Effects of electrostatic forces on the vertical structure of planetary rings

We have calculated the vertical structure of planetary dust rings as it results from a balance between an electrostatic force on the dust grains and the vertical component of the gravitational force from the central planet. The electrostatic force results from the charging of the dust grains by the ambient plasma and a large scale electric field due to a shielding electric field and the resulting vertical dust distribution are strongly dependent on dust size, dust and plasma density, plasma temperature and plasma ion type. The dust density distribution has a different dependence on these parameters in tenuous and in dense dust rings. We solve the relevant equations numerically and also by linearization in the limiting cases of tenuous or dense rings. Our results indicate that the effects treated in this paper may be important in both Jupiter's and Saturn's rings.     

Planetary rings: 2–23 centuries of nearly total ignorance, 4 years of information explosion

Saturn lies at nearly twice Jupiter's distance from the Sun and nearly all parts of its system are characterized by much smaller scales than those which are important in the case of Jupiter. This appears in the structures of the planet's atmosphere, in the sizes of classical satellites other than Titan vis-à-vis those of the Galilean satellites, in the plethora of small Saturnian satellites, especially Lagrangian co-orbiters, in the structure of Saturn's F-Ring as contrasted with that of Jupiter's Ring and finally in the highly structured detail in Saturn's Rings, much finer than seriously considered in past theoretical discussions. Uranus' Rings were unknown until five years ago. The discovery and observation of these rings have revived contributions to theory originally intended for application to Saturn's Rings. Models have also been generated for eccentric rings for application to Uranus' Rings which also apply to those of Saturn. These two classes of model are reviewed in the present paper along with the first tentative steps made down the road to unravelling the complexity of Saturn's Rings.     

Particle erosion mechanisms and mass redistribution in Saturn's rings

A variety of physical processes can erode the surfaces of planetary ring particles. According to current estimates, the most efficient of these over the bulk of Saturn's rings is hypervelocity impact by 100 micron to one centimeter radius meteoroids. The atoms, molecules, and fragments ejected from ring particles by erosion arc across the rings along elliptical orbits to produce a tenuous halo of solid ejecta and an extensive gaseous atmosphere. Continuous exchange of ejecta between different ring regions can lead to net radial transport of mass and angular momentum. The equations governing this ballistic transport process are presented and discussed. Both numerical and analytic studies of idealized ring systems illustrate that ballistic transport can cause significant mass redistribution in the rings, especially near regions of high density contrast, such as the inner edges of the A and B rings. Ejecta exchanges can also alter local particle sizes and compositions and may produce pulverized regoliths at least several centimeters deep. The meteoroid erosion rate is so high that significant global torques and mass loss are possible on times shorter than a solar system life time.     

Pioneer fly-by of Saturn and its rings

We report results from analysis of data from Pioneer Saturn's Imaging Photopolarimeter. These include the discovery of a new ring and satellite, the structure of the atmosphere of Saturn and Titan, the inhomogeneous nature of Saturn's rings, and a model for the rings' formation and bimodal particle size distribution.     

Formation of Saturn's spokes

The scattering properties of the spokes in Saturn's rings suggest that they consist of micron-sized dust particles. We suggest that these grains are elevated above the ring plane by electrostatic charging. We show that electrostatic levitation requires a sufficiently large plasma density near the rings. If the plasma density near the rings exceeds a few 10² cm^?3 levitation may occur at significant rates in the strong electric fields which exist in the wall-sheaths at the ring. Once the dust particles are elevated they drift relative to the plasma (except at synchronous orbit). This relative motion constitutes a current which causes a polarization electric field if the plasma is azimuthally inhomogeneous. The dense plasma will drift radially in response to this electric field and cause levitation of more dust particles as it moves along. It leaves a radially aligned trail of elevated dust particles—the spokes. One way of producing dense plasma is by meteor impact on the rings. We discuss the mechanisms of ring charging, electrostatic levitation and the currents in the plasma-dust mixture. We show that for reasonable conditions spokes of more than 10,000 km radial length can be formed in less than five minutes. We also show that under the same conditions the electrostatic levitation model predicts a dust grain population which peaks at a size of 0.6 microns and can reach optical depths of 0.1.     

