The rings of Saturn: Two-frequency radar observations

rc,taus 30, 104-110 (1977)

The Rings of Saturn: Two-Frequency Radar Observations 1{, ~ I . (~OLI)STEIN AND I1. l{. G R E E N

Jet Propal.sion Laborah)ry, Pasadena, Cah~ornia 91103

G. H. PETTENGILL Department of Earth arid Planetary Scie~ces, Massachusetts It~stitldc of Technology, Cambridge, Massachusetts 02139

AND

D. B. CAMPBELL National Astropwmy a~ut Ionosphere Center, Arecibo, Puerto Rico OOGl2

l/eceived ()c(ober 21, 1975; revised May 18, 1976 Observations of 3.5- and 12.6-cm radar echoes from the rings of Saturn suggest that no significant difference in scattering properties exists in this wavelength interval. The echoes are largely unpolarized at both wavelengths, and yield a radar cross section at 3.5 cm of 7.32 :t: 0.84 X 109km~for each polarization. The combined radar cro~s sections for both polarizations correspond (o 1.37 4- 0.16 times the op|icMly observed projected A- and B-ring areas (excluding that part of the rings shadowed by the planet). The shape of the echo spectrmn is compatible with a homogeneous ring scattering model, except in having excess power at frequencies neat- the center of (he spectrum. A number ()f possible expl'ma(ions for the observed scattering properties are explored. INTRO D UCTION The report by Goldstein and Morris (1973) that radar echoes had been received from the rings of Saturn at a wavelength of 12.6 cm startled m a n y scientists, who had been accustomed to visualizing the rings "~s composed of submillimeter particles. A n u m b e r of a t t e m p t s to reconcile the rad'tr, radiometric, optical, and infrared results have since been made (Pollack et al., 1973; Morrison and Cruikshank, 1974), but the radar results by themselves inarguably d e m a n d t h a t a substantial fraction of the optically observed ring particles be larger than about 1 cm in radius. Some of the models proposed require :~ high degree of echo polarization (Pettengill

and Hagfors, 1974) or permit a marked frequency dependence (Pollack et al., 1973 ; Pollack, 1975). It was in the hope of further narrowing the range of acceptable scattering models t h a t the authors undertook a two-frequency, dual-polarization s t u d y of S'~turn's rings in late 1974 and early 1975. OBSERVATIONS The experiment involved two types of radar operation: monostatic at a 3.5-cm wavelength, and bistatic at "~ 12.6-cm wavelength. For monostatic operation, both transmission and reception were carried out using the 64-m antenna at the Jet l)ropulsion L a b o r a t o r y ' s Goldstone Tracking Station in California. For the bistatic mode, transmission was from the

104 Copyright 1~ 1977 by Academic Press, Inc. All right~ of reproduction in any form reserved.

RINGS OF SATURN newly upgraded 214-1n aperture of tlle Arecibo Observatory, operated by Cornell University iu Puerto Rico, and reception of the echoes was at Goldstonc. Table I gives a summary of the radar parameters. Essentially monochromatic waves were beamed at Saturn and the ring system in both experiments, using a very narrow antenna beam (about 0?04). Even so, the beam subtended an angle more than three times wider than the ring system. Each particle in the system contributed power to the echo with its own distinctive Doppler shift ; hence the received signals were spread over many hundreds of kilohertz. Measurement of this power spectrum was the objective of our experiments, and was expedited by periodic frequency shifting of the transmitted signal to enable the background noise spectrum to be more readily removed. Horizontal (with respect to the Earth's surface), linearly polarized, 12.6-cm waves were transmitted from Arecibo on 2 nights in January 1975. During the observing interval, the position angle of the incident polarization varied from about -V15° to 0 ° with respect to the plane of the rings. After the 2-hr, 14-min round-trip time of flight, the signals were received at Goldstone. The received polarization was also linear and lay alternately in a plane parallel to and perpendicular to that of the transmitted polarization, in 15-rain blocks. The effects of Faraday rotation on the plane of polarization were calculated to be less than 5 °. Blocks of corresponding polarization were summed, yielding two spectrograms with the same echo intensity, within the error of measurement (about 30%). Unfortunately, because of calibration and pointing uncertainties associated with this first use of the new Arecibo S-band transmitter, an absolute radar cross section could not be determined from these measurements. Nevertheless, these measurements were able to establish that the

