Unraveling the Twists and Turns of Saturn’s Rings Josh Colwell Laboratory for Atmospheric and Space Physics University of Colorado UVIS Co-Investigator Larry Esposito Principal Investigator April 25, 2006 CHARM Presentation Image: NASA/JPL/SSI

Outline Rings Tutorial: structure of the rings and the big picture. UVIS Occultation Results: High resolution profiles of ring structure; Three dimensional structure of rings; Waves as probes of ring properties; Some unexplained phenomena; Where things stand and where we go from here. April 25, 2006 CHARM Presentation

Saturn’s Rings: Age and origin unknown Cassini ISS image: SSI (Boulder), NASA/JPL. April 25, 2006 CHARM Presentation

Approach picture from Cassini: May 10, 2004 Dist: 27 million km. Pixel: 161 km. Moon: Prometheus Cassini ISS image: Space Science Institute (Boulder), NASA/JPL. F C B A Earth is to scale. Notice Prometheus. Rings look deceptively bland here. We will see that they are full of features at length scales down to the size of this room. Let’s look at some data to whet the appetite… Encke Gap W~350 km The main rings Cassini Division April 25, 2006 CHARM Presentation

April 25, 2006 CHARM Presentation

Saturn’s Rings Why don’t they make a moon? Planet Near particle feels stronger gravitational attraction from Saturn than far particle. This “tidal force” keeps the particles from sticking together. Further out, the difference is smaller so moons can form. April 25, 2006 CHARM Presentation

D Ring NASA/JPL/SSI PIA07714 April 25, 2006 CHARM Presentation

Inner C Ring Titan 1:0 Ringlet PIA06537 April 25, 2006 NASA/JPL/SSI PIA06537 April 25, 2006 CHARM Presentation

Outer C Ring Maxwell Ringlet PIA06539 April 25, 2006 NASA/JPL/SSI PIA06539 April 25, 2006 CHARM Presentation

Central B Ring Unexplained Structure PIA07610 April 25, 2006 NASA/JPL/SSI PIA07610 April 25, 2006 CHARM Presentation

Outer Edge of B Ring, and Cassini Division B Ring Edge Huygens Ringlet NASA/JPL/SSI PIA06536 April 25, 2006 CHARM Presentation

Outer A Ring and Encke Gap Density Waves Bending Wave Encke Gap NASA/JPL/SSI PIA06534 April 25, 2006 CHARM Presentation

Outer Edge of A Ring and Keeler Gap Encke Gap Keeler Gap Daphnis NASA/JPL/SSI PIA07584 April 25, 2006 CHARM Presentation

F Ring and Prometheus PIA06143 April 25, 2006 CHARM Presentation NASA/JPL/SSI PIA06143 April 25, 2006 CHARM Presentation

Diaphanous G Ring PIA07643 April 25, 2006 CHARM Presentation NASA/JPL/SSI April 25, 2006 CHARM Presentation

Enceladus: Source of the E Ring NASA/JPL/SSI PIA07758 April 25, 2006 CHARM Presentation

Ring Particle Orbital Dynamics Particles orbiting an oblate planet like Saturn have three natural frequencies of motion: Azimuthal Radial Vertical The time for a particle to complete a radial oscillation is longer than the time for it to travel around the planet (azimuthal) which is longer than the time for it to complete a vertical oscillation. The oblateness of the planet leads to a separation of the three orbital frequencies. Orbits are therefore not closed. The longitude of periapse advances and the longitude of the node regresses. April 25, 2006 CHARM Presentation

Resonances and Density Waves Density waves occur when the radial frequency of a ring particle is in resonance with the orbital motion of a moon: - m, n, p are integers, M refers to the moon, and RL is the location of the inner Lindblad resonance. Strongest horizontal forcing when n=p=0 (no contribution from inclination or eccentricity of moon): Top equation results from Fourier analysis of the perturbing potential and the last three terms on the RHS are together the disturbance frequency, small omega, of the moon. Equations on right is approximate because Kappa is close to Omega. This gives resonance nomenclature (e.g. 7:6 is an m=7 inner Lindblad resonance). Replace Kappa with Nu on the LHS of top equation to get inner vertical resonance condition. Then, can get rid of the eccentricity term (p=0), but need to have at n non-zero, and m is non-zero (although there are nodal resonances that are 1:0 (m=p=0, n=1). All vertical resonances are at least second-order. Separation of frequencies means vertical and horizontal resonances are not co-located. Bending waves depend on the vertical (inclined) motion of the moon. Strongest vertical forcing when p=0 and n=1 (no eccentricity and first order in inclination): April 25, 2006 CHARM Presentation

