A calculation of Saturn's gravitational contraction history

A calculation has been made of the gravitational contraction of a homogeneous, quasi-equilibrium Saturn model of solar composition. The calculations begin at a time when the planet's radius is ten times larger than its present size, and the subsequent gravitational contraction is followed for 4.5 × 10⁹ years. For the first million years of evolution, the Saturn model contracts rapidly like a pre-main sequence star and has a much higher luminosity and effective temperature than at present. Later stages of contraction occur more slowly and are analogous to the cooling phase of a degenerate white dwarf star.Examination of the interior structure of the models indicates the presence of a metallic hydrogen region near the center of the planet. Differences in the size of this region for Jupiter and Saturn may, in part, be responsible for Saturn having a weaker magnetic field. While the interior temperatures are much too high for the fluids in the molecular and metallic regions to become solids by the current epoch, the temperature in the outer portion of the metallic zone falls below Stevenson's [Phys. Rev. J. (1975)] phase separation curve for helium after 1.2 billion years of evolution. This would lead to a sinking of helium from the outer to the inner portion of the metallic region, as described by Salpeter [Astrophys. J.181, L83–L86 (1973)].At the current epoch, the radius of the model is about 9% larger, while its excess luminosity is comparable to the observed value of Rieke [Icarus26, 37–44 (1975)], as refined by Wright [Harvard College Obs. Preprint No. 480 (1976)]. This behavior of the Saturn model may be compared to the good agreement with both Jupiter's observed radius and excess luminosity shown by an analogous model of Jupiter [Graboske et al., Astrophys. J.199, 255–264 (1975)]. The discrepancy in radius of our Saturn model may be due to errors in the equations of state and/or our neglect of a rocky core. However, arguments are presented which indicate that helium separation may cause an expansion of the model and thus lead to an even bigger discrepancy in radius. Improvement in the radius may also foster a somewhat larger predicted luminosity. At least part and perhaps most of Saturn's excess luminosity is due to the loss of internal thermal energy that was built up during the early rapid contraction, with a minor contribution coming from Saturn's present rate of contraction. These two sources dominate Jupiter's excess luminosity. If helium separation makes an important contribution to Saturn's excess luminosity, then planetwide segregation is required.Finally, because Saturn's early high luminosity was about an order of magnitude smaller than Jupiter's, water-ice satellites may have been able to form closer to Saturn to Jupiter.     

Implications of Jupiter's early contraction history for the composition of the Galilean satellites

Graboske et al. (1973) have shown that Jupiter's luminosity was orders of magnitude larger during its initial contraction phase than it is today. As a result, during Jupiter's earliest contraction history, ices would have preferentially been prevented from condensing within the region containing the orbits of the inner satellites. The observed variation of the mean density of the Galilean satellites with distance from Jupiter implies that the satellite formation process was operative on a time scale of about five million years. Another consequence of the high luminosity phase is that water should be the only ice present in significant proportions in any of the Galilean satellites.     

Mutual phenomena of Jupiter's Galilean satellites 1973–74

Two series of predictions have been published for the 1973–1974 mutual phenomena of Jupiter's satellites, one (June–October, 1973) by Milbourn and Carey, and the other (February 1973–May 1974) by Brinkmann and Millis. The main purpose of this paper is to investigate some significant discrepancies between these two sets of predictions. New predictions are calculated for the period June 1973–May 1974. They agree very nearly with the predictions by Milbourn and Carey, but frequently differ by several minutes (up to 30 min when Jupiter III and IV are involved) from those by Brinkmann and Millis. Unlike the previous predictions, the new ones also give the estimated light decreases during the phenomena. The method of prediction is documented for future applications to Jupiter's and Saturn's satellites. The paper concludes with a brief discussion of the problems involved in extracting information about the positions, radii, and albedos of the satellites from observed light curves.     

Saturn's ring and nearby faint satellites

Observations of Saturn's rings during passage of the Earth through the ring plane, coupled with those of others, suggest a ring thickness of 1.3 ± 0.3 km. The wide disparity in the optical depth of Cassini's division found by other investigators is resolved, and for conservative isotropic single scattering, a normal optical depth for Cassini's division of 0.060 ± 0.006 is obtained. We find the mean normal optical depth of ring C to be 0.074 ± 0.007. Analysis of all available observations of faint objects near Saturn indicates the presence of at least one previously undiscovered satellite of Saturn. The orbit for Janus determined by Dollfus is supported. These satellites may be major members of an extended ring.     