105 TABLE I R'Ldar System Paramelel's Arecibo (S band)

Frequency (MHz) Power (kW) A n t e n n a gain (db) Noise temp. (°K)

2380 300~ 69~ --

Goldstone (S band)

Goldstone (X band)

--62.0 20

8495 271 b 71.6 b 25

a These are the parameters a p p l y i n g to this early use of the Arecibo S-band radar facility; when the facility becomes fully completed in 1976, the corresponding values are expected to be 400 k W and 72 db, respectively. b These are effective values for the observations reported here.

rings of Saturn have the ability to largely depolarize linearly polarized transmissions. Circular polarization (right-handed) was transmitted at 3.5 cm from Goldstone on 5 nights in December 1974 and January 1975. On 4 of those nights reception was left-handed, circularly polarized, and on 1 night right-handed. Once again, the two resulting spectrograms gave the same echo intensity within about 25%. The rings of Saturn thus appear to depolarize significantly both circularly and linearly polarized incident radiation at 3.5- and 12.6-cm wavelengths, respectively. These results represent the first successful detection of Saturn's rings at a 3.5-cm wavelength. Two prior attempts (in 1967 and in 19731 at nearly this wavelength utilizing the Haystack Observatory's 3.8-cm radar system were unsuccessful; the radar cross section of the rings turned out to be slightly less than the threshold of detectability for the Haystack system (Ingalls and Shapiro, 1975). All the 3.5-cm data (from both polarizations) have been averaged together in Fig. 1, where received power density is plotted against Doppler frequency shift. The data have been folded about the mean Doppler value to reduce the variance further, since the scattering is assumed to be symmetric. A theoretical spectrum (dashed) has been plotted in Fig. 1, computed from the known geometry of the ring system as seen from the Earth, and the assumption that the

106

GOLI)STEIN E T AL.

-

3x10

26 W/Hz

c~ L

FREQUENCY, MHz

Fro. 1. Mean folded spectrum of the X-band echoes. The dashed curve is obtained from a ring model for which the B ring is twice as reflective as the A ring. The maximum possible (i.e., limb) frequency of echoes from the planet itself is marked f2. f~ is described in the text. A typical error (plus and Ininus 1 standard deviation) is shown. n u m b e r density of reflecting particles in the bright inner (B) ring is twice t h a t of the outer (A) ring (Cook et al., 1973). Only one p a r a m e t e r (amplitude) in the theoretical s p e c t r u m w'~s adjusted in order to m a t c h the observed p e a k intensity best. T h e occultation by the p h m e t of the rings was t a k e n into account, as was Cassini's division; the blurring caused b y finite frequency resolution (250 kHz) was also included. The general agreement between the theoretical and measured spectra d e m o n s t r a t e s t h a t the echoes indeed originate from the rings of Saturn. However, the spectral excess at the lower frequencies ( a m o u n t i n g to a b o u t ~1~c~,+ of the total received power) is statistically significant, •rod needs to be accounted for. The total received power a~ 3.5 era, for TABIA,: II (;e<,me(ry of Saturn's l{ings" ],ocation

Radius (10 ~ kin)

Fro jetted area for B = -- 2'I74 b (I{P k m ~)

('orrecte
................................... Outer :\

1.371

Inner A Outer B

1.216 1. 167

hmer B

0.914

5.20

5.10

6.83

5,98

A fter Cook et al. (1973, T a b l e IV). b B is the angle b e t w e e n the line of s i g h t aim the pla ne of Om rings.