Planetary radio astronomy from voyager

The Planetary Radio Astronomy instruments on Voyager 1 and 2 provided new, highly detailed measurements of several different kinds of strong, nonthermal radiation generated in the inner magnetospheres and upper ionospheres of Jupiter and Saturn. At Jupiter, an intense decameter-wavelength component (between a few tenths of a MHz and 39.5 MHz) is characterized by complex, highly organized structure in the frequency-time domain and by a strong dependence on the longitude of the observer and, in some cases, of Io. At frequencies below about 1 MHz there exists a (principally) kilometer-wavelength component of emission that is bursty, relatively broadbanded (typically covering 10 to 1000 kHz), and strongly modulated by planetary rotation. The properties of this component are consistent with a source confined to high latitudes on the dayside hemisphere of Jupiter. A second kilometric component is narrow-banded, relatively weak and exhibits a spectral peak near 100 kHz. The narrowband component also occurs periodically but at a repetition rate that is a few percent slower than that corresponding to the planetary rotation rate. This component is thought to originate at a frequency near the electron plasma frequency in the outer part of the Io plasma torus (8 to 10 R_J) and to reflect the small departures from perfect corotation experienced by plasma there.The Voyager instruments also detected intense, low frequency, radio emissions from the Saturn system. The Saturnian kilometric radiation is observed in a relatively narrow frequency band between 3 kHz and 1.2 MHz, is elliptically or circularly polarized, and is strongly modulated in intensity at Saturn's 10.66-hr rotation period. This emission is believed to be emitted in the right-hand extraordinary mode from regions near or in Saturn's dayside, polar, magnetospheric cusps. Variations in intensity at Saturn's rotation period may correspond to the rotation of a localized magnetic anomaly into the vicinity of the ionospheric footprint of the polar cusp. Variations in activity on time scales of a few days and longer seem to indicate that both the solar wind and the satellite Dione can also influence the generation of the radio emission.     

Scientific results from the pioneer Saturn infrared radiometer

The Pioneer 11 Infrared Radiometer instrument made observations of Saturn and its rings in broadband channels centered at 20 and 45 μm and obtained whole-disk information on Titan. A planetary average effective temperature of 96.5±2.5 K implies a total emission 2.8 times the absorbed sunlight. Correlation with radio science results implies that the molar fraction of H₂ is 90±3% (assuming the rest is He). Temperatures at the 1 bar level are 137 to 140 K; regions appearing cooler may be overlain by a cloud acting as a 124 K blackbody surface. A minimum temperature averaging 87 K is reached near 0.06 bars. Ring boundaries and optical depths are consistent with those at optical wavelengths. Ring temperatures are 64–86 K on the south (illuminated) side, ～54 K on the north (unilluminated) side, and at least 67 K in Saturn's shadow. There is evidence for a south to north drop in ring temperatures. Titan's 45 μm brightness temperature is 75±5 K.     

Radio occultation by Saturn's rings: Observations of structure and particle size with Voyager 1

Voyager 1 radio occultation study of Saturn's rings gives detailed information regarding the rings' radial structure and particle sizes. Structure within the rings is mapped to a radial resolution of few hundred m in the tenuous parts of ring C and the Cassini Division, and few km over ost of ring A. Fine resolution profiles reveal extremely sharp edges, very narrow gaps, and a host of wave phenomena. Particle size distributions obtained from occultation data within several ring regions are roughly consistent with an inverse cube power law with upper size cutoff in the 5 to 10 m radius range.     

Voyager photopolarimeter observations of Saturn and Titan

The Voyager 2 photopolarimeter experiment observed the intensity and polarization of scattered sunlight from the atmospheres of Saturn and Titan in the near-UV at 2640 Å and in the near-IR at 7500 Å. Measurements of Saturn's limb brightening and polarization at several phase angles up to 70° indicate that a significant optical depth of UV absorbers are present in the top 100 mbar of Saturn's atmosphere in the Equatorial Zone and north polar region, and possibly at other latitudes as well. UV absorbers are prominent in polar regions, suggesting that charged particle precipitation from the magnetosphere may be important in their formation.The whole-body polarization of Titan is strongly positive in both the UV and near IR. If spherical particles are responsible for the polarization, no single size distribution or refractive index can account for the polarization at both wavelengths. The model atmosphere proposed by Tomasko and Smith [1], characterized by a gradient in particle size with altitude, seems capable of explaining the Voyager observations. If non-spherical particles predominate, the Voyager observations place important constraints on their scattering properties.     

Interaction of Titan's atmosphere with Saturn's magnetosphere

The Voyager 1 measurements made during the Titan flyby reveal that Saturn's rotating magnetospheric plasma interacts directly with Titan's neutral atmosphere and ionosphere. This results from the lack of an intrinsic magnetic field at Titan. The interaction induces a magnetosphere which deflects the flowing plasma around Titan and forms a plasma wake downstream. Within the tail of the induced magnetosphere, ions of ionospheric origin flow away from Titan. Just outside Titan's magnetosphere, a substantial ion-exosphere forms from an extensive hydrogen-nitrogen exosphere. The exospheric ions are picked up and carried downstream into the wake by the plasma flowing around Titan. Mass loading produced by the addition of exospheric ions slows the wake plasma down considerably in the vicinity of the magnetopause.     

