Radar observations of Saturn's rings at intermediate tilt angles

iCARUS 41,381-388 (1980)

Radar Observations of Saturn's Rings at Intermediate Tilt Angles STEVEN J. OSTRO National Astronomy and Ionosphere Center, l Cornell University, Ithaca, New York 14853

GORDON H. PETTENGILL Department o f Earth and Planetary Sciences, Massachusetts Institute o f Technology, Cambridge, Massachusetts 02139

AND

DONALD B. CAMPBELL National Astronomy and Ionosphere Center, ~Arecibo, Puerto Rico 00612 Received October 5, 1979; revised November 21, 1979 We report 12.6-cm-wavelength radar observations of Saturn's rings made in 1977, 1978, and 1979, corresponding to ring-plane tilt angles of 18.2°, 11.70, and 5.6°, respectively. When combined with the theoretical calculations of J. N. Cuzzi and J. B. Pollack (1978, Icarus 33, 233-262) and previous radar results, our measurements of geometric albedo, a, and circular polarization ratio, /~c, provide significant constraints on ring structure. The observed variation in albedo with tilt angle, D, rules out large-particle monolayer models. On the other hand, many-particle-thick (extendedqayer) models postulating ice or metal particles are consistent with the observed variation in a(D). We determine that/Zc = 0.40 _ 0.05 at D = 11.7°. This value is significantly lower than the 3.5-cm-wavelength value for/~c of 1.00 _+ 0.25 measured by R. M. Goldstein, R. R. Green, G. H. Pettengill, and D. B. Campbell (1977, Icarus 30, 104-110) at D = 24.4 °, suggesting that the radar polarization of Saturn's rings depends on wavelength or tilt angle, or both. These polarization results provide restrictions on ring-particle shape which are more severe for monolayer models than for extended-layer models.

Muhleman, 1973; Berge and Read, 1968; Briggs, 1974; Cuzzi and Dent, 1975; Janssen Current concepts of the physical struc- and Olsen, 1976; Muhleman et al., 1976; ture of Saturn's spectacular ring system Schloerb et al., 1979a,b) yield brightness have been profoundly affected by determi- temperatures an order of magnitude lower nations of the rings' microwave properties. than the physical temperature of the rings Radar observations by Goldstein and given by infrared observations (see review Morris (1973), Goldstein et al. (1977), and by Morrison, 1976), a result which can be Pettengill et al. (1980; see also Ostro, 1978) understood in terms of a very low ringhave revealed that the rings are remarkably particle emissivity (Pollack et al., 1973; efficient back scatterers of 3.5- and 12.6-cm Pollack, 1975). Theoretical calculations by radar waves. Passive radio observations at Cuzzi and Pollack (1978) have demoncomparable wavelengths (Berge and strated that various models of ring structure are consistent with both a low microwave ~Operated by Cornell University under contract emissivity and a high radar reflectivity. with the National Science Foundation and with support from the National Aeronautics and Space Admin- Although these calculations exclude siliistration. cates as the primary ring constituent, sevINTRODUCTION

381 0019-1035/80/030381-08502.00/0 Copyright t~) 1980 by Academic Press, Inc. All rights of reproduction in any form reserved.

382

OSTRO, PETTENGILL, AND CAMPBELL

eral models postulating either metal or wat e r - i c e particles, distributed either in a m o n o l a y e r or in a many-particle-thick extended layer, are apparently permissible. As pointed out by Cuzzi and Pollack, measurements of radar geometric albedo, a, at widely spaced values of the ring-plane tilt angle D, should be able to distinguish a m o n o l a y e r f r o m an extended layer on the basis of the o b s e r v e d a(D) variation. Unfortunately, the early radar observations spanned a limited range of (large) tilt angles: 0.36 < sin D < 0.44. In this p a p e r we report radar observations of the rings at three significantly smaller tilt angles: 18.2 °, 11.7 °, and 5.6 °, corresponding to sin D = 0.31, 0.20, and 0.10, respectively. Our albedo and polarization results significantly narrow the field of acceptable ring models and provide firm restrictions on the radar scattering properties of individual particles. OBSERVATIONS

