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Interferometry of Saturn and its rings at 1.30-cm wavelength
ICARUS 42, 125-135 (1980)
Interferometry of Saturn and Its Rings at 1.30-cm Wavelength I F. P E T E R S C H L O E R B , 2 D U A N E O. M U H L E M A N , AND G L E N N L. B E R G E Division o f Geological and Planetary Sciences and Owens Valley Radio Observatory, California Institute o f Technology, Pasadena, California 91125 Received N o v e m b e r 16, 1979; revised January 15, 1980 We present interferometric observations of Saturn and its ring s y s t e m m a d e at the Hat Creek Radio A s t r o n o m y O b s e r v a t o r y at a wavelength of 1.30 cm. The data have been analyzed by both model-fitting and aperture s y n t h e s i s techniques to determine the brightness t e m p e r a t u r e and optical thickness of the ring s y s t e m and estimate the a m o u n t of planetary limb darkening. We find that the ring optical depth is close to thai o b s e r v e d at visible wavelengths, while the ring brightness t e m p e r a t u r e is only 7 _+ l°K. T h e s e observational constraints require the ring particles to be nearly c o n s e r v a t i v e scatterers at this wavelength. A conservative lower limit to the single-scattering albedo of the particles at 1.30-cm wavelength is 0.95, a n d if their composition is a s s u m e d to be water ice, then this lower limit implies an upper limit of 2.4 m for the radius of a typical ring particle. The aperture s y n t h e s i s m a p s show evidence for a small offset in the position of Saturn from that given in the American Ephemeris and NauticalAlmanac. The direction and magnitude o f this offset are consistent with that found from a similar analysis of 3.71-cm interferometric data w h i c h we have previously presented (F. P. Schloerb, D. O. M u h l e m a n , and G. L. Berge, 1979b, Icarus 39, 232-250). L i m b darkening of the planetary disk has been estimated by solving for the best-fitting disk radius in the models. The best-fitting radius is 0.998 _+ 0.004 times the nominal Saturn radius and indicates that the planet is not appreciably limb dark at 1.30 cm. Since o u r previous 3.71-cm data also indicated that the planet was not strongly limb dark (F. P. Schloerb, D. O. M u h l e m a n , and G. L. Berge, 1979a, Icarus 39, 214-230), we feel that the limb darkening is not strongly wavelength d e p e n d e n t between 1.30 and 3.71 cm. The difference b e t w e e n the best-fitting disk radii at 3.71 and 1.30 cm is +0.007 -- 0.007 times the nominal Saturn radius and suggests that the planet is more limb dark at 1.30 cm than at 3.71 cm. Models of the a t m o s p h e r e which have NHa as the principal source of microwave opacity predict that the planet will be less limb dark at 1.30 cm. H o w e v e r , the magnitude of the effect predicted by the NHa models is - 0 . 0 0 9 and only marginally different from the o b s e r v e d value. INTRODUCTION
In two previous papers (Schloerb et al., 1979a,b) we reported on an extensive set of interferometric observations of Saturn and its ring system at a wavelength of 3.71 cm. The principal conclusions of those studies were that the optical thickness of the ring s y s t e m is nearly the same at visible and m i c r o w a v e wavelengths and that the rings have a very low m i c r o w a v e brightness temperature. Our work and that of others (e.g., Pollack, 1975) have shown that the combiContribution No. 3350 of the Division of Geological and Planetary Sciences. 2 Present address: D e p a r t m e n t of Physics and Ast r o n o m y , University of M a s s a c h u s e t t s , A m h e r s t , Mass. 01003.
nation of these two constraints places severe limits on the properties of the ring particles; they must be nearly conservative scatterers at 3.71 cm and their size must be greater than a few centimeters. These properties are consistent with the bulk composition of the particles being w a t e r ice, a material which has been detected in the rings spectroscopically (Pilcher et al., 1970). If the ring particles are nearly conservative scatterers at 3.71 cm, then the ring brightness t e m p e r a t u r e at this wavelength must be due to emission by Saturn that is scattered to the E a r t h by the ring particles (Cuzzi and Van Blerkom, 1974). At shorter wavelengths w a t e r ice particles will eventually b e c o m e n o n c o n s e r v a t i v e scatterers 125 0019-1035/80/040125-115-2.00/0 Copyright © 1980by Academic Press, Inc. All rights reserved of reproduction in any form reserved.