More on resonances Strongest density wave resonances are m:m-1. 20:19 resonance, ring particle orbits 20 times for every 19 moon orbits. This is m=20 wave (pattern repeated 20 times around Saturn). Can have m=1 (1:0) resonance where orbital motion of moon equals precession rate of ring particle. Ringlet at Titan 1:0 in C ring. Strongest vertical resonances (produce bending waves) are m+1:m-1. Top equation is repeat of horizontal resonance condition. Apsidal resonance is a special case. Bottom illustrates how splitting of frequencies (kappa not equal to omega) means that 4:2 not the same as 2:1, etc. They are usually close enough that the resulting waves overlap and interact. Where are these resonances in Saturn’s rings? Let’s see… April 25, 2006 CHARM Presentation

Mimas m=4 vertical (“bending”) and horizontal (“density”) waves: Every observable feature here is caused by resonance interaction with a moon. Gap is cleared by a moon, and the kinky ringlet is particles on horseshoe orbits with that moon. Notice the separation of the Mimas 5:3 bending and density waves. Encke Gap Cassini ISS image: SSI, NASA/JPL. April 25, 2006 CHARM Presentation

A bending wave and a density (horizontal) wave. Mimas 5:3 Bending Wave Prometheus 12:11 Density Wave Shows the Mimas 5:3 bending wave (right) and the Prometheus 12:11density wave (left). Radial scale of this image is about 500 km. Notice also the dispersion in the wavelength and the rapid damping. These are the properties of satellite-forced waves that enable us to probe some of the basic physical properties of the rings. Cassini ISS image: SSI, NASA/JPL. April 25, 2006 CHARM Presentation

How Resonances Make Waves Consider a perturbation from a satellite with orbital frequency M. Following Goldreich and Tremaine (1978) and Shu (1984): In a frame rotating at M the streamline or path of a ring particle is: One orbit Gravity of satellite excites eccentricity of ring particles; Acceleration due to satellite makes particles reach pericenter later (so pericenter advances to larger longitude); This effect diminishes with increasing distance from resonance. Equation of ellipse to first order in e in inertial frame. Rotate at a pattern speed determined by the natural frequency of a perturbing satellite to get the streamline in that frame. The m in the streamline equation is our friend from the resonance expression. Theta is the true longitude of the ring particle. Streamline is for a collection of particles with identical a and e. The arrow indicates the distance along the m=7 streamline traveled by a particle in one orbit. April 25, 2006 CHARM Presentation

Streamline View of Density Wave m=5 streamlines Unperturbed streamlines Planet Effect of satellite gravity is to advance the streamlines counter-clockwise, with the largest advance for the streamline closest to resonance. This results in… April 25, 2006 CHARM Presentation

Streamlines Perturbed by Moon A spiral density wave where particles are more closely packed at wave peaks and less closely packed at troughs. The gravity of the resulting wave has an m-periodic structure (like the perturbing potential from the moon), so it reinforces the spiral pattern in regions where D (=distance in frequency space from RL) is >0. If D<0 the disk density is 180 degrees out of phase with value needed to maintain the wave. D shifts at RL. Result is density waves propagate toward satellite and bending waves propagate away from satellite. That’s what the moon does. The wavelength of the disturbance is constant. No change with increasing distance from resonance. This is a kinematic wave. There is no restoring force. Now let’s see how the ring itself affects the wave… m-armed spiral density wave April 25, 2006 CHARM Presentation

Perturbed by Moon and Ring Disk gravity exerts a torque on neighboring ring particles resulting in tighter wrapping of the wave pattern. The self-gravity of the ring results in a dispersion of the wave: wave crests apply a torque to the neighboring streamlines outside causing the spiral to wrap tighter and the wavelength to decrease with increasing distance from resonance. April 25, 2006 CHARM Presentation