AND

DATA

ANALYSIS

Saturn's rings were o b s e r v e d with the Arecibo 2380-MHz (S-band) radar on one night in 1977, on six nights in F e b r u a r y 1978, and on six nights in F e b r u a r y 1979. (See Table I for observational p a r a m e t e r s and s y s t e m characteristics.) Each night's observation began with transmission of an unmodulated (CW) w a v e for a duration equal to the difference between the total available hour-angle coverage of Saturn and the round-trip time delay to Saturn. After a nearly 2-hr waiting period, the Doppler-shifted echo was received for a similar duration. The received signal was amplified, c o n v e r t e d to video frequencies, and fed to a 1008-channel digital autocorrelation spectrum analyzer. Each second, the accumulated three-level-by-three-level clipped approximation, r3(t), to the " t r u e " multibit autocorrelation function r(t) was recorded on magnetic tape. Later, r(t) was extracted (Hagen and Farley, 1973; Conklin, 1976) and Fourier t r a n s f o r m e d to yield p o w e r spectra with a fundamental resolution of about 10 k H z . The receiver polariza-

TABLE

I

O B S E R V A T I O N A L PARAMETERS A N D R A D A R SYSTEM CHARACTERISTICS a Dates (UTC)

M e a n time of reception

1977 (April 1)

1978 (Feb. 17 t h r o u g h 22)

1979 (Feb. 13, 18, 20, 21, 22, 23)

01 h53m

05h30 m

051'23 m

18.2 ° 0.31 7.791 02h23 m

11.7 ° 0.20 4.925 02h17 m

5.6 ° 0.10 2.239 02h19 m

1566 sec

9567 sec

7938 sec

(UTC) D sin D Ap, 10 TMm s Round-trip e c h o delay Total integration time Zenith angle o f Saturn at transit Mean system temperature Mean one-way a n t e n n a gain Transmitted power

0°

4°

9°

79°K

71°K

91°K

68.9 db

68.7 db

68.5 db

340 k W

300 k W

390 k W

a H e r e D is ring-plane tilt angle and Ap is the s u m o f the projected areas o f the u n s h a d o w e d A and B rings (see text).

tion was switched once e v e r y 3 min between the s a m e ( " S C " ) rotational sense of circular polarization as had been transmitted, and the o r t h o g o n a l ( " O C " ) sense. Thus, each night's data set consisted of f r o m two to five echo spectra in each sense of circular polarization. The radar cross section (O'oc or O'sc) for each run was determined by simple integration of the u n s m o o t h e d echo p o w e r spectrum. The geometric albedo is a = (6"oc + 6rsc/4 (see Campbell et al., 1977), where the carats denote normalization to the projected geometric cross-sectional area, A o, of the u n s h a d o w e d , c o m b i n e d A and B rings. Finally, the circular polarization ratio was calculated: /zc = trsc/troc. Our measurements of albedo and circular polarization ratio are given in the lower half of Table II. We assign a minimum 25% fractional uncertainty to m e a s u r e m e n t s of& and a to reflect our estimate of systematic errors. Because determinations of polarization ratio should be immune to systematic

383

RADAR OBSERVATIONS OF SATURN'S RINGS TABLE II SUMMARY OF SATURN'S RINGS RADAR RESULTS TO DATE a AUTHORS

D

k(cm)

Goldstein, Morris (1973)

26.4 °

12.6

Goldstein et al. (1977)

24.4 °

3.5 12.6

Pettengill et al. (1980)

21.4 °

12.6

This paper

18.2 ° 11.7° 5.6 °

12.6 12.6 12.6

a

O'OC

/tc

O'SC

]'gL

O'SL

0.68 -+ 0.17 0.34 _+ 0.06

1.00 -+ 0.25

0.68 -+ 0.13

0.68 -+ 0.13 1.0 - 0.3 0.83 -+ 0.21

0.24 _+ 0.06 0.27 -+ 0.07 ~<0.27

0.57 _+ 0.12 0.40 +_ 0.05

0.61 -+ 0.15 0.76 _+ 0.19 <-0.52

0.35 -+ 0.09 0.30 _+ 0.08 <-0.55

Measured values of geometric albedo, ix, normalized radar cross section, &, circular polarization ratio,/~c, and linear polarization ratio, /zl, measured at ring-plane tilt angle, D, and wavelength, k, are listed in chronological order of the radar observations. Receiver polarization is designated as " S C " (same sense of circular polarization as transmitted), " O C " (sense of circular polarization orthogonal to that transmitted), or " S L " (same sense of linear polarization as transmitted).