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( o p t i c a l l y thick) a n d e m i t t h e r m a l r a d i a t i o n . W h e n this o c c u r s t h e b r i g h t n e s s t e m p e r a t u r e o f t h e rings i n c r e a s e s a b o v e t h e 3.71c m v a l u e , a n d t h e n a t u r e o f this i n c r e a s e w o u l d p r o v i d e a s e n s i t i v e c o n s t r a i n t on m o d e l s o f the ring p a r t i c l e s . In this p a p e r , we present interferometric observations w h i c h w e h a v e m a d e at a w a v e l e n g t h o f 1.30 c m in an a t t e m p t to p l a c e c o n s t r a i n t s upon the amount of thermal radiation emitt e d b y t h e ring p a r t i c l e s . N o ring r a d i a t i o n in e x c e s s o f t h e a m o u n t o b s e r v e d at 3.71 cm was observed, indicating that the partic l e s a r e n e a r l y c o n s e r v a t i v e s c a t t e r e r s at 1.30 c m as w e l l as 3.71 c m . O u r n e w observations allow a considerable improvem e n t in t h e u p p e r limit to the size o f a t y p i c a l ice p a r t i c l e w i t h i n t h e rings to be made. OBSERVATIONS T h e o b s e r v a t i o n s w e r e m a d e at t h e U n i versity of California's Hat Creek Radio A s t r o n o m y O b s e r v a t o r y at a f r e q u e n c y o f 23 G H z (1.30-cm w a v e l e n g t h ) d u r i n g N o v e m b e r 2 - 2 2 , 1976. T h e u - v c o v e r a g e o f t h e i n t e r f e r o m e t e r w a s d e s i g n e d to p r o d u c e an aperture synthesis map of the Saturn s y s t e m . N i n e different b a s e l i n e s w e r e u s e d to o b t a i n t h e u - v c o v e r a g e s h o w n in Fig. 1. The Hat Creek interferometer (Welch et a l . , 1977) w a s u s e d in t h e w i d e - b a n d c o n t i n u u m m o d e f o r the S a t u r n o b s e r v a t i o n s . In this m o d e , t h e i n c o m i n g signal is split into t w o o r t h o g o n a l , l i n e a r p o l a r i z a t i o n s at e a c h a n t e n n a a n d all f o u r p o s s i b l e p o l a r i z a t i o n p a i r s are i n d e p e n d e n t l y c o r r e l a t e d . T h e f o u r p o s s i b l e c o n f i g u r a t i o n s p e r m i t t w o parallel-feed and two crossed-feed observat i o n s to b e m a d e s i m u l t a n e o u s l y . F o r t h e Saturn observations, the parallel feeds w e r e a r r a n g e d a l t e r n a t e l y to be e i t h e r parallel a n d p e r p e n d i c u l a r to t h e c e n t r a l m e r i d ian o f S a t u r n ( P A = - 7 °) o r p a r a l l e l a n d p e r p e n d i c u l a r to a p o s i t i o n a n g l e 45 ° a w a y f r o m t h e c e n t r a l m e r i d i a n ( P A = 38°). T h e parallel- and crossed-feed observations obt a i n e d in this w a y p e r m i t t e d all f o u r S t o k e s p a r a m e t e r s o f S a t u r n to b e m a p p e d w i t h t h e
V