Ballistic transport in Saturn's rings: An analytic theory

Ejecta from impacts of micrometeoroids on Saturn's ring particles will, in most cases, remain in orbit about Saturn and eventually be reaccreted by the rings, possibly at a different radial location. The resulting mass transport has been suggested as the cause of some of the features observed in Saturn's rings. Previous attempts to model this transport have used numerical simulations which have not included the effects of the angular momentum transport coincident with mass transport. An analytical model for ballistic mass transport in Saturn's rings is developed. The model includes the effects of angular momentum advection and shows that the net material movement due to angular momentum advection is comparable to that caused by direct ballistic mass transport.     

A Saturnian gas ring and the recycling of Titan's atmosphere

Atoms which escape Titan's atmosphere are unlikely to possess escape velocity from Saturn, and can orbit the planet until lost by ionization or collision with Titan. It is predicted that a toroidal ring of between ～1 and ～10³ atoms or molecules cm^?3 exists around Saturn at a distance of about 10 times the radius of the visible rings. This torus may be detectable from Earth-orbit and detection of nondetection of it may provide some information about the presence or absence of a Saturnian magnetic field, and the exospheric temperature and atmospheric escape rate of Titan. It is estimated that, if Titan has a large exosphere, ～97% or more of the escaping atoms can be recaptured by Titan, thereby decreasing the effective net atmospheric loss rate by up to two orders of magnitude. With such a reduction in atmospheric loss rates, it becomes more plausible to suggest that satellites previously thought too small to retain an atmosphere may have one. It is suggested that Saturn be examined by Lyman-α and other observations to search for the gaseous torus of Titan. If successful, these could then be extended to other satellites.The effect of a hypothetical Saturnian magnetosphere on the atmosphere of Titan is investigated. It is shown that, if Saturn has a magnetic field comparable to Jupiter's (～10 G at the planetary surface), the magnetospheric plasma can supply Titan with hydrogen at a rate comparable to the loss rates in some of the models of Trafton (1972) and Sagan (1973). A major part of the Saturnian ionospheric escape flux (～ 10²⁷ photoelectrons sec^?1) could perhaps be captured by Titan. At the upper limit, this rate of hydrogen input to the satellite could total ～0.1 atm pressure over the lifetime of the solar system, an amount comparable to estimates of the present atmospheric pressure of Titan.     

Collisional breakup of particles in a planetary ring

Jeffreys (1947) estimated the size of fragments resulting from breakup of a satellite inside the Roche limit, obtaining a result of ～100 km. This result does not allow for the further breakup of the fragments due to collisions among themselves, which should reduce the maximum size to ?3 km for rock, or ?1 km for ice. This result affects not only Jeffrey's speculations as to the origin of Saturn's rings, but also recent speculations on the origin of the moon by capture and the possible tidal destruction of satellites of Mercury or Venus.     

Observations of Saturn's outer ring and new satellites during the 1980 edge-on presentation

Observations of Saturn's satellites and external rings during the 1980 edge-on presentation were obtained with a focal coronograph. A faint satellite traveling in the orbit of Dione and leading it by 72° has been detected, together with the two inner satellites already suspected (cf. J. W. Fountain and S. M. Larson, 1978,Icarus36, 92–106). The external ring has been observed on both east and west sides; it may extend up to $\text{?8.3}$ Saturn radii, and appears structured.     

Bending waves and the structure of Saturn's rings

The surface mass density profiles at four locations within Saturn's rings are calculated using Voyager spacecraft images of spiral bending waves. Bending waves are vertical corrugations in Saturn's rings which are excited at vertical resonances of a moon, e.g., Mimas, whose orbit is inclined with respect to the mean plane of the rings. Bending waves propagate toward Saturn by virtue of the rings' self-gravity; their wavelength depends on the local surface mass density of the rings. Observations of bending waves can thus be used to determine the surface density in regions of Saturn's rings near vertical resonances. The average surface density of the outer B ring near Mimas' 4:2 inner vertical resonance is 54 ± 10 g cm^?2. Surface density in this region probably varies by ～ 30% over radial length scales of tens of kilometers; and irregular radial structure is present on similar length scales in this region. Surface densities ranging from 24 g cm^?2 to 45 g cm^?2 are found in the A ring. Small scale variations in surface density are not seen in the A ring, consistent with its more uniform optical appearance.     

Theory of motion of saturn's coorbiting satellites

A simple analytic theory describing the 1:1 orbital resonance is presented and applied to Saturn's coorbiting pair, 1980S1 and 1980S3. These satellites are very small and can approach to within 15,000 km, but are prevented from passing each other by their mutual gravitational interaction. The long-term stability of the S1–S3 orbital configuration is discussed in this paper, and a tie between the 1966 and 1980 observations is establised.     