one polarization, was 1.23 X 10 -19 W, which corresponds to a r a d a r cross section of 7.32 4- 0.84 X 109 k m ~" or 68 :t: 8 % of the visible projected '~rea of the rings (see Table I I for a listing of the assumed ring geometry). R a d a r cross section is equivalent to the cross-sectional area of t h a t perfectly conducting sphere, which at the same distance would return the observed power. This is compared with 68% for the 12.6-cm single-polarization monostatic i'esults reported by Goldstein and" Morris (1973), corrected here from the quoted 6 2 % for the effect of S a t u r n ' s shadowing of the rings, an effect neglected in the earlier paper. T h e r i n g - p l a n e inclination was --26?4 in the e'~rlier observations as compared to - 2 4 ? 4 for tim d a t a here. The error (in s t a n d a r d deviations) for the 3.5-cm results was c o m p u t e d from the scatter in the power m e a s u r e m e n t s corresponding to d a t a from individual nights. I t does not account for errors in estimating the app'~ratus p a r a m e t e r s such "ts a n t e n n a gain, t r a n s m i t t e r power, etc., which m a y further affect tile absolute value of the cross section derived b y as m u c h as 15% of its vMue. Thus, the r a d a r cross section does not a p p e a r to v a r y between 3.5 and 12.6 cm. Combining the results for b o t h polarizations yields a total scattering cross section of 137 i 16~!~ of the projected area.

RINGS OF SATURN Under the assumption, based on optical observation (see Cook et al., 1973), that the A ring is only about half-filled with reflectors (optical depth 0.5), as compared to the B ring, the radar cross section of an individual reflector must, therefore, average 177% of its geometric area. If we consider only the portion of the echo power corresponding to the theoretically explicable echoes from the A and B rings (i.e., the dotted line of Fig. 1), the individual scattering efficiency drops to 145%. But if the B ring is not completely filled with particles, the individual-particle cross section must be proportionately higher. Thus, we have three facts from the radar observations that must be accommodated by any valid model of the ring system: (1) The rings effectively depolarize linearly and circularly polarized incident waves, (2) the ring particles are unusually efficient radar reflectors, yielding approximately the same high total cross section at 12.6 and 3.5 cm; and (3) there is an apparent excess of power observed at the "central" Doppler shifts, as compared to homogeneous scattering models based on the optically observed ring distributions. DISCUSSION Infrared spectra of the rings have been associated with water ice by Pilcher et al. (1970). Furthermore, theoretical studies of solar system evolution by Lewis (1972) show that ices are likely to have formed in the vicinity of the outer planets. Hence particles of ice are a good candidate for the material of Saturn's rings. Singly scattering, transparent ice spheres, of diameter of the order of or much larger than a wavelength, have a very high backscattering coefficient, as pointed out by Pettengill and Hagfors (1974), but would not depolarize the echoes significantly and must be ruled out. Singly scattering, smooth

107

spheres of any other material are also ruled out for the same reason. Pollack et al. (1973) and Pollack (1975) have proposed a multiple-scattering ring model requiring the presence of ice fragments greater than 2 cm (but less than 15 cm) in a radius that fits the 12.6-cmwavelength radar reflectivity and polarization data. Many of their calculations are based on Mie scattering theory which, if interpreted rigorously for smooth spheres, would require the single-scattering component of the observed backscatter radar cross section to increase rapidly with frequency. If the preponderance of particles possess radii near the upper limit of the allowed radius in this model, one might expect the sharply peaked backscatter associated with transparent spheres having large Mie radii to dominate the multiple scattering, leading to a sharp increase with frequency both in the observed radar cross section and in the degree of echo polarization. This is not seen. If the particles have radii predominantly near the low end of the limit where the Mie scattering at the 12.6-cm wavelength lacks a strong backscatter component, multiple scattering will dominate and the increase of the radar cross section with the frequency will be less, although probably still significant. Pollack (1975) claims that his results, although based on Mie scattering calculations, are not critically dependent on the assumption of particle sphericity, since the essence of his model is a high singlescattering integrated (Bond) albedo; thus, because of subsequent multiple scattering he claims that his model is not sensitive to the detailed scattering diagram of a particular particle. In view of the observed independence of radar cross section and echo polarization with wavelength, we feel that the ring particles m u s t be rough at the scale of 3.5 cm. There are two possible roughparticle models that will satisfy all of the available observations~ including the h>w

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(-IOL1)STEIN E T AL.