effects, the uncertainty associated with/xc is the root mean square of the statistical standard errors associated with estimation of the weighted-mean values of ~roc and ~I'SC,

Received power levels in 1977 and 1978 were quite strong, yielding useful estimates of both albedo and polarization ratio. The relatively small fractional uncertainty associated with determination of tZc in 1978, compared to the corresponding value in 1977, reflects the sixfold greater integration time in 1978 (see Table I). Unfortunately, echo strength in 1979 was unexpectedly low and the rings were not detected in either polarization, even after weighting and summing six nights of data. For these observations, we have calculated the received p o w e r levels needed for the optimally processed signals to e x c e e d the rms fluctuation in the associated noise b y a factor of 5. The corresponding upper limits on 6"0o O'sc, and ot are given in Table II. The curves shown in Fig. la correspond to weighted sums of all the spectra obtained in F e b r u a r y 1978, smoothed to a resolution o f 100 kHz. The solid curve in Fig. lb is the sum of all 1978 spectra in both polarizations, folded about zero Doppler shift to

improve signal to noise; the dotted curve is the spectrum calculated for a model consisting only o f an A ring and a B ring, with the A ring 86% as reflective as the B ring, as suggested by least-squares inversion of 1976 delay-Doppler data (Ostro, 1978; Pettengill et al., 1980). The arrows in Fig. 1 denote spectral edges of the echo expected for such a model. [Throughout this paper we use boundaries for the A ring (2.03 to 2.29 Saturn radii) and the B ring (1.53 to 1.95 Saturn radii) consistent with Pettengill et al. (1977), Ostro (1978), and Cuzzi and Pollack (1978)]. Within limits set by the background fluctuations, there is no evidence for the low-Doppler excess power reported by Goldstein and Morris (1973) and Goldstein et al. (1977). This particular subject is discussed in detail by Ostro (1978) and Pettengill et al. (1980). DISCUSSION

Included in Table II are reflectivity and polarization results obtained from early studies of the rings at large tilt angles. The only observation of the rings at a wavelength, h, of 3.5 cm (Goldstein et al., 1977) provided estimates of both/Xc and ot at D = 24.4 °. There have been two single polariza-

384

OSTRO, PETTENGILL, AND CAMPBELL 16

I

I

I

I

I

~'1

I

f

[

,

,1

t2

i 48 ~

b.li •

o_

,

i

,

600

500

0

-:300-600 (KHz) ¢

,

0

200

1 400

600

Doppler Frequency

FIG. 1. (a) Saturn's rings' 1978 spectra measured in "SC" (dotted curve) and "OC" (solid curve) polarization senses. Received power, in units of standard deviations of the accompanying noise, is plotted against Doppler shift. Zero frequency corresponds to the Doppler shift of the center of mass of the Saturn system. Arrows delineate spectral "edges" expected from a model withjust A and B rings (see text). (b) Comparison of the folded sum (solid curve) of OC and SC echo spectra with the spectrum (dashed curve) calculated for the ring model described in the text. Note that the abscissa scales in (a) and (b) are different.

tion measurements of radar cross section at a 12.6-cm wavelength and large tilt angles: Goldstein and Morris (1973) measured &oc = 0.68 - 0.17 (Goldstein, 1977) at D = 26.4 ° and Pettengill et al. (1980) measured &SL = 0.83 --+ 0.21 at D = 21.4 ° . Unfortunately, the orthogonally polarized contributions were not determined in either of these two studies, precluding estimation of the geometric albedo. The only available estimate of the rings' 12.6-cm polarization behavior at large tilt angles is the value (1.0 _ 0.3) for the linear polarization ratio, /-gL = O ' O L / O r S L , reported by Goldstein et el. (1977). Their experiment involved two nights of bistatic (two-station) observation. Bistatic operation c o m p o u n d s the difficulty inherent in linearly polarized radar measurements, which require extreme care with regard to polarizationplane position angles; relatively small errors in angle determination can result in overestimation of/~L. In this light, we feel that the uncertainty assigned to the measurement of /£L by Goldstein et al. (1977) may have been too small, and have doubled their lower error bar accordingly. On the other hand, circularly polarized

