Physical properties of Uranian delta ring from a possible density wave
Abstract
The Voyager PPS stellar occultation observations of the Uranian δ ring show evidence for a moonlet interior to the δ ring, which excites a density wave at 48,299.6 ± 0.4 km. The identification of a density wave is from the wavelength and amplitude behavior and the morphology of the observed feature. Sixty-five discrete locations are possible for the orbit of this unseen moonlet. Allowing for these 65 possible locations, we find the surface mass density of the δ ring 5 ⪅ σ ⪅ 10 g/cm2, the viscosity 10 ⪅ ν ⪅ 40 cm2/sec, and the local ring height 7 ⪅ h ⪅ 20 m. These values are comparable to some parts of Saturn's rings. All of the inner and outer first order Lindblad resonances were calculated for the 65 possible moonlet locations. The 65 locations for the moonlet are labeled by azimuth number of m of the resonance associated with each location that would excite the density wave in the δ ring. Moonlet 101, located at 47,984.1 ± 0.4 km has resonances which can also shepherd the inner edge of the δ ring and the outer edge of the γ ring.
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Cited by (20)
From an analysis of 31 Earth-based stellar occultations and three Voyager 2 occultations spanning 1977–2006 (French et al. 2023a), we determine the keplerian orbital elements of the centerlines of the nine main Uranian rings to high accuracy, with typical RMS residuals of 0.2–0.4 km and 1- formal errors in and of order 0.1 km, registered on an absolute radius scale accurate to 0.2 km at the 2- level. The ring shows more substantial scatter, with few secure detections. We identify a host of free and forced normal modes in several of the ring centerlines and inner and outer edges. In addition to the previously-known free modes in the ring and in the ring, we find two additional outer Lindblad resonance (OLR) modes ( and ) and a possible inner Lindblad resonance (ILR) mode in the ring. No normal modes are detected for rings 6, 5, 4, , or . Five separate normal modes are forced by small moonlets: the 3:2 inner ILR of Cressida with the ring, the 6:5 ILR of Ophelia with the ring, the 23:22 ILR of Cordelia with the ring, the 14:13 ILR of Ophelia with the outer edge of the ring, and the counterpart 25:24 OLR of Cordelia with the ring’s inner edge. The phases of the modes and their pattern speeds are consistent with the mean longitudes and mean motions of the satellites, confirming their dynamical roles in the ring system. We find no evidence of normal modes excited by internal planetary oscillations. We determine the width–radius relations for nearly all of the detected modes, with positive width–radius slopes for ILR modes (including the elliptical orbits) and negative slopes for most of the detected OLR modes, supporting the standard self-gravity model for ring apse alignment. We find no convincing evidence for librations of any of the rings. The Uranus J2000 pole direction at epoch TDB 1986 Jan 19 12:00 is and . The slight pole precession predicted by Jacobson (2023) is not detectable in our orbit fits, and the absolute radius scale is not strongly correlated with the pole direction. From Monte Carlo fits to the measured apsidal precession and nodal regression rates of the eccentric and inclined rings, we determine the zonal gravitational coefficients , and fixed at , with a correlation coefficient , for a reference radius km. This result differs significantly from both earlier and more recent results (Jacobson 2014, 2023), owing to our inclusion of previously neglected systematic effects, such as the offset of semimajor axes of the geometric ring centerlines from their estimated dynamical centers of mass and the significant contributions of Cordelia and Ophelia to the precession rate of the ring. Although we cannot set useful independent limits on , we obtain strong joint constraints on combinations of and that are consistent with our measurements. These can be used to limit the range of realistic models of the planet’s internal density distribution and wind profile with depth. The observed anomalous apsidal and nodal precession rates of the and rings are consistent with the presence of unseen moonlets with masses and orbital radii predicted by Chancia and Hedman (2016). The ring’s putative mode does not appear to be forced by a satellite, whose predicted size would be too large to have avoided prior detection. If this mode is excluded from the orbit fit, the solution for the ring has a very large anomalous apsidal precession rate of unknown origin. From the amplitudes and resonance radii of normal modes forced by moonlets, we determine the masses of Cressida, Cordelia, and Ophelia. Their estimated densities decrease systematically with increasing orbital radius and generally follow the radial trend of the Roche critical density for a shape parameter .
