Shepherding of the Uranian rings. I. Kinematics

We identify several orbital resonances involving the newly discovered satellites, 1986U7 and 1986U8, and the Uranian rings. The most important resonances in eccentric rings are known as eccentric reson­ances and are generalizations of the more familiar Lindblad resonances. In keeping with the notation established for Lindblad resonances, we distinguish inner and outer eccentric resonances by the symbols IER and OER. We show that by reducing the absolute radius scale of the Uranian ring system by 0.0124% the 24:25 OER of 1986U7 and the 14:13 IER of 1986U8 fall at the inner and outer edges of the Є ring. The same scale change also brings the 23:22 IER of 1986U7 into coincidence with the outer edge of the δ ring and the 6:5 IER of 1986U8 close to the center of the γ ring. Furthermore, adopting the latest Voyager value of GM_u and our reduced radius scale, we find that the pattern speed of the m = 2 distortion in the δ ring corresponds to that expected for a normal mode excited either by an internal viscous overstability or parametrically by shepherd satellites. These kinematic results make a compel­ ling case for our proposed reduction in the ring radius scale and also imply that 1986U7 and 1986U8 are the inner and outer shepherds for the Є ring, that 1986U7 is the outer shepherd for the δ ring, and that 1986U8 is an outer shepherd for the γ ring

Dynamics of the Sharp Edges of Broad Planetary Rings

(Abridged) The following describes a model of a broad planetary ring whose sharp edge is confined by a satellite's m^th Lindblad resonance (LR). This model uses a streamline formalism to calculate the ring's internal forces, namely, ring gravity, pressure, viscosity, as well as a hypothetical drag force. The model calculates the streamlines' forced orbit elements and surface density throughout the perturbed ring. The model is then applied to the outer edge of Saturn's B ring, which is maintained by an m=2 inner LR with the satellite Mimas. Ring models are used to illustrate how a ring's perturbed state depends on the ring's physical properties: surface density, viscosity, dispersion velocity, and the hypothetical drag force. A comparison of models to the observed outer B ring suggests that the ring's surface density there is between 10 and 280 gm/cm^2. The ring's edge also indicates where the viscous torque counterbalances the perturbing satellite's gravitational torque on the ring. But an examination of seemingly conventional viscous B ring models shows that they all fail to balance these torques at the ring's edge. This is due ring self-gravity and the fact that a viscous ring tends to be nearly peri-aligned with the satellite, which reduces the satellite's torque on the ring and makes the ring's edge more difficult to maintain. Nonetheless, the following shows that a torque balance can still be achieved in a viscous B ring, but only in an extreme case where the ratio of the ring's bulk/shear viscosities satisfy ~10^4. However, if the dissipation of the ring's forced motions is instead dominated by a weak drag force, then the satellite can exert a much stronger torque that can counterbalance the ring's viscous torque.Comment: Accepted for publication in the Astrophysical Journal on April 3, 200

Phase light curves for extrasolar Jupiters and Saturns

We predict how a remote observer would see the brightness variations of giant planets similar to Jupiter and Saturn as they orbit their central stars. We model the geometry of Jupiter, Saturn and Saturn's rings for varying orbital and viewing parameters. Scattering properties for the planets and rings at wavelenghts 0.6-0.7 microns follow Pioneer and Voyager observations, namely, planets are forward scattering and rings are backward scattering. Images of the planet with or without rings are simulated and used to calculate the disk-averaged luminosity varying along the orbit, that is, a light curve is generated. We find that the different scattering properties of Jupiter and Saturn (without rings) make a substantial difference in the shape of their light curves. Saturn-size rings increase the apparent luminosity of the planet by a factor of 2-3 for a wide range of geometries. Rings produce asymmetric light curves that are distinct from the light curve of the planet without rings. If radial velocity data are available for the planet, the effect of the ring on the light curve can be distinguished from effects due to orbital eccentricity. Non-ringed planets on eccentric orbits produce light curves with maxima shifted relative to the position of the maximum planet's phase. Given radial velocity data, the amount of the shift restricts the planet's unknown orbital inclination and therefore its mass. Combination of radial velocity data and a light curve for a non-ringed planet on an eccentric orbit can also be used to constrain the surface scattering properties of the planet. To summarize our results for the detectability of exoplanets in reflected light, we present a chart of light curve amplitudes of non-ringed planets for different eccentricities, inclinations, and the viewing azimuthal angles of the observer.Comment: 40 pages, 13 figures, submitted to Ap.