FIG. 1. u-v coverage of 1976 HCRO 1.30-cm observations, u and v are the components of the interferometer baselines, expressed in wavelengths, projected onto the planet Saturn. The v axis is at a position angle of -6°7 so that it is aligned with the central meridian of Saturn. The axes intersect at u = 0, v = 0. The u axis increases to the left (east) in units of 10,000 wavelengths for Saturn at the distance of 8 AU. The v axis increases upward at the same scale. The visibility function at a point u, v is equal to its complex conjugate at - u , -v. Therefore, both values are plotted since there is information about the source at both locations. m a x i m u m s e n s i t i v i t y . N o p o l a r i z a t i o n eff e c t s w e r e o b s e r v e d , a n d w e shall o n l y present the data obtained with the parallel f e e d s in this p a p e r . T y p i c a l l y , five 200-sec Saturn integrations were vector averaged into a single 1000-sec i n t e g r a t i o n to m a k e t h e d a t a set m o r e c o m p a c t . A p p r o x i m a t e l y o n c e e v e r y 2.5 hr d u r i n g the Saturn observations, a point source of k n o w n flux d e n s i t y a n d p o s i t i o n w a s o b s e r v e d in o r d e r to c a l i b r a t e the g a i n a n d p h a s e o f the i n t e r f e r o m e t e r . T h e i n t e g r a t i o n t i m e on c a l i b r a t o r s w a s t y p i c a l l y 30 min. T h e c a l i b r a t o r s u s e d are l i s t e d in T a b l e I a l o n g w i t h t h e i r m e a s u r e d flux d e n s i t i e s . T h e flux d e n s i t y a n d p h a s e o f C A S A w e r e n o t u s e d to c a l i b r a t e t h e i n t e r f e r o m e t r i c o b s e r v a t i o n s d i r e c t l y , b u t r a t h e r t h e flux d e n s i t y v a l u e in t h e t a b l e w a s u s e d in t h e calibration of the other calibrators. Each of t h e c a l i b r a t o r s in T a b l e I is k n o w n to b e
SATURN'S RINGS AT 1.30 cm TABLE I CALIBRATORS FOR SATURN OBSERVATIONS AT 23 G H z Source
Flux density (Jansky)
CAS A ~ 3C84 3C120 3C273B
256.5 46.2 7.7 36.5
Flux d ensity from s p e c t r u m of J a n s s e n et al. (1974).
time variable, and therefore, their relative flux densities were checked m a n y times during the observing run. Since no variation was detected, their flux densities were assumed to be constant during the observations. The flux density of 3C84 was determined by using one of the 20-ft antennas to measure the relative flux densities of 3C84 and CAS A. The flux density of CAS A at 23 G H z has b e e n taken from a fit to its spectrum by Janssen et al. (1974) which includes their absolute m e a s u r e m e n t at 22.285 Ghz. The value in Table I has b e e n corrected for the decrease in the flux density of 0.6% per year (Dent et al., 1974). The flux density of 3C84 determined by the single antenna observations has also been c o r r e c t e d for the partial resolution o f CAS A by the antenna b e a m with a correction factor of 1.08 __ 0.01 (Janssen et al., 1974). The final value of the flux density of 3C84 is 46.2 _+ 2.5 Jansky, 3 and the flux densities o f the other calibrators in Table I were determined by c o m p a r ison to 3C84 using the interferometer. As can be seen from the discussion in the preceding paragraph, the flux density calibration, which is based upon the measurement of 3C84 relative to CAS A, is accurate to about 6% excluding the uncertainty in the a s s u m e d flux density o f CAS A. This 6% uncertainty is based upon the scatter of the 3C84 to CAS A m e a s u r e m e n t s and 3 1 J a n s k y = 10-26 W m -2 Hz -t.
