DDA 2015 – How massive is Saturn’s B ring – Clues from cryptic density waves

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Matthew M. Hedman (Cornell)

Abstract

The B ring is the brightest and most opaque of Saturn’s rings, but it is also amongst the least well understood because basic parameters like its surface mass density are still poorly constrained. Elsewhere in the rings, spiral density waves driven by resonances with Saturn’s various moons provide precise and robust mass density estimates, but for most the B ring extremely high opacities and strong stochastic optical depth variations obscure the signal from these wave patterns. We have developed a new wavelet-based technique that combines data from multiple stellar occultations (observed by the Visual and Infrared Mapping Spectrometer (VIMS) instrument onboard the Cassini spacecraft) that has allowed us to identify signals that may be due to waves generated by three of the strongest resonances in the central and outer B ring. These wave signatures yield new estimates of the B-ring’s mass density and indicate that the B-ring’s total mass could be quite low, perhaps a fraction of the mass of Saturn’s moon Mimas.

Notes

  • B ring long assumedto be the most massive ring structure
    • essentially opaque
  • Density (and bending) waves
    • $k(r) = \dfrac{3(m-1)M(r-r_L)}{2 \pi \sigma_0 r^4_L}$
    • Wavenumbers can be quantified using wavelets
    • frequency chirping at moon (e.g., Prometheus, Pandora, Enceladus) MMRs
  • Few waveshave been identified in Saturn’s B ring(!)
    • $\rightarrow$ mass density poorly constrained
    • Expect to see density waves, but…
      • resonances in opaque region
      • a lot of the structure in the rings is of unknown origin
        • some are likely density waves, some not
    • Wave-like signatures not obvious in wavelet transforms
  • Solution? Include phase information inwavelet analysis
    • Different occultations cut through the spiral pattern at different places
      • Noise fluctuations confuse the signal
      • Normally ignored
    • Calculate what phase shifts ought to have been and remove them
      • can average components
      • Ideally, noise averages to zero
      • $\rightarrow$ suppresses background mess
    • Cannow measure wavenumber of resonances!
      • even in region where opacity is ~3
      • $\rightarrow$ mass density
    • Regions with same mass density can have very different optical depths
      • (from scatter in the data)
      • Don’t know why
    • Indications: B ring mass density lower than expected

DDA 2015 – How massive is Saturn's B ring – Clues from cryptic density waves

Matthew M. Hedman (Cornell)

Abstract

The B ring is the brightest and most opaque of Saturn’s rings, but it is also amongst the least well understood because basic parameters like its surface mass density are still poorly constrained. Elsewhere in the rings, spiral density waves driven by resonances with Saturn’s various moons provide precise and robust mass density estimates, but for most the B ring extremely high opacities and strong stochastic optical depth variations obscure the signal from these wave patterns. We have developed a new wavelet-based technique that combines data from multiple stellar occultations (observed by the Visual and Infrared Mapping Spectrometer (VIMS) instrument onboard the Cassini spacecraft) that has allowed us to identify signals that may be due to waves generated by three of the strongest resonances in the central and outer B ring. These wave signatures yield new estimates of the B-ring’s mass density and indicate that the B-ring’s total mass could be quite low, perhaps a fraction of the mass of Saturn’s moon Mimas.

Notes

  • B ring long assumed to be the most massive ring structure
    • essentially opaque
  • Density (and bending) waves
    • $k(r) = dfrac{3(m-1)M(r-r_L)}{2 pi sigma_0 r^4_L}$
    • Wavenumbers can be quantified using wavelets
    • frequency chirping at moon (e.g., Prometheus, Pandora, Enceladus) MMRs
  • Few waves have been identified in Saturn’s B ring(!)
    • $rightarrow$ mass density poorly constrained
    • Expect to see density waves, but…
      • resonances in opaque region
      • a lot of the structure in the rings is of unknown origin
        • some are likely density waves, some not
    • Wave-like signatures not obvious in wavelet transforms
  • Solution? Include phase information in wavelet analysis
    • Different occultations cut through the spiral pattern at different places
      • Noise fluctuations confuse the signal
      • Normally ignored
    • Calculate what phase shifts ought to have been and remove them
      • can average components
      • Ideally, noise averages to zero
      • $rightarrow$ suppresses background mess
    • Can now measure wave number of resonances!
      • even in region where opacity is ~3
      • $rightarrow$ mass density
    • Regions with same mass density can have very different optical depths
      • (from scatter in the data)
      • Don’t know why
    • Indications: B ring mass density lower than expected