observations obviate involvement with position angles. We believe that the 12.6-cmwavelength measurement of/Xc at D = 11.7° (this paper) and the 3.5-cm-wavelength measurement of/~c at D -- 24.4 ° (Goldstein et al., 1977), both of which resulted from at least five nights of observations, are probably the most reliable values in Table II. As discussed at length below, these results suggest that the rings' polarization properties depend on wavelength or tilt angle, or both. Figure 2 shows all existing estimates of albedo as a function of tilt angle. For the single-polarization measurements, we designate limits on the albedo: a = (1 + /-0 &/4 under the assumption that 0.4 -< /~ -< 1.0. The theoretical ring models of Cuzzi and Pollack (1978), hereafter referred to as " C P , " include five classes of monolayer models: (1) very large (radius, a, much larger than 1 m) metallic particles, (2) very large " a s s e m b l a g e s " of small, high albedo scattering elements embedded in an essentially transparent matrix; (3) centimeter- to meter-sized ice particles; (4) centimeter- to meter-sized silicate particles; and (5) centimeter- to meter-sized metal particles. The last two classes are excluded by CP due to

RADAR OBSERVATIONS OF SATURN'S RINGS

nonspherical particle is well represented by

0.t

0.2

sin D 0.3

0.4

0.5

I

I

I

I

I

0.70

~ " ~ , , Monolayer of ~..r cje particles 0.6C

0.5(2 O

k

Monolayer of ~, smollice particles ~

0.30

020

' I

516

385

T' i ..-~o

'

:

I

k I

~

,'/~ L" 0-4 :

i

--

I

I

~o. I

I

tt.7 t82. 21.4 24.4 ~ . 4 D (degrees)

FIG. 2. Geometric albedo, ~t, is plotted against tilt angle, D. Observational estimates of the 12.6-cmwavelength albedo are shown as filled circles; the only available 3.5-cm-wavelength estimate is shown as an empty circle. Error bars designate uncertainties assigned to measured values of albedo except for the data point at sin D = 0.1 corresponding to the upper limit on albedo set by the 1979 observations. As discussed in the text, the albedo for tilt angles 21.4 ° and 26.4 ° must be inferred from measured values of single-polarization radar cross sections, &, and poorly known polarization ratios, /~. Dotted vertical lines indicate the range of albedo values estimated from c~ = (1 + / z ) & / 4 for 0.4 <-/.~ -< 1.0. The two curves illustrate the variation in a(D) expected for monolayer models (after Fig. 15 of Cuzzi and Pollack, 1978).

insufficient radar reflectivity. The geometric albedo for the first two classes is inversely proportional to the rings' projected area, yielding a variation: a(D) - 1/sin D, as indicated in Fig. 2. Despite uncertainties in the radar m e a s u r e m e n t s , the albedo corresponding to the projected area of the unshadowed, c o m b i n e d A and B rings clearly has not increased this dramatically, so large-particle m o n o l a y e r models must be excluded. The radar albedos calculated by CP for their more promising small-ice-particle m o n o l a y e r models are displayed in Table III. CP define a shape p a r a m e t e r , x0, equal to the m a x i m u m value of x = 2rra/h for which the scattering phase function of a

the theoretical phase function of a sphere of equal volume and of the same refractive index. All three models in the table assume particle shapes characterized by x0 = 8. T w o models postulate narrow distributions of particle size about a specified mean radius; the third model a s s u m e s a broader power-law distribution [n(a) - a-3, a -> 1 cm]. As illustrated in Fig. 2, the variation a(D) against D for the entire third class of m o n o l a y e r models is less than that for the large-particle classes. Because of the uncertainty in the 12.6-cm albedo at large tilt angles, this third class cannot be excluded on the basis of its predicted a(D) dependence. H o w e v e r , the power-law model is unique in that it predicts a wavelengthindependent albedo. I f this model were valid, one would expect the curve drawn in Fig. 2 to intercept the 3.5-cm data point and the 12.6-cm points. Such variation is ruled out b y the 1979 u p p e r limit on albedo at D = 5.6°; therefore a m o n o l a y e r of powerlaw-distributed small ice particles is not permitted. On the other hand, the radar reflectivity of an e x t r e m e l y narrow size distribution can be substantially wavelength dependent. In particular, interpolation between CP models III-3 and III-4 in Table I I I suggests that a m o n o l a y e r of ice particles with m e a n radius near 6 cm might have different albedos at the two radar wavelengths in a m a n n e r quite consistent with the Fig. 2 data. A variety of CP extended-layer models, postulating either ice or metal particles T A B L E III ALBEDOS (~) OF SELECTED CUZZI--POLLACK IcE-PARTICLE MONOLAYER MODELSa Model

