Acknowledgement. We thank Science for their permission to use an excerpt from:
Lane, A. L., et al. 1982. Photopolarimetry from Voyager 2: Preliminary Results on Saturn, Titan, and the Rings Science 215 (4532), 537-543. (Excerpt from pp. 541-543.)
Saturn's rings. On 25 August 1981, the PPS observed the bright ultraviolet star delta Scorpii as it was occulted by Saturn's rings (21). The star was observed continuously in the 2640-Angstrom filter of the instrument from its emersion from behind Saturn's disk through the D, C, B, A, and F rings. Every 10 msec the instrument recorded the star brightness and thus the ring opacity: successive data points are separated by a distance of approximately 100 m from Saturn's center. This observation thus provides a continuous cut through the entire ring system with resolution unachievable by other means.
For ease of presentation, we have converted subsets of our data into two dimensional images, assuming azimuthal symmetry in the rings. These images represent false-color pictures of what an observer or camera might see from a close-up vantage point where the resolution is the same as that provided by the PPS star occultation. Figure 7 shows a view of the main strand of Saturn's F ring, first discovered by Pioneer 11 (22). We have degraded our resolution by smoothing over 1-km intervals. The total width of the strand is approximately 40 km and thus would appear as a single feature to the television cameras. We see at least ten individual elements in this strand, but, lacking azimuthal information, we cannot conclude anything about possible braiding.
Figure 8a shows the derived optical depth in the region from which the picture in Fig. 7 was created. The optical depth in the thickest part of the F ring is as large as that in many parts of the A and B rings. How this material is constrained into a region less than 3 km wide is of considerable interest. To examine this, we look at the individual, thickest feature in the F ring at our best resolution (~ 100 m) (Fig.8b). At that resolution, even this strand shows structure: lower opacity is seen at the center, with ridges at both the inner and outer edge. It appears that material attempting to diffuse out of this feature meets some barrier at the edges. A similar morphology was seen for many broader ringlets by the radio science occultation experiment on Voyager 1 and in the eta ring of Uranus (23).
Figure 9 shows a two-dimensional representation of the Encke division, a narrow feature in the outer A ring. The resolution is degraded to about 1 km. A regular, wavelike undulation is present in the A ring inward of the gap. The inner edge of the A ring shows both a narrow gap and a narrow ringlet. A multiple ringlet appears in the center of the gap. The imaging team (24) has seen a single, discontinuous, kinky ringlet at several locations within the Encke gap.
Because our line of sight to the star is not perpendicular to the ring plane, the ray from the star at any instant samples material at different radii from Saturn, unless the ring system is infinitesimally thin. This geometry provides a source of smearing in our data; the smearing length is proportional to the thickness of the ring material in the vertical (perpendicular to the ring plane) direction. By looking at sharp transitions between opaque and transparent regions in the rings, we can find an upper limit to the smearing, which in turn provides an upper limit on the vertical extent of the rings at those locations. These local measurements are preferable to Earth-based determinations (25) of the ring thickness because they are not confused by the possible warping of the ring plane itself.
We have examined several such features in the rings. At an absolutely sharp boundary with a rectangular cross section in the radial direction, the inferred optical depth is a linear function of the distance of the observed point from Saturn because of the nonnormal line of sight. The slope of this change in optical depth is
dtau/dx = - Delta tau/(h tan(theta')) (Eq. 1)
where Delta tau is the magnitude of the jump in optical depth, h is the vertical thickness, and theta prime is the angle the line of sight makes with the normal to the ring plane projected onto the radial direction. In several cases the observed slope is indistinguishable from the time response of the instrument to a sudden change in light level. This lower limit to the observable slope sets an upper limit to the thickness of the rings of 200 m at the locations of these edges. Like all earlier measurements of the thickness of the visible rings, we achieve only an upper limit; nonetheless, this value is the smallest ever determined.
The star occultation provides a solid confirmation of the existence of spiral density waves in Saturn's rings. Such waves were first proposed by Goldreich and Tremaine (26) to explain the width of the Cassini division. Cuzzi et al. (27) interpreted features within the Cassini division as a train of such spiral waves of exceptional long wavelength excited by the apsidal resonance of the ring particles with the mean motion of Iapetus. However, the camera resolution limit of 10 km prevented them from seeing waves with shorter wavelengths. One such wave train is seen in our data on the inner B ring.
Figure 10 shows the occultation data in this region. The shortening of the wavelength with increasing distance from the resonance is characteristic of the propagation of spiral density waves. Figure 11 shows the separation between successive wave crests as a function of distance from the predicted location of the 2:1 (m = 2, l = 2) resonance with Saturn's co-orbital satellite 1980S1. We have overplotted the best fit to these data by a function of the form
lambda = A_0/(x - x_0)
where lambda is wavelength. This is the predicted behavior for outward- propagating long spiral waves near their inner Lindblad resonance (26, 27). The offset of the start of the wave train from its predicted location is given by x_0. We find x_0 ~ 100 km; this is consistent with its being at the predicted location within the precision allowed by the preliminary trajectory tape from which the location of the waves was calculated. The parameter A_0 is proportional to the surface mass density of the resonance. Our value gives the mass density sigma = 60 g/cm^2. Cuzzi et al. (27) have measured sigma in the outer Cassini division by the same method. Their value is 16 g/cm^2: this is in good agreement with our result since the average optical depth (tau ~= 0.16) is smaller by a factor of 4 in the Cassini division than in the part of the inner B ring from which the waves are propagating (tau ~= 0.6). Thus, the ratio of optical depth to mass density is the same at the two locations.