DDA 2015 – Saturn’s F ring – A decade of perturbations and collisions

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Carl D Murray (Queen Mary University of London)

Abstract

We present an overview of the gravitational and collisional processes at work in Saturn’s F ring deduced from images obtained by the Imaging Science Subsystem (ISS) on the Cassini spacecraft since 2004. The moon Prometheus exerts the dominant gravitational perturbation on the ring. As well as creating the observed periodic tistreamer-channelti structures in the ring, there is evidence that Prometheus also causes the formation and orbital evolution of clumps that can, in turn, perturb local ring particles. We show how Prometheus’ effect can be understood in terms of a simple epicyclic model. Jets of material seen emanating from the F ring are produced when objects orbiting nearby collide with material in the core. We show that there are fundamental differences between the larger and smaller jets even though both are caused by collisions. A comparison between the morphology seen in ISS observations and the results of simulations suggests that both the impactors and the core material are in the form of aggregates of material. We present the results of a study of one particular sheared jet and its associated clumps over a two-month interval in early 2008, deriving orbits for the clumps and showing how they change as they encounter Prometheus.

Notes

  • F ring:
    • 16,150 images
    • FWHM is $16 \pm 9$km
    • eccentric
    • Clear evidence of grav. effect of Prometheus, collisions with smaller bodies
    • Jets & strands are the result of collisions
    • “streamer channels” from both Prometheus and Pandora
  • Evidence for embedded eccentric objects
    • “Fan” structures (Beurle et al. 2010)
  • Evidence for collisions in F ring core
    • “mini-jets”
    • $\Delta a = a \Delta e$
    • ~1 m/s impacts
    • Appearsto be clusters of objects colliding with clusters of objects
      • from collisional simulations
      • best agreement with observations
  • Clumps in strands
    • $\Delta a > a \Delta e$
    • $\rightarrow$ suppression of $\Delta e$ by apse alignment?

DDA 2015 – Saturn Ring Seismology – How ring dynamics reveal the internal structure of the planet

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Jim Fuller (CalTech)

Abstract

Seismology allows for direct observational constraints on the interior structures of stars and planets. Recent observations of Saturn’s ring system have revealed the presence of density waves within the rings excited by oscillation modes within Saturn, allowing for precise measurements of a limited set of the planet’s mode frequencies. Additional ring waves are created at Lindblad resonances with density inhomogeneities in the planet, allowing for measurements of internal differential rotation. I construct interior structure models of Saturn, compute the corresponding mode frequencies, and compare them with the observed mode frequencies. The observed modes, some of which are finely split in frequency, can only be reproduced in models containing gravity modes that propagate in a stably stratified region of the planet. The stable stratification must exist deep within the planet near the large density gradients between the core and envelope. The planetary oscillation modes may in turn influence the evolution of the rings by depositing angular momentum at Lindblad resonances. In particular, the Maxwell gap is likely opened due to a resonance with Saturn’s $l=m=2$ fundamental mode.

Notes

  • Internal structures of giant planets  poorly constrained
    • Haven’t been able to do seismology…until Cassini @ Saturn
  • Consider just the C ring spiral density waves.
    • Pattern speed & pattern number: diagnostics.
    • Excited at Lindblad resonances.
      • $m(\Omega – \Omega_p) = \kappa$
      • $\Omega_p = -\sigma_\alpha/m$
    • Very tiny perturbations cause these density waves.
      • mode periods: ~hours
      • mode amplitudes (inside Saturn): ~1 m
  • Planet model:
    • inner core, stable outer core, g-mode cavity, f-mode cavity, convective outer envelope
    • resonances with $l=m$ f modes
    • unexpected: frequency fine-splitting! (Maxwell Gap)
    • new: implies stable stratification region
      • generates families of g modes ($2^{nd}$ order)
      • fast rotation $\rightarrow$ mode mixing
        • mess!
        • analogous to hydrogen atom in strong electromagnetic field
        • strongest mixing near f-mode freq’s
      • $\rightarrow$ lots of modes generated in the rings that are currently to “faint” to see
  • Conclusions:
    • Evidence for stable stratification (non-adiabatic interior) of Saturn
    • Helium rain, core erosion, both, something else?
    • Missing ingredient: differential rotation?
    • Some evidence for density inhomogeneities within Saturn