Mean radius

a (3.5 cm)

a (12.6 cm)

Ill-3 Ill-4 111-6

4 cm 8 cm Power law

0.64 0.31 0.36

0.19 0.62 0.36

o Reproduced, with permission, from Table II1 of Cuzzi and Pollack (1978).

386

OSTRO, PETTENGILL, AND CAMPBELL

1.0 distributed in a many-particle-thick ring, X=3.5crn yield the large radar cross sections reported O = 24.4 ° f o r D > 24°. The variation in albedo with tilt 0.8 angle is much less dramatic for CP's manyparticle-thick ring models than for their 0.6 monolayer models. In fact, it remains Y-c nearly constant over the range 5.6 ° - D ,~. : ~ 2 . 6 ¢ m 0.4 26.4 ° . Within the uncertainties in the data, D :~| 17 0 such theoretical behavior is consistent with 0.2 the radar reflectivity measurements. Extended-layer models (as well as the single permissible monolayer model disI I I I I I I ~11 I 0 0 0.2 0.4 0.6 0.8 1.0 cussed above) must also explain the rings' F radar polarization properties. In particular, FIG. 3. The function /~c(/t*,F) = [(1 + p~*) an acceptable ring model must explain the - (1 - tt*)F]/[(l + tt*) + (1 - /~*)F] is plotted for observed discrepancy between the rings' several values of /z*. Here /Zc is the net circular circular polarization ratio at different wave- polarization ratio due to both single scattering and lengths and tilt angles (see Table II). The multiple scattering,/z* is the single-scattering circular radar echo from the rings can be modeled polarization ratio, and F is the fraction o f echo power due to single scattering. The multiple-scattering circuas the sum of a singly scattered component lar polarization ratio is assumed to be unity. Brackets characterized by a circular polarization ra- designate observed values of/~c observed at particular tio/Zc = /.t*, and a multiply scattered com- wavelengths, 3,, and tilt angles, D. ponent, assumed to be completely depolarized (/~c -- 1). [This assumption is Although current understanding of sineminently reasonable. Liou and Schotland gle-particle, single-scattering polarization (1971) have shown that jt.~L 0.8 for twice- behavior is far from complete, the magniscattered radiation from spherical particles tudes of the above values of/~* seem realisseveral wavelengths in radius. Deviations tic for irregular Mie particles. [Singly scatfrom sphericity and inclusion of higher or- tered radiation from spheres (Pettengill and ders o f multiple scattering would further Hagfors, 1974) and from Rayleigh-sized randomize the polarization, forcing t~L and particles (Chandrasekhar, 1950, p. 37) is /zc to approach unity.] The net circular completely polarized (/.L* = 0).] Empirical polarization ratio therefore depends on /.~* studies (Sassen, 1975; McNeil and and on the fraction, F , of echo power due to Carswell, 1975; Pal and Carswell, 1977) single scattering: indicate that 0.3 < ~[.L ~. 0.5 for irregular particles with 2zra - 10h, corresponding to (1 + /z*) - (1 - /z*)F /Zc(/~*, F ) = a -6cmath= 3.5cmanda -20croat (1 + /x*) + (1 - #*)F" = 12.6 cm. Empirical and theoretical expeIn Fig. 3,/~c is plotted as a function o f F for rience suggests that in general, /~c -> /-~L. several values of p.*. (As one case in point, the singly scattered For a monolayer, multiple scattering is echo from a distribution of randomly oriassumed to be negligible. Therefore, F =-- 1, ented dipoles would have /~c = l, ~[~L /-~c --= g*, and the measurements o f / ~ c in 1/3; Long, 1965.) While a particle's value Table II necessarily correspond to the in- of/~* will obviously depend on its particutrinsic single-scattering behavior of individ- lar structural configuration, values of /z* ual particles: /~* > 0.75 at ~ = 3.5 cm and between 0.45 and 0.75 seem reasonable for ~* = 0.43 _+ 0.05 (i.e., the weighted mean 6-cm irregular particles observed at either of the 1977 and 1978 estimates) at h = 12.6 radar wavelength. cm. For a monolayer of 6-cm particles to ~