Sizes of Particles in the Rings Broad distribution of sizes in main rings follows a power-law: n(a)~a-q. q~3 between ~1 cm and several m. Small particles more abundant than large particles. C, Cassini Division, F rings have more “dust” (sub-mm). G, E, and D rings are mainly dust. Moonlets coexist within rings. April 25, 2006 CHARM Presentation

Abundance of cm-sized particles in A ring RSS occultation data. NASA/JPL April 25, 2006 CHARM Presentation PIA07960

Evidence for 100 m Moonlet in A Ring NASA/JPL/SSI PIA07791 April 25, 2006 CHARM Presentation

Composition of the Rings Water Ice And Dirt April 25, 2006 CHARM Presentation

Infrared Spectrum Shows Distribution of Water Ice PA06350 NASA/JPL/University of Arizona April 25, 2006 CHARM Presentation

Ultraviolet Spectrum Shows Water Ice Abundance Ta-da! Color variations carry information about history of ring darkening from meteoroid bombardment. PIA0575 April 25, 2006 CHARM Presentation NASA/JPL/University of Colorado

Rings Summary D, E, G rings are broad and very tenuous and dusty. Main rings: C, B, Cassini Division, A, and F C and Cassini Division have small particles, low opacity, and several gaps and narrow ringlets. B ring is broad, most massive, lots of unexplained structure; A ring has intermediate opacity, two gaps with known moons, and most observed structure are waves excited by moons. Composition mostly water ice. Dusty rings are more contaminated by dark material. April 25, 2006 CHARM Presentation

The Age Problem The rings are bright: micrometeoroid impacts would darken pure ice to the present level in ~108 years. The rings are spreading: collisions transport angular momentum outward and dissipate energy. Moons act as gravitational bookends, but evolutionary timescales are also ~108 years. Moons are short-lived: embedded and nearby moons have lifetimes against impact disruption of 106-109 years. April 25, 2006 CHARM Presentation

Other Big Picture Problems What causes the structures on various scales in the rings? What role does limited accretion play? What did the rings look like 100 million years ago, and what will they look like in 100 million years? April 25, 2006 CHARM Presentation

Critical Pieces of Information Need to know mass of rings and size distribution of particles. Need to know energy dissipation in individual collisions. Need to know impact flux. Challenge is to extract this information from observations of the rings. Stellar occultations are highest resolution probes of ring structure and hence dynamics. April 25, 2006 CHARM Presentation

Stellar Occultation Geometry 2 ms sampling provides ~7-20 m resolution. Discuss technique of stellar occultations, process of planning. Mention diffraction limit comparable to sampling resolution. Much of the rest of the talk will be based on analysis of structure observed in stellar occultations. Full resolution of this occ (Sig Sgr Rev011) is 20 m. April 25, 2006 CHARM Presentation

Sig Sgr Stellar Occultation at 50 km Resolution B Ring C Ring A Ring First measurements of opacities in central B ring. Still opaque to signal in some regions (tau>4). Next slide shows an area equal to the width of the body of the arrow. April 25, 2006 CHARM Presentation

Janus 2:1 Density Wave Sig Sgr Notice that this ring extends for more than 400 km, that the wavelength decreases with increasing radius, and that the amplitude of the wave peaks is greater than the background value (non-linear). Surface mass density: ~60 g/cm2 100 km April 25, 2006 CHARM Presentation

Alpha Virginis A Ring Opacities Ingress and Egress at 10 km Resolution Encke Gap Cassini Division April 25, 2006 CHARM Presentation

Ring Plane Radius (km) April 25, 2006 CHARM Presentation

Prometheus 8:7 Density Wave in A Ring Power spectrum density contours Prometheus 8:7 Density Wave in A Ring Damping length gives viscosity Slope gives  = 38 g/cm2 Resonance location Ring Plane Radius (km) April 25, 2006 CHARM Presentation

Atlas 5:4 Density Wave in Cassini Division Power spectrum density contours 10 km  = 1.6 g/cm2 This technique allows us to map surface mass densities and viscosities (or equivalently, scale heights), but only where there are waves (mostly in the A ring). Wavelet software from Torrence and Compo (1998). April 25, 2006 CHARM Presentation