DDA 2015 – The Titan -1:0 bending wave in Saturn’s C ring

Philip D. Nicholson (Cornell)

Abstract

In 1988 Rosen & Lissauer identified an unusual wavelike feature in Saturn’s inner C ring as a bending wave driven by a nodal resonance with Titan (Science 241, 690) This is sometimes referred to as the -1:0 resonance since it occurs where the local nodal regression rate is approximately equal to $-n_T$, where $n_T = 22.577$ deg/day is Titan’s orbital mean motion. We have used a series of 44 stellar occultation profiles of this wave observed by the Cassini VIMS instrument to test their hypothesis. We find that, as predicted, this wave is an outward-propagating m=1 spiral with a leading orientation and a retrograde paRern speed equal to $-n_T$. Applying the standard linear dispersion relation (Shu 1984), we find a mean background surface mass density of $0.7\ g/cm^2$, similar to previous estimates for the inner C ring.

But the most intriguing feature of the wave is a narrow, incomplete gap which lies ~7 km outside the resonance. This gap varies noticeably in width and is seen in roughly 3/4 of the occultation profiles, appearing to rotate with the wave in a retrograde direction. We have developed a simple, kinematical model which accounts for the observations and consists of a continuous but very narrow gap (radial width = 0.5 km), the edges of which are vertically distorted by the propagating bending wave as it crosses the region. Differences in viewing geometry then largely account for the apparent width variations. We find a vertical amplitude of 3.8 km for the inner edge and 1.2 km for the outer edge, with nodes misaligned by ~110 deg. Moreover, both edges of the gap are slightly eccentric, with pericenters aligned with Titan, suggesting that the eccentricities are forced by the nearby Titan apsidal resonance. We hypothesize that the gap forms because the local slope of the ring becomes so great that nonlinear effects result in the physical disruption of the ring within the first wavelength of the bending wave. However, the vertical relief on the gap edges is ~10 times the predicted amplitude of the bending wave, so this story may be incomplete.

Notes

  • Stellar occultation with VIMS
  • Small region of interest:
    • resolution ~2 km
    • bending wave
      • nodal precession = rate of Titan’s motion: -1:0 MMR
    • Colombo ringlet (in Colombo Gap)
      • Titan 1:0 MMR
        • pericenter of ring locked to position of Titan
  • That -1:0 bending wave:
    • wave amplitude varies occultation to occultation
      • (angle of view)
    • resonance location just inside of wave
    • episodic appearance of a ~1-5 km gap!
      • about half the time, there’s a density peak instead of a gap!
      • variation appears to be due to viewing geometry
      • $\rightarrow$ leading spiral density wave
        • Adjust for viewing geometry, and regular pattern emerges
        • gap features associated with bending wave
    • $W(\lambda,t) = W_0\, – \Delta z(\theta) \cos (\lambda\, – \lambda_{star})/\tan (B_{star})$
      • (B = star-ring plane angle)
      • pretty decent fit to peaklets & gaplets
    • Allow each gap edge to be eccentric:
      • 10 parameters to fit
      • eccentric at ~1 km amplitude
      • vertical displacements: about $110^{\circ}$ out of phase
  • So what’s going on?
    • bending wave propagating outward
    • gap forms when local slope of wave first exceeds unity
    • beyond gap, wave re-establishes itself with a smaller amplitude
      • Don’t know why
    • gap is probably a nonlinear response of ring to the steep local slope, leading to vertical ‘tearing’ of the ring surface