=

RADAR OBSERVATIONS OF SATURN'S RINGS satisfy the radar observations, /z* must be about twice as high at 3.5 cm as at 12.6 cm. The measurements of/Zc suggest that the scale of particle irregularities might be closer to the shorter wavelength. Unfortunately, empirical investigations of variation in/z*(h) for real particles are scarce. In one study by Schotland et al. (1971), lidar observations of ice crystals gave /ZL ~ 0.4 for 16h ~< a ~< 80h and /'~L > 0.8 for a > 280h. Whether a similar trend holds for irregular particles only a few wavelengths in size is unknown; it certainly is plausible. An irregular particle with a -~ 6 cm and shape parameter x0 = 8 would " l o o k " spherical (in terms of its scattering phase function) at h = 12.6 cm but not at h = 3.5 cm. Again, the possibility that real particles might duplicate this behavior in terms of their polarization properties cannot be ruled out. A many-particle-thick ring, whose radar echo presumably includes a strong multiply scattered component, can have F less than unity and/x* less than/xc (see Fig. 3). The 1978 measurement of/-~c therefore requires that b** ~< 0.45 at 12.6-cm wavelength. Qualitatively this means that large (a > 12.6 cm) particles must not be extremely irregular a n d / o r that their surfaces cannot be extremely rough at scales ~>12.6 cm. If low (~<0.15) values o f F are acceptable, there are no analogous restrictions on 3.5-cmwavelength values of/~*. The curves in Fig. 3 suggest that a constant, wavelength-independent value of/z* less than about 0.45 could satisfy the data if the singly scattered fraction of echo power were allowed to increase several-fold as the tilt angle dropped from 24.4 ° to 11.7 ° , Although the CP extended-layer models predict an increase in F as the rings close up, the specific F(D) variation (Cuzzi, 1979) is too gentle by a factor of about 2 to mollify the requirement that/z* be wavelength dependent. H o w e v e r , given the presumed complexity of a many-particle-thick ring, it would be premature to exclude F(D) variation as a partial explanation for the radar polarization results.

387

CONCLUSION

The measurements of Saturn's rings' radar albedo reported here, when coupled with previous observational results and theoretical analyses, rule out all large-particle monolayer models of Saturn's rings. Polarization and albedo measurements apparently demand that if the rings are only one particle thick, most of the constituent particles must be irregular grapefruit-sized chunks of ice displaying wavelength-dependent circular polarization properties. Specifically, the most reliable radar results require that/z* >~ 0.75 at h = 3.5 cm and/z* = 0.43 ± 0.05 at h = 12.6 cm. On the other hand, extended-layer models postulating ice or metal particles are compatible with the radar albedo measurements, and are less severely restricted by the polarization data. F o r these models, variation in F(D) could remove, or at least alleviate, the requirement that/z* be wavelength dependent. Theoretical limits on F(D) for extended layers should be investigated further. Similarly, continued empirical studies of the single-scattering polarization properties of irregular particles are sorely needed. Although Saturn's declination lies outside the coverage of the Arecibo telescope until 1996, the rings remain observable with the Jet Propulsion L a b o r a t o r y ' s Goldstone radar. Additional radar measurements at 3.5-cm and 12.6-cm wavelengths should be made as the rings open up, to settle the question of whether the rings' radar behavior depends on wavelength or tilt angle, or both. ACKNOWLEDGMENTS We gratefully acknowledge the assistance of the staffofthe Arecibo Observatory during the 1977, 1978, and 1979 observations. We particularly appreciate the help of Ray Velez with operation of the S-band transmitter and the telescope pointing system. We thank Jeff Cuzzi for valuable discussions of theoretical ring models. The MIT portion of this research was supported by NASA Grant NGR 22-009-672. The Arecibo Observatory is part of the National Astronomy and Ionosphere Center.

388

OSTRO, PETTENGILL, REFERENCES

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