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does not include all o f the possible systematic effects which might occur. As a further c h e c k on the calibration, we o b s e r v e d Jupiter with the interferometer on its shortest baseline (40 ft) and c o m p a r e d it to 3C84. This observation was corrected for the partial resolution of Jupiter by the interferometer and gave a disk t e m p e r a t u r e of 146 _+ 7°K assuming the disk dimensions in the American Ephemeris and Nautical Almanac. It shall be seen in subsequent sections
that the disk t e m p e r a t u r e of Saturn is 140 _+ 2°K ( A E N A dimensions) which gives a Saturn-to-Jupiter ratio o f 0.95 _+ 0.06. This ratio is in good agreement with those of other o b s e r v e r s at this wavelength, whose values fall b e t w e e n 0.95 and 0.90 (Janssen, 1974). The disk t e m p e r a t u r e s of both planets are about 8% higher than those of other o b s e r v e r s (cf., Klein and Gulkis, 1978; Klein et al., 1978), but this difference is within the experimental errors. DATA ANALYSIS AND RESULTS
We have used both model-fitting and aperture synthesis techniques to analyze the H a t Creek (1.30 cm) data, and we have treated the data in the same manner as o u r previous 3.71-cm data obtained at the Owens Valley Radio O b s e r v a t o r y . The model-fitting analysis is identical to that p e r f o r m e d on the O w e n s Valley data by Schloerb et al. (1979a) in all of its essential characteristics. The planetary and ring dimensions of C o o k et al. (1973) were used to define the sizes o f the model c o m p o n e n t s , and the a p p a r e n t polar radius was taken to be that appropriate for a ring tilt of 15°.3. The distance to the planet and its geocentric position given in the A E N A were adopted for the observations. The data errors, which are used to weight the data in the model fit, were determined from the scatter o f the 1000-sec data points so that the various possible systematic errors that could affect the data are included in the estimation to some extent. The errors on the amplitudes and phases of the visibility function were estimated separately
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since amplitude and phase errors are thought to be mostly independent of each other. The s y s t e m of weights used to fit the models to the H a t Creek data was designed to take into account both the relative data errors and the amount of new information about Saturn provided by each additional data point. The amplitude and phase errors on a given baseline were taken to be the same for all points on that baseline, and the inverse square of these errors provides the basic weight applied to a given data point. H o w e v e r , a further consideration of the weighting system is required since certain regions of the u - v plane were sampled more densely than others. I f the data were we!ghted only on the basis of the data errors, then these highly sampled regions would dominate the model fitting even though they might not be very sensitive to certain model parameters. In order to correct this effect, the baselines were grouped together according to their resolution and the observations on a given baseline were downweighted by the total n u m b e r of observations in that baseline's resolution group. This downweighting m a k e s each group about equally important in determining the best fitting model. The baseline groups were chosen to be: the shortest baseline, the longest n o r t h - s o u t h baseline, the intermediate n o r t h - s o u t h baseline, the e a s t - w e s t baselines whose resolutions were equivalent to or greater than the longest n o r t h - s o u t h baseline, and the e a s t - w e s t baselines whose resolutions were equivalent to the intermediate n o r t h - s o u t h baseline. The 1.30-cm aperture synthesis maps shown here were also produced in the same m a n n e r as the 3.71-cm m a p s of Schloerb e t a l . (1979b). The measured visibility function was Fourier transformed and " c l e a n e d " to produce a m a p which is free from the effects o f sidelobes of the synthesized beam. The synthesized b e a m is obtained by Fourier transforming the u - v coverage obtained by the interferometer, shown in Fig. 1, and we h a v e given a map
DIRTY BEAM
1976 tiCBO
1.30 CM
D 0 /
