The eccentric Saturnian ringlets at 1.29Rs and 1.45Rs

doi:10.1016/0019-1035(84)90134-9

Icarus

Volume 60, Issue 1, October 1984, Pages 1-16

https://doi.org/10.1016/0019-1035(84)90134-9 Get rights and content

Abstract

The shapes and kinematics of the two major eccentric ringlets in Saturn's C ring are studied in data acquired by four Voyager experiments: imaging science (ISS), radio science (RSS), ultraviolet spectrometer (UVS), and photopolarimeter (PPS). It is found that the ringlets have mean widths of ∼25 km (Titan, 1.29 R_s) and ∼64 km (Maxwell, 1.45R_s), eccentricities of order 10⁻⁴, sharp edges on a scale of ∼1 km, normal optical depths τ ∼ 1−2, and are embedded in essentially empty gaps (τ < 0.05). In addition, they exhibit positive linear width-radius relations, suggesting that differential precession across the ringlets is being prevented by the self-gravity of the ring particles. The kinematics of the Maxwell ringlet are determined solely by Saturn's nonspherical gravity field; the kinematics of the Titan ringlet are apparently determined by its interaction with Titan. Masses, mean surface mass densities, and mass extinction coefficients have been calculated. The comparatively large optical depths and mass extinction coefficients in these features suggest an environment and particle size distribution different from the remainder of the C ring and presumably caused by the mechanism responsible for ring confinement.

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Cited by (47)