Because of conservation of angular momentum and the 1/x decrease in wavelength, we expect the wave amplitude to grow linearly with distance from the resonance. Unfortunately, for a resonance as strong as that seen here, the wave must quickly become nonlinear as the predicted fractional amplitude exceeds unity - in fact, in about one wavelength. Our data yield a distance to nonlinearity of less than about 50 km. The calculated distance from the linear theory and an estimate of the mass of 1980S1 [derived by assuming it to be an oblate spheroid with axes given by Smith et al. (24) and a mass density of 1.2 g/cm^2] gives a theoretical value of 40 km. The two co-orbital satellites are not at exactly the same distance from Saturn, and so their respective wave trains should be offset by about 30 km. We see some slight evidence of beating in the nonrandom residuals in Fig. 11; nonetheless, ~ 80 percent of the mass is in the leading coorbital (1980S1), and in the above analysis we have considered it alone. This agreement, coupled with the agreement in location in the wavelength dependence and in the local mass density, convinces us that we are actually seeing the propagation of spiral density waves excited by the resonance with the coorbital satellites.
Goldreich and Tremaine (26, 28) provided a formulation to calculate viscous losses due to interparticle collisions. From our data, the decrease in amplitude gives a damping length of ~ 300 km. If this is due entirely to viscous effects, it implies a kinematic viscosity, nu ~= 20 cm^2/sec. From Goldreich and Tremaine (26), we have
nu = c^2/(2 Omega) tau/(1 + tau^2)
where c is the one-dimensional velocity dispersion and Omega is the angular orbital velocity. Solving for c gives c ~ 0.1 cm/sec, an average random velocity of 1 mm/sec.
There are several reasons why we should treat this value with caution. First, this analysis assumes equal-sized particles: in a medium with particles of many sizes, equipartition of energy leads to different velocities for each particle size. Second, this formulation neglects interparticle gravitational interactions (29). This small velocity is less than the free-fall velocity onto a 10-m particle, and so gravitational focusing and scattering could be just as important. Third, if we calculate Toomre's stability criterion (30),
Q = (K c) / (pi G sigma)
where K is the epicyclic frequency of a particle and G is the gravitational constant, then Q ~ 2. This means that the disk is only marginally stable to axisymmetric collapse (30). This also violates an assumption of Goldreich and Tremaine (28). In summary, the physical situation gives little confidence in the calculation of the random velocity: at best, a value for c of ~ 0.1 cm/sec gives only an upper limit; more likely, only the largest particles in a steep particle size distribution actually obey this upper limit. The vertical excursion of monodisperse particles in the ring with random velocity c (for c ~ 1 mm/sec) is
h ~ c/Omega = 10 m
This provides a theoretical vertical thickness for the rings which is comfortably inside our observed upper limit of 200 m (see Eq. 1).
What are the implications of these findings for the structure and evolution of Saturn's rings? The basic question remains: What causes and maintains the multitude of structures visible in Saturn's rings? A popular view before the Voyager 2 flyby was that most of these structures were due to embedded moonlets (31). However, an exhaustive search was made by the imaging team for the largest of these, and none was found (24). Even moonlets too small to be seen by the cameras would leave small gaps in the rings with a width of > 2 km; these could easily be resolved by the PPS occultation. An in-depth look at several regions of our data shows no evidence of such gaps.
Goldreich and Tremaine (26) suggested that angular momentum carried by spiral density waves could clear broad gaps such as the Cassini division. The confirmation of the existence of such waves from the Voyager data supports such a mechanism. Nonetheless, our data are not consistent with this idea as a complete explanation. For example, we see no gap whatever at one location (see Fig. 10). A simple application of the spiral wave-clearing mechanism would predict a gap of width 40 km to be opened in less than 1e^5 years.
Our data are consistent with a mechanism of dynamic instability proposed by Ward (32) and Lin and Bodenheimer (33). In this model, an instability grows in which the low density regions of the rings depopulate themselves by viscous interactions with the neighboring material. The velocity dispersion decreases in the thicker regions while it increases in the thinner regions. A comparison of our derived dispersion velocity in the inner B ring (c ~< 0.1 cm/sec; tau = 0.6) with that found by Cuzzi et al. (27) (c ~< 0.6 cm/ sec; tau = 0.14) does not contradict this model. However, since other mechanisms may contribute to wave damping, these values for c are upper limits; thus, we cannot construe this argument as support for this instability.
These findings suggest that the ring structure is much more dynamic than was earlier believed. The influence of permanent structures created by moons is surely insufficient. Features such as density waves, gravitational instabilities, and dissipative instability may play the dominant role. As the above determinations of ring mass density and viscosity show, we now have an opportunity to probe the physical nature of the ring system through its dynamic interactions.
Last updated Feb-27-1997