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FIG. 2. Contour map of the synthesized beam of the 1976 HCRO observations. The contour levels are 90, 70, 50, 30, 10, -10, and -30% of the peak response. The center of the beam is at the center of the map; east is to the left and north is upward. The intervals at the map boundaries are 10 arcsec for Saturn at a distance of 8 AU. of the b e a m obtained in this w a y in Fig. 2. The synthesized b e a m of the H a t Creek observations has lower sidelobes and less resolution than the counterpart from the O w e n s Valley 3.71-cm observations. The aperture synthesis maps compliment the model fitting analysis since they are free from m a n y of the assumptions which go into the models. Thus, they provide a check on the model-fitting results and permit us to search for new, unmodeled features o f the Saturn radio emission. The model-fitting results are s u m m a r i z e d in Table II. Unfortunately, we were unable to obtain useful results for all o f the models which were fit to the O w e n s Valley Saturn data since the H a t Creek data set was insensitive to the C-ring parameters. This insensitivity was primarily due to the lower ring tilt angle, which made the separation of the C ring from the other rings more difficult than it had been earlier in 1976 when the 3.71-cm observations were made. In addition, the H a t C r e e k observations
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SATURN'S RINGS AT 1.30 cm TABLE II MODEL FITTING RESULTS FOR H C R O DATA AT 1 . 3 0 - c m WAVELENGTH
TDISK" (°K) T~ P l a n e t (°K) T~ B l o c k e d b (°K) TB A + B R i n g (°K) X Offset ( e q u a t o r i a l radii) Y Offset ( e q u a t o r i a l radii) Effective disk radius I m p r o v e m e n t in r e s i d u a l s from Model C (%)
Model A (uniform disk)
Model B
Model C
138 139.6 _+ 0 . 6 --0c
137 151.0 -+ 1.0 56.3 ± 6.2 -0c
140 150.0 ± 1.0 5 2 . 9 ± 6.1 6.0 + 1.1 0c
0c
0c
0c
1~ - 23.7
1c - 3.2
Ic 0
Model D
140 153.1 --+ 1.0 26.4 ± 5.9 6 . 8 ± 1.2 0.028 + 0.009 -0.038
+ 0.009 Ic 3.2
Model E
140 153.1 ± 1.0 2 6 . 4 ± 6.0 6.8 _+ 1.2 0.028 c -0.038 c 0.998 ± 0.004 3.2
a Ta~s k = ( h Z / 2 k ) × ( m o d e l flux d e n s i t y / s o l i d a n g l e o f d i s k w i t h A E N A d i m e n s i o n s ) . b Refers to the region of the planet blocked by both the A and B rings. c P a r a m e t e r f i x e d f o r m o d e l fit.
have somewhat less spatial resolution than those obtained at the Owens Valley, making the separation even more difficult. Thus, we are unable to extend the 3.71-cm C-ring results to the 1.30-cm wavelength. Our inability to fit models which include the C ring might raise some questions about the believability of models which include the A and B rings. Therefore, we have fit two models that do not include any radiation from the rings, Models A and B, in order to demonstrate that the ring radiation found in a model that includes the rings, Model C, is significant. Model A is a simple uniformly bright, elliptical disk with Saturn's dimensions. In Model B, we include the effect o f the ring opacity blocking the planetary emission where the rings cross the planet, but constrain the ring brightness temperature to be zero. Finally, in Model C we allow the rings to block the planet and have a nonzero brightness temperature. We note that the residuals to the model that includes all o f the effects of the rings (Model C) are significantly lower than those which do not include all o f the effects (Models A and B) and that the parameters in Model C are all much larger than their errors. The former point might be viewed skeptically since even the addition of irrele-
vant parameters to the model is expected to improve the residuals to the fit. H o w e v e r , we have verified that the improvement in the residuals is significant by comparing it to the improvement shown by other models with three or more parameters. Thus, it is quite likely that the ring radiation in Model C is a real detection. We can also demonstrate our sensitivity to the ring features in a way that is independent o f any model by producing an aperture synthesis map of the ring system. In Fig. 3a we show a map o f the Saturn data which has had the response o f a uniformly bright disk removed from it. The brightness temperature of the disk was adopted to be 140°K since this was the value obtained in Model A. (The brightness temperature is appropriate for the dimensions o f Cook et al. (1973) which were used to do the disk subtraction.) The map shows residual features in the region where the rings cross in front o f the planet and at the positions of the ansae. The negative feature (dashed contours) that appears at the position where the rings cross the planet is due to the opacity of the rings and indicates that they reduce the planetary brightness at that poisition. The positive features at the positions of the ansae are direct detections of