emissivity and high opacity found by Berge and Muhleman (1973) and Briggs (1974) at eentimetrie wavelengths. First we consider jagged, h)ssless ice particles of size of the order of a wavelength or larger. These would have radar cross sections comparable to their geometric cross sections on average and wouhl be effective depolarizers by virtue of multiple internal reflections as well as multiple external scattering, as suggested t)y Pollock. If there were appreciable space t)etween the particles, the overall radar cross section (normalized by the ring area) wouhl be less than 1. With an increase in the density of partMes per unit area, the radar cross section wouhl also increase until mutual shadowing and multiple scattering became effective. Thus, the overall scattering would tend toward the Lambert law; i.e., for a fixed angle of illumination, the apparent surface brightness would be independent of the angle of observation. The radar cross section for L a m b e r t scattering (normalized l)y projected ring area) is = 2 sin]B], where B is the angle of the E a r t h above the ring phme. For our observations B = - 2 4 ? 4 , yielding z = 0.83, too low to fit the data. if more particles are added to the model, making the ring system thick, less radiation would emerge from the far side than from the near. The normalized cross section would then tend toward the limit = 4 sin[B I . I n this way, the radar data can just be •recounted for. A thick ring, however, m a y run into dynamical difficulties. Cook et al. (1973) have shown that collisions between particles drive the system toward a monolayer. Thus, for this scattering model (as for Pollack's) some mechanism must be found to maintain a ring thickness perhal)s 10-100 m deel). We note, howeve,', th'tt Ol)tic'd observations

made during tile Earth's passage through tile ring plane are consistent with a thickhess of 1-10 km (Foeas and Dollfus, 1969). A second type of rough-particle model requires relatively large (meter-sized) metallic particles. If these are rough at the scale of the radar wavelength, their backscattering dh'ectivity of 8,/3, combined with their high intrinsic reflectivity (conductivity), could yield the necessary high radar cross sections per particle. The diffuse scattering woukt also give a high degree of depolarization, although the surfaces must t)c very jtLgged to depolarize coherent incident radiation as efficiently as interparticle multiple scattering. The surfaces of these metallic fragments are assumed to be covered with water frost in order to m'ttch the. optical, infrared, and millimeter ra(lio observations. The high metallic conductivity, of course, serves equally well in reducing thermal emissivity as in reflecting the incident radar energy. A difficulty with this model, of course, is the necessity of finding metallic particles where they ,night not otherwise be expected. The problem of explaining tile "excess" power observed in the central part of the spectrum remains. Three possibilities which might seem naively phmsible are: (1) Particles in the ring phme which lie outside the visible rings. Such scatterers move more slowly and thus have mu'rower spectra. (2) Particles at the radii of the observed rings, but in orbits of high inclination to tile line of sight. Their Doppler shifts would be low, yielding narrow spectr'~. (3) Particles entrained in the S'~turnian atmosphere, and thus obliged to corotate with the planet. These wouht, therefore, have the necess'u'y low velocities. Discussing these possibilities in order, we note t h a t tile partMes of the first postulate must fall within the observing beamwidth ,,f 0?04. C,ah'ulation shows that the spectral sha.pe corresponding io echoes from particles

RINGS OF SATURN at this outer limit will h a v e a m i n i m u m at zero and a m a x i m u m near a 0.49-MHz Doppler shift at a 3.5-cm wavelength (marked as f~ in Fig. 1), in conflict with the r a d a r results. In a n y event, it seems i m p r o b a b l e t h a t the n u m b e r of particles implied would have escaped optical detection in these orbits. T h e second possibility is intriguing, since the requisite n u m b e r of particles would be so widely and thinly distributed (as a halo) t h a t t h e y could well escape optical detection. The chief objection appears to center on how t h e y would escape collisions with the visible ring material which h a v e served to concentrate those rings into a narrow plane. I t is barely possible t h a t t h e y could exist at radii just outside the A ring, and escape collision b y virtue of low-density, minimal perturbation, and consequent "safe" orbits, but this seems unlikely. If spherically distributed, their m e a n p e r t u r b ing effects on the rings inside t h e m would be nil. T h e third possibility requires t h a t particles large enough to support r a d a r echoes exist in the a t m o s p h e r e of Saturn above those regions where the atmospheric pressure-broadened a m m o n i a absorption line would otherwise a t t e n u a t e the radio signals. Since the severely a t t e n u a t i n g region lies below a b o u t 2 bars of pressure, it is hard to see what m e c h a n i s m could create or support such large particles in such a thin atmosphere. We feel t h a t this possibility, therefore, is also v e r y unlikely. Nevertheless, we note t h a t the limb Doppler shift of atmospherically entrained scatterers is 0.53 M H z (marked as f2 in Fig. 1) and t h a t the corresponding spectral "excess" fits the observations well for a p l a n e t a r y r a d a r cross section equal to 15% of the p l a n e t a r y geometric cross section. I t is obvious t h a t the next generation of r a d a r observations should include b o t h time-delay and frequency resolution, in order to locate the source of the a n o m a lously echoing component. Suet1 observa-

