Moon­influenced ringlets and edges in Saturn's rings Nicole Albers, Miodrag Sremčević, and Larry W. Esposito The B ring edge@Voyager epoch: As extraordinary as ever Abstract

PS3.1 Z33 ­ 13484 Moon­influenced ringlets and edges in Saturn's rings
Nicole Albers, Miodrag Sremčević, and Larry W. Esposito
Laboratory for Atmospheric and Space Physics, University of Colorado at Boulder, USA
Cassini observations during Saturn equinox have revealed a perplexing amount of structure at the B ring edge. It is still a matter of ongoing debate just how much of the observed structure is intrinsic to the rings and how much is attributable to the influences of ring­moons. We have analyzed ring edges and ringlets in order to disentangle the question of the structure's origin using primarily Cassini UVIS data. Among others objects of study include the Maxwell ringlet in the C ring (which does not have a ring­moon associated resonance), the Titan ringlet (Titan 1:0 ILR), the Huygens ringlet (weakly associated with the Mimas 2:1 ILR), and the outer B ring edge (Mimas 2:1 ILR).
The B ring edge@Voyager epoch: As extraordinary as ever
Cassini UVIS: B ring edge residuals
Cassini UVIS observations of the B ring edge are fit best using the SP2010 streamline model:
m=2 (forced, Mimas 2:1 ILR) m=1 (free, precession) m=2 (free, circulation) and
m=3 (free, resonant cavity)
The Maxwell ringlet exhibits a clear m=1 pattern consistent with a freely precessing ringlet; the Titan and Huygens ringlet have pattern speeds slightly faster than the free precession expected at their location. While the Maxwell ringlet has a clearly linear radius­width­relation consistent with uniform precession, neither the Huygens nor Titan ringlet do. The later also show much stronger deviations from a single m­
mode shape of their edges, suggestion non­trivial contributions from the ring­moons.
Saturn's outer B ring edge is the most prominent of the moon­influenced ring edges. Voyager 2 imaging provides a previously unpublished, nearly 270deg azimuthal coverage and high­resolution images that show a dominant m=2 pattern as well as local disturbances similar to those reported in Cassini imaging [SP2010]. The shape of the edge is clearly dominated by the influence of the moon Mimas while its orientation seems to librate following Mimas' orbital changes.
a=117570.5km; m=2f: as SP2010
m=1: 5.084deg/day
m=2: 382.077deg/day
m=3: 507.699deg/day
But post­fit residuals with RMS of 9.6km and a Chi2/DOF of ~100 suggest the presence of further high­frequency modes, similar to those recently reported from Cassini VIMS and RSS, and HST data [N2011].
The Implications
Cassini UVIS Stellar Occultations
The Cassini Ultra Violet Imaging Spectrograph (UVIS) High Speed Photometer (HSP) is sensitive to photons ranging between 110 nm and 190 nm, and is primarily used to record stellar occultations of O and B stars by e.g. Saturn's rings. With a typical sampling interval of 1ms the instrument achieves spatial resolutions of a few to a few hundred meters in the ring plane (Saturn's equatorial plane). Since 2004 UVIS has observed more than 110 stellar occultations at various times, longitudes and elevation angles. For each of the edge­features discussed here an ephemeris time has been obtained and a corresponding ring place radius and longitude inferred, where the absolute occultation geometry has been corrected to match well­known “quasi­circular” ring features. Streamline Modeling of Ringlets and Ring Edges
Each of the edge features is modeled using a potentially multi­mode streamline description which in essence is an expansion of the Keplerian orbit for small eccentricities [e.g. B1984]:
r=a 1−∑i=0 e i cos[ mi∗ f i ]
f i =−0 i −i∗t−t 0 
r: ring plane radius; a: semimajor axis; e: eccentricity; 
M: mode number; : pattern speed; : epoch;
: ring plane longitude; : pattern longitudinal offset
Above: Two previously unpublished B ring edge panorama. Images were take by the ISS onboard the Voyager 1 and 2 spacecrafts and reveal the very same edge variability recently reported using Cassini ISS images [SP2010]. Right: Reprojected Voyager 2 image (C4396833) used to determine the dominant m=2 shape of the edge at Voyager epoch [P1984]. It reveals prominent discontinuities on short azimuthal distances (here ~10deg) that are inconsistent with a smooth streamline model but reminiscent of the reported region A and B which seemingly move at local Kepler speed.
The Titan, Maxwell, and Huygens Ringlets
[Titan1:0 ILR @ 77846km]
Edge variability using only a free m=2 mode
[Mimas2:1 ILR@117553km]
Eccentric edges are typically well­described by an m=1 streamline whose pattern speed is expected to match the apsidal precession rate at given radial distance from Saturn. For eccentric, narrow ringlets to maintain their shape these have to show apse­alignment of inner and outer edges. Uniform precession (UP, [GT1979]), where the precession rates are modified owing to the self­gravity of a sufficiently optically thick ringlet, could maintain apse­alignment and would reveal itself in a linear width­radius relation.
MaxwellR: consistent with UP [E1983, P1984]
i 
̇i  ≈  ̇o , 1≤≤6
Titan and Huygens R: close to resonance locations; periapse and minimum width are azimuthally offset; inconsistent with UP; evidence for higher m­modes in post­fit residuals; both edges driven i 
 P ≈ P ̇i  ̇o , ≥1
Measurement error is given by the accuracy of the occultation geometry solution which is ~1km
In spite of different scenarios all three ringlets share the same kinematic characteristics.
The value of Mimas' mean motion employed by SP2010 (n=381.9835deg/day) for the forced m=2 pattern speed is clearly optimized for the Cassini epoch. However, such pattern speed accumulates about 80deg offset if propagated backwards in time to the Voyager epoch.
Due to its near­resonance with Tethys and perturbations by yet farther moons Mimas librates with an amplitude of >1000km. As Mimas slowly librates it seemingly "drags" the B ring edge along with it, i.e. all involved m­modes needed to describe the shape of the edge at any given time. This naturally explains the ~80deg­100deg shift between expected orientation of the dominant m=2 mode at the Voyager and Cassini epoch.
The currently best kinematic description of the B ring edge is based on the multi­
mode streamline approach involving in total 4 different, mostly free modes [SP2010]. However, the unexpected, yet surprisingly good match of the “shifted”­
SP2010 model to Voyager 1 and 2 ISS data suggests:
a) the multiple free modes are not necessarily “free” but, at least, indirectly driven and b) the B ring edge is directly responding to the external perturbations of the moon Mimas. In further support, the near match of the observed free m=3 pattern speed to the predicted pattern speed and m­number of the nearby Mimas 4:2 ILR. Thus, following a more conservative approach, initial results suggest that the B ring edge variability may solely be explained by the gravitational perturbations of external moons. Continued work on circular, driven, and eccentric edges and ringlets as well as other ring dynamics tracers like embedded moonlets will help to solve other kinematic puzzles and reveal whether the gravitational influence of both the ring itself and external moons has been under­recognized.
This work was supported by the Cassini­Huygens project.
References: [B1984]
Borderies et al. (1984, Icarus)
Esposito et al. (1983, Science)
Goldreich and Tremaine (1979, AJ) [SP2010]
Nicholson et al. (2011, DDA)
Porco et al. (1984, Icarus)
Spitale and Porco (2010, APJL)