Ganymede,Europa, Callisto,and Saturn's rings: Compositional analysis from reflectance spectroscopy

The reflectance spectra of Ganymede, Europa, Callisto, and Saturn's rings are analyzed using recent laboratory reflectance studies of water frost, water ice, and water and mineral mixtures. It is found that the spectra of the icy Galilean satellites are characteristic of water ice (e.g., ice blocks or possibly very large ice crystals ? 1 cm) or frost on ice rather than pure water frost, and that the decrease in reflectance at visible wavelengths is caused by other mineral grains in the surface. The spectra of Saturn's rings are more characteristic of water frost with some other mineral grains mixed in the frost but not on the surface. The impurities on all these objects are not in spectrally isolated patches but appear to be intimately mixed with the water. The impurity grains appear to have reflectance spectra typical of minerals containing Fe³⁺. Some carbonaceous chondrite meteorite spectra show the necessary spectral shape. Ganymede is found to have more water ice on the surface than previously thought (～90 wt%), as is Callisto (30–90 wt%). The surface of Europa has a vast frozen water surface with only a few percent impurities. Saturn's rings also have only a few percent impurities. The amount of bound water or bound OH for these objects is 5 ± 5 wt% averaged over the entire surface. Thus with the small amount of nonicy material present on these objects, no hydrated minerals can be ruled out. A new absorption feature is identified in Ganymede, Callisto, and probably Europa at 1.5 μm which is also seen in the spectra of Io but not in Saturn's rings. This feature has not been seen in laboratory studies and its cause is unknown.     

Evolution of the Janus-Epimetheus coorbital resonance due to torques from Saturn's ring

We analyze the interactions between Saturn's coorbital satellites, Janus and Epimetheus, and the outer edge of the A ring, which is presumably maintained by these moons at their 7:6 resonance. Using two distinct but conceptually related methods, we show that ring torques are driving these satellites into a tighter lock. Unless there is a counterbalancing force which we have neglected, their orbital configuration will evolve from the current horseshoe-type lock to one of tadpole orbits around a single Lagrange point in ～20 myr. This finding adds an additional member to the list of short time scale problems associated with the interactions between Saturn's rings and its inner moons     

Comment on radar scattering from Saturn's rings

Transparent particle scattering is proposed to explain the unexpectedly large radar cross section recently observed for Saturn's rings. According to this theory, only 10% of the optically observed material in the A, B, and C rings need consist of smooth ice fragments larger than 8 cm in radius to yield the radar results.     

Saturn's rings: 3-mm low-inclination observations and derived properties

Recent 3-mm observations of Saturn at low ring inclinations are combined with previous observations of E. E. Epstein, M. A. Janssen, J. N. Cuzzi, W. G. Fogarty, and J. Mottmann (Icarus41, 103–118) to determine a much more precise brightness temperature for Saturn's rings. Allowing for uncertainties in the optical depth and uniformity of the A and B rings and for ambiguities due to the C ring, but assuming the ring brightness to remain approximately constant with inclination, a mean brightness temperature for the A and B rings of 17 ± 4°K was determined. The portion of this brightness attributed to ring particle thermal emission is 11 ± 5°K. The disk temperature of Saturn without the rings would be 156 ± 6°K, relative to B. L. Ulich, J. H. Davis, P. J. Rhodes, and J. M. Hollis' (1980, IEEE Trans. Antennas Propag.AP-28, 367–376) absolutely calibrated disk temperature for Jupiter. Assuming that the ring particles are pure water ice, a simple slab emission model leads to an estimate of typical particle sizes of ≈0.3 m. A multiple-scattering model gives a ring particle effective isotropic single-scattering albedo of 0.85 ± 0.05. This albedo has been compared with theoretical Mie calculations of average albedo for various combinations of particle size distribution and refractive indices. If the maximum particle radius (≈5 m) deduced from Voyager bistatic radar observations (E. A. Marouf, G. L. Tyler, H. A. Zebker, V. R. Eshleman, 1983, Icarus54, 189–211) is correct, our results indicate either (a) a particle distribution between 1 cm and several meters radius of the form r^?s with 3.3 ? s ? 3.6, or (b) a material absorption coefficient between 3 and 10 times lower than that of pure water ice Ih at 85°K, or both. Merely decreasing the density of the ice Ih particles by increasing their porosity will not produce the observed particle albedo. The low ring brightness temperature allows an upper limit on the ring particle silicate content of ≈10% by mass if the rocky material is uniformly distributed; however, there could be considerably more silicate material if it is segregated from the icy material.     