109

tions are planned b y the authors in early 1976. CONCLUSION We h a v e examined the three m a j o r properties of r a d a r echoes from the rings of S a t u r n : the almost total depolarization, the extremely large and (at least between 3.5 and 12.6 cm) frequency-independent scattering cross section, and the a n o m a lously large a m o u n t of low-frequency echo power. N o n e of our t e n t a t i v e l y offered explanations for these characteristics is completely free of difficulty. Nevertheless, a model which hypothesizes a thick cloud of irregular chunks of water ice a few centimeters or larger in radius, and one which postulates a m o n o l a y e r of multimeter-sized water-frost-coated metallic chunks both seem capable of explaining the first two of the m a j o r r a d a r properties. N o n e of the suggested explanations for the excess low-frequency spectral power appears completely free of difficulty. ACKNOWLEDGMENTS We grateful|y acknowledge support by the National Aeronautics and Space Administration for the research reported here under NASA Contract NAS 7-100 (at the Jet Propulsion Laboratory) and under NASA Grant NGR 22-009-672 (at the Massachusetts Institute of Technology). We are also particularly indebted to the efforts of Thomas l)ickinson and the other staff of the Arecibo Observatory in overcoming several last-minute problems and in bringing the new S-band transmitter into operatiou in time to allow these measurements to be made. The Arecibo Observatory of the Natiolml A.stronomy and Ionosphere Center is operated by Cornell University with support from the National Science Foundation and from the National Aeronautics and Space Administratiou. REFERENCES B~':RG,,:,G. L., A~D MUHLEMAN,D. O. (1973). High angular resolution observations of Saturn at 21.1-cra wavelength. Astrophys. J. 185, 373-382. BRINGS, F. H. (1974). The microwave properties of Saturn's rings. Astrophys. J. 189, 367-377. COOK, A. F., FRANKLIN, F. A., AND PALLUCONI, F. I). (1973). S'~lurn's rings--a survey. Icarus 19~ 317-337.

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FOCAS, ft., AND DOLLFUS, A. (1969). Propri6t6s optiques et l'epaisseur des anneaux de Saturne observds par la tranche en 1966. Compt. RetM. 268, 100-103. GOLDSTFIN, R. 3f., AND MoJtms, (;. A. (1973). Radar observatio~ls of the rings (Jf Saltll'll. Icarus 20, 260-262. IN'gALLS, R. P., AND SH.teIltO, [. I. (1975). Privale conmiutlieaI ion. Ll.:w~s, J. S. (1972). Low temperatu~'e co~ldensal.ion froth1 the solar nebula. Icarus 16, 241252. MORRISON, D., ,XND CI~UIr:SUANK, ]). P. (1974). Physical properties of the nalural salellites. Space Sci. Rev. 15, 722-732.

PETTENGILL, G. tt., AND HAGFORS, T. (1974). Comment on radar scattering from Saturn's rings. Icarus 21, 188-190.

PII.CHER, C. B.~ CHAPMAN'~C. R., LEBOBSKY~L. A., .XND KIr:FFmb H. H. (1970). Saturn's rings: ldeatificatinlt of water fn~st. Science 167, 13721373. POLLACK, J. 13. (1975). The rings of Saturn. Space So/. Re~,. 18, 3 97.

POLLACK~ J. B.~ SUMMERS~ i.~ AND BALD'WIN~B. (1973). Estimates of the size of the particles in the rings of Saturn and their cosmogonic implications. Icarus 20, 263-279.