Measured Surface Mass Densities April 25, 2006 CHARM Presentation

Density Wave Summary Mass of A ring ~ 41021 g (35 g/cm2) equivalent moon radius ~ 100 km. Mass of B ring ~ 1022 g (60 g/cm2). Equivalent moon radius of ring system: Rmoon ~ 150 km Viscosity ~ 5 cm2/s in Cassini Division gives H ~ 10 m. A ring: H ~ 20-30 m. Lifetime of 150 km moon is ~ 1010 years at current epoch. April 25, 2006 CHARM Presentation

A Ring Azimuthal Transparency Asymmetry April 25, 2006 CHARM Presentation

A Ring Azimuthal Transparency Asymmetry Opacity variations with azimuthal view angle. April 25, 2006 CHARM Presentation

FUV Observation of 26 Tau (8) April 25, 2006 CHARM Presentation

FUV Observation of Del Aqr Occultation April 25, 2006 CHARM Presentation

FUV Observation of Alp Leo April 25, 2006 CHARM Presentation

Azimuthal View Angle Dependence on Opacity April 25, 2006 CHARM Presentation

Stellar Occultation Variation Summary April 25, 2006 CHARM Presentation

Self-Gravity “Wake” Model April 25, 2006 CHARM Presentation

Example Model Fit to Data Mention that we cannot constrain length with this simple model and the observations currently in hand. April 25, 2006 CHARM Presentation

Self-Gravity Wake Properties in A Ring Point out inflections near strong density waves indicating disruption of wakes. April 25, 2006 CHARM Presentation

Spacing April 25, 2006 CHARM Presentation Spread in fit values increases in outer A ring for two reasons: fewer measurements and more complicated wake structure there compared to inner and middle A ring. April 25, 2006 CHARM Presentation

Observed  > Poisson  Measuring Self-Gravity Wake Sizes from Occultation Statistics Particles << sample size. Particles (or clumps) ~ sample size. Measure star brightness typically every 2 ms. Brightest stars have ~1000 counts in one sample. Observed  = Poisson  Observed  > Poisson  Region of ring observed in one sample. April 25, 2006 CHARM Presentation

Expected and Measured Variance C Ring B Ring A Ring Here is the mean value from 26 Tau (rev 8). Signal is high where rings are clear or absent, low where rings are opaque. For poisson statistics, the variance would equal this mean value. April 25, 2006 CHARM Presentation

Expected and Measured Variance C Ring B Ring A Ring The variance in green lies on top of the mean signal for most of the B and C rings and the Cassini division and deviates dramatically in the A ring. In the middle B ring, the signal is totally blocked and we are seeing background only. April 25, 2006 CHARM Presentation

Expected and Measured Variance C Ring B Ring A Ring The ratio shows regions of excess variance (wherever the ratio is greater than 1). This shows largest clumps in the middle of the A ring, consistent with the analysis of the azimuthal transparency asymmetry. April 25, 2006 CHARM Presentation

Measuring 3D Structure of Clumps Different views of clumps show different amounts of excess variance, as seen graphically here for the same star observed on ingress and egress. Putting these together from multiple occultations provides sensitive measurement of clump size and shape in 3D. Observation footprint is a complication. April 25, 2006 CHARM Presentation

Blue represents larger clusters of particles. Bright represents higher opacity. 100 m Simulation: John Weiss and Glen Stewart April 25, 2006 CHARM Presentation

Self-Gravity Wake Summary Self-gravity wakes are highly flattened (H/W~0.2) and relatively closely packed (Separation ~ Width). Inter-wake space is nearly empty (~0.1). Self-gravity wakes become less regular and organized in outer A ring (lower surface mass density). Auto-correlation lengths consistent with N-body simulations. Strong density waves disrupt wakes. April 25, 2006 CHARM Presentation

And now for something completely different… Huygens Ringlet and Asymmetric Feature And now for something completely different… Point out that there must be moons in this and other gaps that have not yet been observed. Inner edge of band 1 looks like there’s a wave, but no known resonance with it. Narrow feature is either arc or complicated m>1 inclined ring. Very sharp edges. Dynamic system. This is Alpha Leo Rev 9. April 25, 2006 CHARM Presentation

Huygens Ringlet and Asymmetric Feature April 25, 2006 CHARM Presentation