On the presumed capture origin of Jupiter's outer satellites

The problem of the origin of Jupiter's outer satellites is treated within the framework of the theory of capture through collinear libration points. Lower bounds for the satellites' semimajor axes are found from a corrected rederivation of Bailey's capture theory. Upper bounds are found from a new derivation of the stability limit for satellites, based on Floquet stability theory.It is shown that if the bodies had near-zero relative velocity when passing the libration point, direct orbits would lie outside retrograde orbits, which is not the case for Jupiter. It is found that the dimensions and distributions of the direct group are well explained by libration-point capture with $\text{Jupiter's mass}\text{=}\text{1}\text{1730}$ solar mass, which is interpreted as indicating capture soon after Jupiter's formation. But ad hoc assumptions are required for this capture model to explain the retrograde group. It is concluded that the direct and retrograde groups may have had different mechanisms of origin.     

Photometric properties of Saturn's rings

The spectral reflectivity of Saturn's rings between 0.36 and 1.06 μm is derived from observations of the combined light of the Saturn system and the previously determined spectrum of the disk of Saturn. The rings are red relative to the Sun for wavelengths λ? 0.7 μm; at longer wavelengths, the spectral reflectivity declines. The amplitude of the opposition effect (anomalous brightening at very small phase angles) shows a maximum at both ends of our spectral range.     

Size distribution of particles in planetary rings

Harris (Icarus24, 190–192) has suggested that the maximum size of particles in a planetary ring is controlled by collisional fragmentation rather than by tidal stress. While this conclusion is probably true, estimated radius limits must be revised upward from Harris' values of a few kilometers by at least an order of magnitude. Accretion of particles within Roche's limit is also possible. These considerations affect theories concerning the evolution of Saturn's rings, of the Moon, and of possible former satellites of Mercury and Venus. In the case of Saturn's rings, comparison of various theoretical scenarios with available observational evidence suggests that the rings formed from the breakup of larger particles rather than from original condensation as small particles. This process implies a distribution of particle sizes in Saturn's rings possibly ranging up to ～100 km but with most cross-section in cm-scale particles.     

Saturn's rings: Resonance about an oblate planet

Classical resonance theory is extended to include corrections due to Saturn's oblateness. A single classical resonance splits into a band structure, with individual resonances almost evenly spaced in radius from the planet. When applied to Saturn's rings this theory predicts, in detail, the structure of Cassini's division.     

Ultraviolet observations of small bodies in the solar system by OAO-2

Broadband filter photometry from 2100 to 4300 Å has been obtained by OAO-2 for the following objects: The Galilean satellites; Titan; the rings of Saturn; and three asteroids. Agreement with independent ground-based photometry in the region of overlap is good. The previously known decrease in reflectivity from visual to ground-based ultraviolet wavelengths continues to 2590 Å for all these objects. Europa's reflectivity continues to decline towards 2110 Å, and the rings' reflectivity levels off from 2590 to 2110 Å. Other targets were too faint at 2110 Å to be measured reliably by OAO-2.The low ultraviolet albedo of Titan has important implications for that planet's atmospheric structure (Caldwell, Larach, and Danielson, 1973; Danielson, Caldwell, and Larach, 1973; Caldwell, 1974b). The ultraviolet reflectivity of Saturn's rings is suggestive of a two-component system, one being pure H₂O particles. The ultraviolet albedos of the Galilean satellites are consistent with existing upper limits for atmospheric abundances, but require either that former estimates of the fractional coverage of H₂O frost are too high, an unlikely circumstance, or that the frost has been darkened by some external agent in the space environment.     

Some consequences of meteoroid impacts on Saturn's rings

High-velocity impacts of interplanetary meteoroids on Saturn's rings are discussed. It is shown that the neutral gas emitted by impact vaporization may be responsible, to a large part, for the observed neutral ring atmosphere. Both the predicted neutral gas injection rate and the gas temperature (or kinetic energy) are compatible with the measurements (see Broadfoot, A. L., B. R. Sandel, D. E. Shemansky, J. B. Holberg, G. R. Smith, D. F. Strobel, J. C. McConnell, S. Kumar, D. M. Hunten, S. K. Atreya, T. M. Dohnahne, H. W. Moos, J. L. Bertaux, J. E. Blamont, R. B. Pomphrey, and S. Linik, Science212, 206–211, 1981). Heavy ejecta particles produce a particulate ring “halo”. The physical properties of this halo are calculated, and it appears to be identical with the tenous particle population discussed by Baum and Kreidl (1982). Erosion of Saturn's ring particles, the resulting mass balance, and regolith formation are estimated. This provides some constraints on surface properties and optical albedo.