Cassini UVIS observations of Saturn's rings
1998, Planetary and Space ScienceThe Cassini Ultra-violet Imaging Spectrograph (UVIS) is part of the remote sensing payload of the Cassini Orbiter spacecraft. Its science objectives include investigation of the chemistry, clouds, and energy balance of the Titan and Saturn atmospheres ; neutrals in the magnetosphere ; D/H ratio for Titan and Saturn ; and structure and evolution of Saturns rings. The UVIS has two spectrographic channels which provide images and spectra covering the ranges from 56–118 nm and 110–190 nm. A third optical path with a solar blind CsI photocathode is used for high signal to noise ratio stellar occultations by rings and atmospheres. A separate hydrogen-deuterium absorption cell (HDAC) measures the relative abundance D/H from their Lyman-alpha emission. The rings of Saturn are the best-studied of planetary rings and contain the majority of the ring material in the solar system. The four-year Cassini tour provides multiple observation opportunities and long time coverage. The UVIS observations include photometry, imaging, spectroscopy, and stellar occultations. Numerous diffraction-limited star occultations by the rings are a prime objective for the UVIS. The 2 ms integration period in this mode will give a ring radial resolution of better than 20 m. The counting rate is 50 × greater than the Voyager star occultations in a resolution element 5 × smaller. Multiple opportunities on the same Saturn passage will define temporal and azimuthal variation. We expect to observe waves, wakes and ring edges—all characteristics of ring dynamics and history. The imaging resolution is 1 mrad, or 1000 km from a viewing range of 106 km. The UVIS is sensitive to the shortest wavelengths of all the remote sensing experiments, and thus the scattered light from the smallest ring particles. In combination with images from ISS and VIMS, CIRS spectra, and
Using a modifiedN-body code to include periodic boundary conditions in a perturbed shear flow, we investigate the role of viscosity on the dynamics of perturbed rings with optical depth τ ∼ 1. In particular, we are concerned with rings such thatq=a(de/da) ≠ 0, whereais the semi-major axis andeis the eccentricity. We confirm the possibility that, for a sufficiently perturbed ring, the angular momentum luminosity may reverse direction with respect to the unperturbed ring (Borderies, N., P. Goldreich, and S. Tremaine 1983a.Icarus55, 124–132). We use observationally constrained parameters for the δ and ϵ uranian rings, as well as the outer portion of Saturn'sBring. We find that understanding the effects of viscosity for the uranian rings requires that both local and non-local transport terms be considered if the coefficient of restitution experimentally obtained by Bridgeset al.(Bridges, F. G., A. Hatzes, and D. N. C. Lin 1984.Nature309, 333–335.) is appropriate for ring particles. We also find evidence that the criterion for viscous overstability is satisfied in the case of high optical depth rings, as originally proposed by Borderieset al.(Borderies, N., P. Goldreich, and S. Tremaine 1985.Icarus63,406–420.), making viscous overstability a leading candidate mechanism to explain the non-axisymmetric structure present in the outer portion of Saturn'sBring. To better understand our patch-code results we extend a non-local and incompressible fluid model used by Borderieset al.for dense rings. We incorporate local and non-local transport terms as well as compressibility, while retaining the same number of arbitrary model parameters.
Damping of Orbital Inclinations by Bending Waves
1994, IcarusAn inclined secondary orbiting in a disk will launch bending waves from resonance sites where the Doppler shifted forcing frequency matches the disk's natural frequency for vertical oscillations. These vertical resonances are of two types: external resonances falling interior and exterior to the perturber's semimajor axis that excite its inclination and coorbiting resonances that fall at the perturber's orbit and damp its inclination. We show that torques from coorbiting resonances dominate the bending wave interaction for a constant density disk. In this case the inclination ultimately decays and an estimate of the characteristic time scale for this process is made.
Comparison of density waves in the rings of Saturn and Uranus
1992, Advances in Space ResearchPlanetary rings respond to resonant satellite perturbations in a variety of ways, giving rise to different structures. Possible responses include generation of waves, wakes, creation of sharp edges and confinement of rings, best illustrated in Saturn's rings /1,2,3/, but not in the Uranian rings. Two possible waves have been identified in the Voyager 2 photopolarimeter (PPS) occultation profiles of the ε ring close to predicted satellite resonances /4/; and one density wave inferred in the δ ring /5/. These are the first possible waves in narrow, eccentric and inclined rings and will be compared to the waves in Saturn's rings.
The Voyager 2 spacecraft encountered the Uranian system in January 1986. Several occultations of the Uranian rings were observed including a radio science (RSS) earth occultation and two stellar occultations. The photopolarimeter (PPS) and ultraviolet spectrometer (UVS) observed the stars σ Sagitarii and β Persei as they were occulted by the δ ring. An inner diffuse companion of the δ ring was detected in the RSS data taken at λ = 3.6 cm and in both the PPS and the UVS σ Sagitarii occultation data taken at λ = 0.26 and λ = 0.11 μm, respectively. The diffuse companion was not observable above the background noise level in the PPS β Persei data because of low signal to noise ratio nor in the UVS β Persei data because of high magnetospheric background. The companion has also been observed in Earth-based stellar occultation observations. Using the PPS σ Sagitarii and RSS data, we found the inner diffuse companion of the δ ring to have an average width of 12 km with an average RSS equivalent depth of 0.60 ± 0.080 km and an average PPS equivalent depth of 0.36 ± 0.054 km. The RSS opacity is roughly twice that of the PPS opacity because the RSS extinction coefficient is twice that of PPS, which accounts for the factor of two. From comparing the widths and equivalent depth between the two sets of data, we found that the particles that contribute the most to the integrated opacities of the companion are particles which have sizes in the several centimeter or greater regime. These particles seem to be located away from the PPS edges, where there may be particles that have sizes smaller than a few centimeters. This would account for the higher equivalent depths and larger widths seen in the PPS data.