1. 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

2. 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

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

4. 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

5. April 25, 2006
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6. 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

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

8. Inner C Ring Titan 1:0 Ringlet PIA06537 April 25, 2006
NASA/JPL/SSI
PIA06537
April 25, 2006
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9. Outer C Ring Maxwell Ringlet PIA06539 April 25, 2006
NASA/JPL/SSI
PIA06539
April 25, 2006
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10. Central B Ring Unexplained Structure PIA07610 April 25, 2006
NASA/JPL/SSI
PIA07610
April 25, 2006
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11. Outer Edge of B Ring, and Cassini Division
B Ring Edge
Huygens Ringlet
NASA/JPL/SSI
PIA06536
April 25, 2006
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12. Outer A Ring and Encke Gap
Density Waves
Bending Wave
Encke Gap
NASA/JPL/SSI
PIA06534
April 25, 2006
CHARM Presentation

13. Outer Edge of A Ring and Keeler Gap
Encke Gap
Keeler Gap
Daphnis
NASA/JPL/SSI
PIA07584
April 25, 2006
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14. F Ring and Prometheus PIA06143 April 25, 2006 CHARM Presentation
NASA/JPL/SSI
PIA06143
April 25, 2006
CHARM Presentation

15. Diaphanous G Ring PIA07643 April 25, 2006 CHARM Presentation
NASA/JPL/SSI
April 25, 2006
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16. Enceladus: Source of the E Ring
NASA/JPL/SSI
PIA07758
April 25, 2006
CHARM Presentation

17. 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

18. 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

19. 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

20. 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
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21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

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

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

29. Composition of the Rings
Water Ice
And Dirt
April 25, 2006
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30. Infrared Spectrum Shows Distribution of Water Ice
PA06350
NASA/JPL/University of Arizona
April 25, 2006
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31. 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

32. 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

33. 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 years.
April 25, 2006
CHARM Presentation

34. 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

35. 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

36. 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

37. 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

38. 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

39. Alpha Virginis A Ring Opacities Ingress and Egress at 10 km Resolution
Encke Gap
Cassini Division
April 25, 2006
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40. Ring Plane Radius (km)
April 25, 2006
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41. 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

42. 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

43. Measured Surface Mass Densities
April 25, 2006
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44. 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 ~ m.
Lifetime of 150 km moon is ~ 1010 years at current epoch.
April 25, 2006
CHARM Presentation

45. A Ring Azimuthal Transparency Asymmetry
April 25, 2006
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46. A Ring Azimuthal Transparency Asymmetry
Opacity variations with azimuthal view angle.
April 25, 2006
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47. FUV Observation of 26 Tau (8)
April 25, 2006
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48. FUV Observation of Del Aqr Occultation
April 25, 2006
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49. FUV Observation of Alp Leo
April 25, 2006
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50. Azimuthal View Angle Dependence on Opacity
April 25, 2006
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51. Stellar Occultation Variation Summary
April 25, 2006
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52. Self-Gravity “Wake” Model
April 25, 2006
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53. Example Model Fit to Data
Mention that we cannot constrain length with this simple model and the observations currently in hand.
April 25, 2006
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54. Self-Gravity Wake Properties in A Ring
Point out inflections near strong density waves indicating disruption of wakes.
April 25, 2006
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55. 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

56. 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

57. 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

58. 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

59. 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

60. 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

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

62. 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

63. 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

64. Huygens Ringlet and Asymmetric Feature
April 25, 2006
CHARM Presentation