Physical characteristics and non-keplerian orbital motion of "propeller" moons embedded in Saturn's rings

We report the discovery of several large "propeller" moons in the outer part of Saturn's A ring, objects large enough to be followed over the 5-year duration of the Cassini mission. These are the first objects ever discovered that can be tracked as individual moons, but do not orbit in empty space. We infer sizes up to 1--2 km for the unseen moonlets at the center of the propeller-shaped structures, though many structural and photometric properties of propeller structures remain unclear. Finally, we demonstrate that some propellers undergo sustained non-keplerian orbit motion. (Note: This arXiv version of the paper contains supplementary tables that were left out of the ApJL version due to lack of space).Comment: 9 pages, 4 figures; Published in ApJ

The population of propellers in Saturn's A Ring

We present an extensive data set of ~150 localized features from Cassini images of Saturn's Ring A, a third of which are demonstrated to be persistent by their appearance in multiple images, and half of which are resolved well enough to reveal a characteristic "propeller" shape. We interpret these features as the signatures of small moonlets embedded within the ring, with diameters between 40 and 500 meters. The lack of significant brightening at high phase angle indicates that they are likely composed primarily of macroscopic particles, rather than dust. With the exception of two features found exterior to the Encke Gap, these objects are concentrated entirely within three narrow (~1000 km) bands in the mid-A Ring that happen to be free from local disturbances from strong density waves. However, other nearby regions are similarly free of major disturbances but contain no propellers. It is unclear whether these bands are due to specific events in which a parent body or bodies broke up into the current moonlets, or whether a larger initial moonlet population has been sculpted into bands by other ring processes.Comment: 31 pages, 10 figures; Accepted at A

Saturn’s visible lightning, its radio emissions, and the structure of the 2009–2011 lightning storms

Visible lightning on Saturn was first detected by the Cassini camera in 2009 at ∼35° South latitude. We report more lightning observations at ∼35° South later in 2009, and lightning in the 2010–2011 giant lightning storm at ∼35° North. The 2009 lightning is detected on the night side of Saturn in a broadband clear filter. The 2011 lightning is detected on the day side in blue wavelengths only. In other wavelengths the 2011 images lacked sensitivity to detect lightning, which leaves the lightning spectrum unknown. The prominent clouds at the west edge, or the “head” of the 2010–2011 storm periodically spawn large anticyclones, which drift off to the east with a longitude spacing of 10–15° (∼10,000 km). The wavy boundary of the storm’s envelope drifts with the anticyclones. The relative vorticity of the anticyclones ranges up to −f/3, where f is the planetary vorticity. The lightning occurs in the diagonal gaps between the large anticyclones. The vorticity of the gaps is cyclonic, and the atmosphere there is clear down to level of the deep clouds. In these respects, the diagonal gaps resemble the jovian belts, which are the principal sites of jovian lightning. The size of the flash-illuminated cloud tops is similar to previous detections, with diameter ∼200 km. This suggests that all lightning on Saturn is generated at similar depths, ∼125–250 km below the cloud tops, probably in the water clouds. Optical energies of individual flashes for both southern storms and the giant storm range up to 8 × 10^9 J, which is larger than the previous 2009 equinox estimate of 1.7 × 10^9 J. Cassini radio measurements at 1–16 MHz suggest that, assuming lightning radio emissions range up to 10 GHz, lightning radio energies are of the same order of magnitude as the optical energies. Southern storms flash at a rate ∼1–2 per minute. The 2011 storm flashes hundreds of times more often, ∼5 times per second, and produces ∼10^(10) W of optical power. Based on this power, the storm’s total convective power is of the order 10^(17) W, which is uncertain by at least an order of magnitude, and probably is underestimated. This power is similar to Saturn’s global internal power radiated to space. It suggests that storms like the 2010–2011 giant storm are important players in Saturn’s cooling and thermal evolution