Saturn's equatorial haze

We have measured the amount of Raman scattering in Saturn's equatorial zone and polar regions near the central meridian at the wavelengths of the H and K Ca II solar lines, 3934 Å and 3969 Å. Approximately 2.1% of the sunlight in this wavelength range is Raman scattered out of this range in Saturn's equatorial zone. Modeling the aerosol particle distribution as a clear, Rayleigh- and Raman-scattering gas over a dense haze yields an H₂ column abundance of about 40 km-Amagats. Comparison with results obtained by Pioneer 11 suggests that either the equatorial haze was 2.5 times deeper at the time of these observations (May, 1981) than at the time of the Pioneer 11 flyby (Sept., 1979); or the haze particles are much more strongly polarizing in blue light than they are in red light.     

Electrostatic discharges in Saturn's B-ring

The Voyager observations of electrical discharges in Saturn's rings strongly support earlier speculations on the role played by electrostatics, magnetic fields, and lightning phenomena in the primitive solar system. They also suggest conditions then by direct analogy rather than by extrapolating backwards through time from conditions now. The observed discharges show a pronounced 10^h periodicity, which suggests a source in Keplerian orbit at 1.80 ± 0.01 Saturn radii (1 R_S = 60,330 km). In that region, the B ring is thicker than optical depth 1.8 for about 5,000 km. At 1.805 ± 0.001 Saturn radii, however, the ring is virtually transparent for a gap of width 200 m. We conclude that a small satellite orbits Saturn at that radius and clears the gap. The gap edges must prevent diffusive filling of the gap by fine material which is especially abundant at this position in the rings and would otherwise destroy the gap in minutes. The discharges represent the satellite's interaction with the outer edge of the gap. Spoke formation may involve the interaction of ring material in the vicinity of the gap.     

Photopolarimetric sensing of planetary surfaces

Polarization measurements over the surfaces of the Moon, Mercury, Mars and Saturn's rings, and global data for the Galilean satellites, have been recorded with telescopes in France. A number of asteroids were measured by B. Zellner in USA. The curves of polarization are diagnostic of the micro-texture of the surface, and demonstrate that all the atmosphereless Solar System objects so far observed (except Callisto trailing hemisphere) have their surfaces covered with a regolith of fines, as for the Moon, which is produced by the cumulative effect of meteoroid impacts. For all the silicaceous objects down to a diameter of 700 km, namely Mars, Mercury, the Moon, Callisto (for the apex hemisphere), the mean grain sizes are no larger than 20um. The asteroids have coarser grained regoliths, apparently because of their smaller gravitational escape velocities. The C type asteroid surfaces, assumed to be carbon rich, appear finer grained than the silicaceous S types. The M astereroids assumed to be metallic, are also covered with small fragments, becuase metals loose their ductile properties at low temperature and behave at impact like brittle silicates. The trailing hemisphere of Callisto has a texture almost reminiscent of bare rocks. Orbital considerations to excluse significant impact effects, and a scenario for the past evolution of the satellite are implied.The planet Mars, with wind effects due to a tenuous atmosphere, several intense past volcanic episodes, a high tectonic activity and a permafrost underground has a more diversified surface regolith. A detailed analysis was achieved with photopolarimeters placed on board the soviet Mars Orbiter Spacecraft MARS-5.The Saturn's rings, anisotropic multiple scattering effects are observed and exhibit variations often in few days or weeks. Mutual interactions and gravitational forces are at work to produce organized structures, whereas disorganization forces occur and the competition produced ephemeral situations.     

Stability and mass flow in Saturn's rings

Besides gravitational effects, interesting electrodynamical processes could also take place in the vicinity of the rings of Saturn. In part, this is because of the electrostatic charging of the ring particles by the magnetospheric and ionospheric plasma, and in part, the generation of impact plasma by meteoroid bombardment at the ring plane could lead to strong coupling between the rings and the ionosphere via a variety of current systems. The mass transport and angular momentum transfer in association with the ring-ionosphere coupling may cause quite large changes in the ring configuration over the age of the solar system. The presence of the sharp boundary between the B and the C rings perhaps is a good example. To highlight these new developments, we describe several of the electrodynamical mechanisms (with emphasis on their corresponding electric fields and current systems) which have been postulated to be of importance in determining the mass transport of the ring system. Further points are made that, besides mass exchange between the rings and the planetary atmosphere, the mass injection from the rings could also have significant effect on the mass and energy budget of the magnetosphere, maintenance of the E ring, the Titan hydrogen torus as well as aeronomic process in the upper atmosphere of Titan.     