130
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FIG. 3. (a) CLEAN 1.30-cm aperture synthesis map of Saturn with the response to a uniformly bright, 140°Kdisk removed from the center of the map. The disk dimensions are 20.62 x 18.66 arcsec at a Saturn distance of 8 AU. (b) CLEAN map of the residuals to Model C in Table II. (c) CLEAN map of the residuals to Model D, which includes a position offset from the AENA ephemeris. Model D parameters are given in Table II. All of the above maps have the same dimensions and contours. East is to the left and north is upward; the intervals at the map edge are 10 arcsec for Saturn at a distance of 8 AU. The CLEAN beam HPBW is 8 arcsec E-W and 15 arcsec N-S. The deflections in the maps are in units of brightness temperature averaged over the CLEAN beam. The contour values are: 5, 4, 3, 2, -2, -3, -4, and -5°K. Dashed contours represent negative values. the ring r a d i a t i o n a n d f u r t h e r i n d i c a t e that the ring r a d i a t i o n d e t e c t e d in M o d e l C is a real effect. T h e detailed differences b e t w e e n the d a t a a n d M o d e l C m a y be e x a m i n e d b y cons t r u c t i n g an a p e r t u r e s y n t h e s i s m a p of the r e s i d u a l s to M o d e l C. A r e s i d u a l s m a p is produced by Fourier transforming and " c l e a n i n g " the v e c t o r difference b e t w e e n the data a n d the visibility f u n c t i o n o f M o d e l C, a n d this m a p is s h o w n in Fig. 3b. T h e m a p s h o w s a significant n e g a t i v e f e a t u r e o n the e a s t e r n limb o f the p l a n e t a n d small p o s i t i v e f e a t u r e s o n the w e s t e r n a n s a a n d n o r t h e r n limb. This d i s t r i b u t i o n of r e s i d u a l
f e a t u r e s is similar to that f o u n d in the a n a l o g o u s 3.71-cm m a p a n d is p r o b a b l y due to a n e r r o r in the A E N A e p h e m e r i s . T o c h e c k the m a g n i t u d e of this error, we have fit M o d e l D to the data. M o d e l D allows the b r i g h t n e s s r e g i o n s of M o d e l C to be offset from the n o m i n a l A E N A p o s i t i o n a n d s o l v e s for the b e s t fitting offset a n d n e w b r i g h t n e s s t e m p e r a t u r e s at that position. T h e offset v a l u e s in T a b l e II are e x p r e s s e d in u n i t s o f p l a n e t a r y radii since the fit was d o n e after d i s t a n c e n o r m a l i z a t i o n o f the data. I f we use the t y p i c a l d i s t a n c e a n d p o s i t i o n angle o f S a t u r n at the time o f the o b s e r v a t i o n s to d e t e r m i n e the offsets in
SATURN'S RINGS AT 1.30 cm right ascension and declination, then the values are (best p o s i t i o n - - A E N A ) : ARA
=
0.31 _+ 0.08 arcsec,
ADEC = - 0 . 3 2 + 0.08 arcsec.
131
of Saturn is not k n o w n to sufficient precision and since changing the radius is only an approximation to limb darkening. On the other hand, a c o m p a r i s o n of the effective radii determined at 1.30 and 3.71 cm m a y be used to see whether the planetary limb darkening is wavelength dependent, since the uncertainties in the method should affect both sets of data in about the same way. The 3.71-cm effective radius has been determined by a fit of the 1976 Owens Valley data to the identical model used for the 1.30-cm data. Its value of 1.005 _+ 0.003 times the radius of Saturn is 20- larger than the 1.30-cm effective radius, indicating that the planet is marginally less limb dark at 3.71 cm than at 1.30 cm. Interestingly enough, even though the o b s e r v e d variation is only marginally significant, it is in the opposite sense to that e x p e c t e d by models o f the a t m o s p h e r e in which NH3 is the dominant source of opacity at these wavelengths (E. Olsen, private communication). H o w e v e r , the difference between the 3.71- and 1.30-cm effective radii that is e x p e c t e d by the NH3 models is only - 0 . 0 0 9 (as determined by the change in the first zero crossing of the visibility function). Thus, since the o b s e r v e d difference is +0.007 _+ 0.007, it is probably not possible to say that we have detected a significant deviation from the model prediction.