Apse-alignment in narrow-eccentric ringlets and its implications for the ϵ-ring of Uranus and the ring system of (10199) Chariklo
2020, Icarus
The discovery of ring systems around objects of the outer Solar System provides a strong motivation to apply theoretical models in order to better estimate their physical and orbital parameters, which can constrain scenarios for their origin.
We review the criterion for maintaining apse-alignment across a ring and the balance between the energy input rate provided by a close by satellite and the internal dissipation rate occurring through ring particle collisions that is required to maintain ring eccentricity, as derived from the equations of motion governing the Lagrangian-displacements of the ring-particle orbits. We use the case of the ϵ-ring of Uranus, to calibrate our theoretical discussion and illustrate the basic dynamics governing these types of ring.
In the case of the ring system of (10199) Chariklo, where the evidence that the rings are eccentric is not conclusive, we apply the theory of apse-alignment to derive information about the most plausible combination of values of the surface density and eccentricity-gradient, as well as the masses and locations of their postulated but - presently undetected - shepherd-satellites.
When the balance conditions that we predict are applied to the ring system of (10199) Chariklo, we are able to estimate the minimum mass of a shepherd satellite required to prevent eccentricity decay, as a function of its orbital location, for two different models of dissipation. We conclude that the satellite mass required to maintain the m = 1 eccentric mode in the ring, would be similar or smaller than that needed to confine the rings radially.
Our estimation of the most plausible combinations of eccentricity gradient and surface density consistent with apse-alignment are based on a standard model for the radial form of the surface density distribution, which approximately agrees with the optical depth profile derived by the stellar occultations. We find a diverse range of solutions, with combinations of eccentricity gradient and surface mass density that tend to minimize required enhanced collisional effects, having adopted estimated values of the form factor of the second degree harmonic of the gravitational potential.
Kronoseismology III: Waves in Saturn's inner C ring
2019, Icarus
We investigate waves driven in Saturn’s rings by planetary normal modes, concentrating on the previously unexplored inner C ring. In this region, the known waves all have exceptionally short wavelengths, which has proven problematic for previous studies that depended on the accurate estimate of wave phases for wave identification. However, detailed study of over 200 stellar and radio occultations observed by Cassini, involving measurements of  ∼ 65 circular ring features, has resulted in a radius scale for the rings which has absolute errors of  ∼ 250 m and internal (relative) uncertainties of  ∼ 150 m (French et al., 2017). This permits us to measure the phases of waves with wavelengths as short as  ∼ 1 km, or even less, which has enabled the identification of additional waves in the inner C ring. Using a variety of wavelet-based approaches and employing stellar occultation data acquired by the Visual and Infrared Mapping Spectrometer (VIMS) instrument, we have identified three new Saturn-driven outer Lindblad resonance density waves: W76.02 (radius near 76020 km, wavenumber $m = - 9$ ), W76.44 $(m = - 2),$ and W76.46 $(m = - 7)$ . We also identify a new class of waves driven by Saturn’s internal oscillations: vertical (bending) waves W74.67 $(m = - 7),$ W74.93 $(m = - 4),$ W74.94 $(m = - 9),$ and W76.24 $(m = - 8)$ . All of these identifications are based on the three observational parameters that can be derived from the wave profiles: their m-values (or number of spiral arms), their pattern speeds Ω_P, and their directions of propagation. These results, when combined with previous identifications of Saturn-driven waves, provide significant constraints on Saturn’s internal structure.
A vertical rift in Saturn's inner C ring
2016, Icarus
Citation Excerpt :
Studies of the Titan ringlet by Porco et al. (1984) demonstrated that it is well-described by a simple keplerian ellipse, precessing under the influence of Saturn’s zonal gravity harmonics. But because it is located very near the Titan 1:0 ILR, and because its apoapse is closely aligned with Titan, Porco et al. (1984) concluded that the ringlet’s eccentricity is likely to be forced by the apsidal resonance. This idea was further pursued by Nicholson and Porco (1988), who used the ringlet’s eccentricity to place a constraint on Saturn’s zonal gravity harmonics.
In 1988 Rosen and 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 $n_{T} = 22 . 577^{\circ} d^{- 1}$ 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 pattern speed approximately equal to $- n_{T} .$ But the most intriguing feature associated with the wave is a narrow gap that 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 that accounts for the observations and consists of a continuous but very narrow gap (radial width ≃ 0.6 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 vertical amplitudes of 3.8 km for the inner edge and 1.2 km for the outer edge in 2008, with nodes misaligned by ∼110°. 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 slopes in the bending wave become so great that nonlinear effects result in the physical disruption of the ring within its first wavelength, beyond which point the wave re-establishes itself with a reduced amplitude.
Deciphering the embedded wave in Saturn's Maxwell ringlet
2016, Icarus
Citation Excerpt :
Embedded within a broad gap in the outer C ring, the eccentric Maxwell ringlet was first identified and its basic properties described from Voyager observations (Esposito et al., 1983; Porco et al., 1984a).
The eccentric Maxwell ringlet in Saturn’s C ring is home to a prominent wavelike structure that varies strongly and systematically with true anomaly, as revealed by nearly a decade of high-SNR Cassini occultation observations. Using a simple linear “accordion” model to compensate for the compression and expansion of the ringlet and the wave, we derive a mean optical depth profile for the ringlet and a set of rescaled, background-subtracted radial wave profiles. We use wavelet analysis to identify the wave as a 2-armed trailing spiral, consistent with a density wave driven by an $m = 2$ outer Lindblad resonance (OLR), with a pattern speed $Ω_{p} = 1769.17 °$ d⁻¹ and a corresponding resonance radius $a_{res} = 87530.0$ km. Estimates of the surface mass density of the Maxwell ringlet range from a mean value of $11 g {cm}^{- 2}$ derived from the self-gravity model to $5 - 12 g {cm}^{- 2}$ , as inferred from the wave’s phase profile and a theoretical dispersion relation. The corresponding opacity is about $0.12 {cm}^{2} g^{- 1}$ , comparable to several plateaus in the outer C ring (Hedman, M.N., Nicholson, P.D. [2014]. Mont. Not. Roy. Astron. Soc. 444, 1369–1388). A linear density wave model using the derived wave phase profile nicely matches the wave’s amplitude, wavelength, and phase in most of our observations, confirming the accuracy of the pattern speed and demonstrating the wave’s coherence over a period of 8 years. However, the linear model fails to reproduce the narrow, spike-like structures that are prominent in the observed optical depth profiles. Using a symplectic N-body streamline-based dynamical code (Hahn, J.M., Spitale, J.N. [2013]. Astrophys. J. 772, 122), we simulate analogs of the Maxwell ringlet, modeled as an eccentric ringlet with an embedded wave driven by a fictitious satellite with an OLR located within the ring. The simulations reproduce many of the features of the actual observations, including strongly asymmetric peaks and troughs in the inward-propagating density wave. We argue that the Maxwell ringlet wave is generated by a sectoral normal-mode oscillation inside Saturn with $ℓ = m = 2$ , similar to other planetary internal modes that have been inferred from density waves observed in Saturn’s C ring (Hedman, M.N., Nicholson, P.D. [2013]. Astron. J. 146, 12; Hedman, M.N., Nicholson, P.D. [2014]. Mont. Not. Roy. Astron. Soc. 444, 1369–1388). Our identification of a third $m = 2$ mode associated with saturnian internal oscillations supports the suggestions of mode splitting by Fuller et al. (Fuller, J., Lai, D., Storch, N.I. [2014]. Icarus 231, 34–50) and Fuller (Fuller, J. [2014]. Icarus 242, 283–296). The fitted amplitude of the wave, if it is interpreted as driven by the $ℓ = m = 2$ f-mode, implies a radial amplitude at the 1 bar level of ∼ 50 cm, according to the models of Marley and Porco (Marley, M.S., Porco, C.C. [1993]. Icarus 106, 508).