Planetary rings

The individual ring systems are described with dust/magnetosphere interactions high-lighted somewhat. Jupiter's main ring is tenuous and enveloped by the magnetosphere; it principally contains micron-sized silicate grains. A vertically-extended, radially-localized “halo” of submicron particles lies inward of the main ring while a newly-discovered very faint ring lies outside it. The classical Saturnian system is composed of water ice chunks with sizes principally between cm and meters. Satellite resonances determine some ring structure but most is not understood. The faint exterior rings (E, G, F and one just identified between the A and F rings) are intimately associated with magnetospheric particles and contain mainly small grains, which are also prominent in the “spokes” located in the dense, middle portion of the B ring. Most of the nine narrow Uranian rings are slightly inclined and eccentric, and presumably lie within the putative Uranian magnetosphere. Particles are likely carbonaceous; sizes are thought to be larger than microns.     

Kinematics of Saturn's spokes

Voyager 2 images of Saturn's rings have been analyzed for spoke activity. More than 80 and 40 different spokes have been measured at the morning and at the evening ansa, respectively. Higher rate of spoke formation has been found at 145° ± 15° SLS and at 305° ± 15° SLS which persisted for at least 3 Saturn revolutions. Higher spoke activity (formation and growth in width) by more than a factor 3 has been observed over the nightside hemisphere of Saturn than over the dayside hemisphere. The age distribution (i.e. time from radial formation until observation, assuming Keplerian shear) of the leading (old) edges of spokes has its maximum at ～ 9,000 s and ～ 6,000 s for spokes observed at the morning ansa and at the evening ansa, respectively. The highest spoke age observed is ～ 20,000 s. The age distribution of the trailing (young) edges of spokes peaks at < 2,000 s at both ansae but has its mean at ～ 4,500 s and ～ 3,500 s, respectively. On the average the observed spokes grew in width for ～ 4,500 s at the morning ansa and for ～ 2,500 s at the evening ansa. The maximum time of growth in width was ～ 12,000 s.     

The study of a plasma jet injected by an on-board plasma thruster

The injected plasma jet-ionosphere interaction features were studied in experiments carried out on board two METEOR satellites. The injected plasma jet propagation depends considerably on jet injection pitch-angle. The impactless jet spreading took place without considerable interaction with the ionosphere plasma, when injected along the magnetic field. By injection across the magnetic field very effective plasma jet-ionosphere plasma and the Earth's magnetic field interaction was observed. Plasma jet injection provoked the generation of electromagnetic fields near the satellite.     

Analysis of electromagnetic and electrostatic effects of particle impacts on spacecraft

Particle impacts on spacecraft can cause considerable damage, even leading to complete failure. A theory for the resulting vehicle potential changes and the electromagnetic radiation from impact-induced plasma has been published by Close et al. (2010). Here we compare this theory to impacts registered by the Radio and Plasma Wave Science instrumentation on the Cassini spacecraft. We study both low-velocity (16 km/s) large particles (2.6 μm radius) detected in Saturn’s rings and high-velocity (450 km/s) small particles (1 nm radius) in the solar wind. The agreement with the theory is quite good. We also apply these results to earth orbit and conclude that both Electrostatic Discharge and Electromagnetic Pulse radiation are likely and could lead to spacecraft failure.     

Entry of dust particles into planetary magnetospheres

While interplanetary dust constitutes a primary source of cosmic particulate matter in planetary magnetospheres, the debris produced by its impact with small satellites and ring material provides an important secondary source. Internal processes, such as volcanic activity, particularly in the smaller satellites, could result in a third source. In the case of the terrestrial magnetosphere there are also artificial (internal) sources: 1–10μ sized A?₂O₃ particles injected by solid rocket mortar burns between near earth and geosynchronous orbit constitute one such source, while the fragments of larger bodies (artificial satellites) due to explosions (e.g., “killer satellites”) and collisions constitute another. Finally, if we include the purely induced cometary magnetosphere among planetary magnetospheres, the injection of cometary dust into it due to entrainment by the outflowing gases constitutes another source.As a result of being immersed in a radiative and plasma environment these dust grains get electrically charged up to some potential (positive or negative). Particularly in those regions where the magnetospheric plasma is hot and dense and their own spatial density is low, the dust grains could get charged to numerically large negative potentials.While this charging may have physical consequences for the larger grains, such as electrostatic erosion (“chipping”) and disruption, it also can effect the dynamics of the smaller grains. Indeed, the small but finite capacitance of these grains, which leads to a phase lag in the gyrophase oscillation of the grain potential, could even lead to the permanent magneto-gravitational capture of interplanetary grains within planetary magnetospheres in certain situations. Here we will review the sources of dust in planetary magnetospheres and discuss their physics and their dynamics under the combined action of both planetary gravitational and magnetospheric electromagnetic forces.     

Formation of Jupiter's rings

An excellent review of the present understanding of the structure and formation of Jupiter's rings has recently been published by Burns et al. /1/. Therefore I will only summarize the basic ideas and open questions concerning the physical phenomena governing Jupiter's rings.