/M02 *Vesc2/Tstir In the second equation, we replaced Vrel2 by Vesc2: This is equivalent to viscous stirring by aggregates of mass M. This is no longer a pure predator-prey model, but it better mimics the ring dynamics.

F ring model, forced by Prometheus

Phase Lag Moon flyby or density wave passage excites forced eccentricity; streamlines crowd; relative velocity is damped by successive passes through crests This drives the collective aggregation/ dis-aggregation system at a frequency below its natural limit-cycle frequency Mass aggregation M(t) lags by π for pure sinusoidal forcing at synodic period

What Happens at Higher Amplitudes? The moonlet perturbations may be strong enough to force the system into chaotic behavior or into a different basin of attraction around another fixed point (see Wisdom for driven pendulum); or Individual aggregates may suffer events that cause them to accrete: then the solid body orbits at the Kepler rate

Living at the Edge of Saturn’s Rings F ring The F ring is a dusty ringlet located just beyond the main ring system at a distance of 140,200km from the center of Saturn. At this dynamically peculiar location, the Roche zone, the tendency for ring particles to merge due to gravity is balanced by the tidal effects of the planet acting to tear them apart. The F ring has a complicated, continually changing structure dominated by a bright, ~50km-wide core; the adjacent strands have a spiral structure and are thought to the icy debris from small objects which have impacted the ring. The gravity of the small moon Prometheus (86km wide) produces “channels” across the F ring when it passes and these shear over time. However, new results from the Cassini spacecraft have shown that Prometheus does more than just create pretty patterns and that it has an interesting dynamical history. The F ring itself may be the “signature” of a process by which new moons are formed regularly at the outer edge of Saturn’s ring system. Cassini scientists have shown that Prometheus triggers the gravitational collapse of ring particles in the F ring core. The resulting objects have sufficient mass to perturb the surrounding material and create “fan” structures which reveal their presence. Similar processes on a much larger scale are thought to have operated in the early history of the solar system as planets formed out of clouds of dust and gas. Prometheus “channels” F ring core Additional research has shown that there are checks and balances that determine the lifetimes of the objects formed in the F ring by Prometheus. As more objects form there is an increase in the number and speed of collisions. Over time this ultimately acts to decrease the number of objects, but then they start to grow again. The whole process can be studied using “predator-prey” models from ecology systems theory. Prometheus is just one of many small, icy moons with elongated shapes on the outskirts of Saturn’s rings. Recent work has shown that such moons must have accreted in the outer part of Saturn’s main rings (perhaps agitated by predator-prey cycles) and evolved outwards due to their gravitational interaction with the rings within the last 10 million years, creating the F ring on their path outwards. In many ways Saturn’s rings behave like a miniature protoplanetary disk. sheared “channels” F ring core Janus “fan” Atlas Prometheus Pandora Epimetheus Two images of a 40,000km-long section of Saturn’s F ring taken by Cassini’s cameras on June 1st, 2010. The small moon Prometheus can be seen in the upper image along with several channel structures it has created in the ring. In the lower image, taken 50 minutes later, Prometheus has moved out of the field of view but a “fan” structure in the rings indicates the presence of an object in the ring’s core. 20km A selection of the small, icy, irregularly-shaped moons orbiting just outside the main ring system. Their odd shapes are due to the strong tides of Saturn.

Conclusions UVIS occultations show aggregation/disaggregation A predator-prey model indicates moon perturbations can excite cyclic aggregation at the B ring edge and in the F ring, with a natural phase lag Model: Impulse, crowding, damping, aggregation, stirring, disaggregation Stochastic events in this agitated system can lead to accreted bodies that orbit at Kepler rate: equinox objects?

Backup Slides

UVIS occultations UVIS has observed over 100 star occultations by Saturn’s rings Time resolution of 1-2 msec allows diffraction- limited spatial resolution of tens of meters in the ring plane Multiple occultations provide a 3D ‘CAT scan’ of the ring structure Spectral analysis gives characteristics of ring structures and their dimensions

Living at the edge of Saturn’s rings Cassini finds clues to the way moons form and evolve F ring Saturn’s F ring is at a special location in the rings where there is a balance between self-gravity causing ring particles to accrete into moons, and tidal forces trying to tear them apart. As the moon Prometheus (86km wide) passes the F ring its gravity creates a signature “channel” pattern (see upper left), similar to the wake made by a boat moving across a lake. Prometheus triggers the collapse of the icy ring material to form mountain-sized snowballs at the core of the F ring. These leave tell-tale “fan” structures in the ring (see lower left). Over time the number of objects can rise and fall in cycles, similar to the behavior of ‘predator-prey’ models of ecological systems. Many of Saturn’s small moons (see below) are now thought to have formed at the outer edge of the rings and evolved outwards over the last 10 million years. Prometheus “channels” F ring core “fan” sheared “channels” F ring core Atlas Prometheus Pandora Epimetheus Janus 20km Two Cassini images of Saturn’s F ring taken 50 minutes apart on June 1, 2010 Saturn’s rings behave like a miniature version of the disk out of which the planets formed – the same physical processes operate even though the scales are vastly different. Cassini images of the small moons of Saturn that lie just outside the main rings. The images are to the same scale.

We conclude that the agitation by the moons at both these locations in the F ring and at the B ring outer edge drives aggregation and disaggregation in the forcing frame. This agitation of the ring material allows fortuitous formation of solid objects from the temporary clumps, via stochastic processes like compaction, adhesion, sintering or reorganization that drives the denser parts of the aggregate to the center or ejects the lighter elements. Such processes can create the equinox objects seen at the B ring edge and in the F ring, explain the ragged nature of those ring regions and allow for rare events to aggregate ring particles into solid particles, recycling the ring material and extending the ring lifetime.  

Structure increasing near B ring edge

F ring Predator-Prey model with periodic forcing

B ring Impulsive forcing

MASS (t)

Vrel2(t)