Noncircular features in saturn's rings II: The C ring
2014, Icarus
Citation Excerpt :
Our goal has been to identify and characterize all measurably noncircular features, with the ultimate aims of understanding the role played by satellite resonances in sculpting the C ring, and of increasing our understanding of the internal dynamics of narrow ringlets in general and their interactions with the gaps that harbor them. As first noted by Esposito (1983), Porco et al. (1984b) and Porco and Nicholson (1987), the four prominent narrow gaps in the C ring each either contain a noncircular ringlet, or have one or more measurably noncircular edges. In some cases we find that these distortions are forced by nearby resonances with external satellites, but in others they represent either freely-precessing keplerian ellipses or more complex modes of oscillation, which we refer to as normal modes.
We present a comprehensive survey of sharp-edged features in Saturn’s C ring, using data from radio and stellar occultation experiments carried out by the Cassini spacecraft over a period of more than five years. Over 100 occultations are included in the combined data set, enabling us to identify systematic radial perturbations as small as 200 m on the edges of ringlets and gaps. We systematically examine all of the noncircular features in the C ring, refine the eccentricities, precession rates and width variations of the known eccentric ringlets, identify connections between several noncircular gap and ringlet edges and nearby satellite resonances, and report the discovery of a host of free normal modes on ring and gap edges. We confirm a close association between the Titan (or Colombo) ringlet (a = 77878.7 km) and the Titan 1:0 apsidal resonance: the apoapse of the ringlet is nearly aligned with Titan’s mean longitude, and the pattern speed closely matches Titan’s mean motion. Similar forced perturbations associated with the Titan resonance are detectable in more than two dozen other features located throughout the inner C ring as far as 3500 km from the Titan resonance. The inner edge of the Titan ringlet exhibits several strong outer Lindblad resonance (OLR-type) normal modes, and scans of the outer edge reveal inner Lindblad resonance (ILR-type) normal modes. The Maxwell ringlet (a = 87,510 km), in contrast, appears to be a freely-precessing eccentric ringlet, with post-fit RMS residuals for the inner and outer edges of only 0.23 and 0.16 km, respectively. The best-fitting edge precession rates differ by over 10 times the estimated uncertainty in the rate of the inner edge, consistent with a slow libration about an equilibrium configuration on a decadal timescale. Using self-gravity models for ringlet apse alignment, we estimate the masses and surface densities of the Titan and Maxwell ringlets. The Bond ringlet (a = 88,710 km), about 17 km wide, shows no free eccentricity but lies near two strong resonances: the Mimas 3:1 inner vertical resonance (IVR) at 88702.2 km and the Prometheus 2:1 ILR at 88713.1 km. We find no measurable perturbation from the Mimas IVR, but a clear $m = 2$ signature of the appropriate phase and pattern speed for the Prometheus ILR on the outer edge of the ringlet, along with free ILR-type normal modes with wave numbers $m = 3$ ,4, 5, 6 and 7. The Dawes gap, located at 90,210 km, and its associated embedded ringlet, also show both free and forced perturbations, and as in the case of the Maxwell gap, the outer edge of the Dawes gap appears to be sympathetically forced by the nearby ringlet. The pattern of newly identified normal modes coexisting on the sharp edges of ringlets and gaps is in excellent agreement with theoretical predictions, with ILR-type modes on outer ringlet (and inner gap) edges and OLR-type modes on inner ringlet (and outer gap) edges, representing standing waves between the resonance locations and the ring edges. Modes with larger $| m |$ generally have narrower resonant cavities, and of the dozens of detected normal modes, none has been identified with a resonance radius that falls outside the ring material.
Probing the inner boundaries of Saturn's A ring with the Iapetus -1:0 nodal bending wave
2013, Icarus
The Iapetus −1:0 nodal bending wave, the first spiral wave ever described in Saturn’s rings, has been seen again for the first time in 29 years. We demonstrate that it is in fact the nodal bending wave, not the 1:0 apsidal density wave as previously reported. We use wavelet analysis to determine the wavelength profile, thus deriving the surface density at every point in the region covered by the bending wave. This profile is consistent with surface densities measured from more localized spiral density waves in the outer Cassini Division and the inner and mid-A Ring, varying smoothly from the low values of the former to the higher values of the latter.
Most remarkably, our analysis indicates that there is no significant change in surface density across the boundary between the outer Cassini Division and the inner-A ring, despite the very abrupt increase in optical depth and reflected brightness at this location. We consider anew the nature of the classically identified “inner edge of the A ring,” given that it does not appear to be correlated with any abrupt increase in surface density. There is an abrupt increase in surface density at the Pandora 5:4 density wave, ∼300 km outward of the A ring’s inner edge. Further study is needed to robustly interpret our findings in terms of particle properties and abundances, much less to explain the origins of the implied structure.

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^☆: Contribution 3960 of the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, Calif. 91125.

²: Now at Lunar and Planetary Laboratory, University of Arizona, Tucson, Ariz. 85721.

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The eccentric Saturnian ringlets at 1.29Rs and 1.45Rs☆

Abstract

Icarus

Icarus

Data Reduction and Error Analysis for the Physical Sciences

The dynamics of elliptical rings

Astron. J.

The Fourier Transform and Its Application

The wavy edges of Encke's gap

The eccentric ringlet in the Huygens gap at 1.45 Saturn radii: Multi-instrument Voyager observations

Science

Saturn's rings: Structure, dynamics, and particle properties

Towards a theory for the Uranian rings

Nature

Precession of the ε ring of Uranus

Astron. J.

The origin of the eccentricities of the rings of Uranus

Astrophys. J.

The dynamics of planetary rings

Annu. Rev. Astron. Astrophys.

The eccentric Saturnian ringlets at 1.29R_s and 1.45R_s☆