This offset is consistent with that determined in June 1976 at 3.71 c m by Schloerb et al. (1979b) and supports our claim to have detected a small error in the A E N A position since the two e x p e r i m e n t s are totally independent of each o t h e r ? A m a p of the residuals to Model D is shown in Fig. 3c. Although one feature greater than 10remains on the planet, its position on the region of the planet blocked by the rings m a k e s it unlikely to be due to incorrect modeling of the brightness t e m p e r a t u r e regions in Model D. Thus, this single negative lobe must be due to either an unmodeled feature or noise. Since the feature is less than 20- and was not seen in the 3.71-cm maps, it is reasonable to interpret it as noise, and our fit to Model D, therefore, has probably r e m o v e d all of the features of the Saturn radio emission that are detectable given the signal to noise on our data. Finally, we have searched for the effects of limb darkening in our data by solving for the best-fitting disk radius (effective radius) in our models by an analysis of variance method (Schloerb et al., 1979a). The effective radius of Saturn at 1.30 cm is 0.998 _+ DISCUSSION 0.004 times the nominal radius for a model which has been fit with the position offset Ring Brightness Temperature and Optical determined in Model D. This new model, Depth Model E, is also given in Table II, and the The ring brightness t e m p e r a t u r e and optieffective radius result might be taken to cal depth results of Model D are shown in indicate that the planet is not appreciably Table III. The ring brightness t e m p e r a t u r e s limb dark at 1.30 cm. Such a direct interprein this table are normalized by the brighttation of the effective radius is probably not ness t e m p e r a t u r e of the planet since the warranted, however, since the true radius interferometer m a k e s an accurate relative m e a s u r e m e n t of the quantities and since the 4 Pioneer Saturn data have recently been used to produce a new Saturn ephemeris, JPL DE-108 planet is the illuminating source o f the (Miles Standish, private communication). The difscattered radiation from the rings. The optiference between the DE-108 and AENA Ephemercal depths listed in Table I I I refer to the ides agrees with our determination of the position average ring optical depth o v e r the region offset from AENA in June 1976 at 3.71 cm and o f the planet blocked by either the A or B November 1976 at 1.30 cm to within the probable errors (-0.1 arcsec). rings. T h e s e values are model dependent
SCHLOERB, MUHLEMAN, AND BERGE
132
T A B L E III COMPARISON OF 1.30- AND 3.71-cm RING RESULTS
Data Set
Wavelength (cm)
B
fBa
TA+Bb
TB A + B ring TBp l a n ~ (%)
1976 H C R O 1976 OVRO 1973-1974 OVRO
1.30 3.71 3.71
-15°.3 -200.8 - 260.5
0.63 0.68 0.95
0.54 _+ 0.I0 0.66 _+ 0.10 0.97 _+ 0.16
4.4 _+ 0.8 4.2 +_ 0.7 3.1 _+ 0.7
a Fraction of area on planet blocked by the A and B rings that is blocked by B ring. b Optical depth of the combined A and B rings.
since they treat the A and B rings and the Cassini division as a single ring of uniform optical depth. We will consider the effects of variations in optical depth within this ring later in the discussion. The calculation of the value allows for the diffusely scattered component of the ring brightness from this area by assuming that the brightness of the rings is uniform and equal to that determined from the ansae by the models. We have also fit a model identical to Model D to the 3.71-cm data obtained in 1976 and included these results in Table III. Finally, the values for the 3.71-cm data obtained in 1973-1974 which have been included in the table were derived from a model like Model C in this paper since we had no aperture synthesis data to suggest the presence of a position offset. A comparison of the 3.71- and 1.30-cm ring brightness temperatures shows that they are identical within the errors. We further note that the 1.30-cm ring brightness temperature is even more consistent with the 3.71-cm models which included the C ring, h o w e v e r we have not used these results to make comparisons between the two wavelengths since the models are not identical. The lack of any increase in the ring brightness temperature between the two wavelengths indicates that no thermal radiation is required to explain the brightness temperature value at 1.30 cm. The interpretation of the optical depths in Table III is less straightforward than that of the ring brightness temperatures since the A and B rings blocked different relative
areas of the planet during the three sets o f observations. The simplest comparison that can be made is between the 1976 3.71- and 1.30-cm optical depths since the relative areas blocked by the two rings are similar. The solutions for the effective opacity of the combined A and B rings in the two data sets are only lot apart, suggesting that the opacity of the rings is the same at the two wavelengths. This conclusion receives more support if we compare the results of all three experiments to a simple model of the variation of the effective optical depth of the combined A and B rings with ring tilt angle (B). In order to make such a model, we must decide how to weight the individual optical depths of the A and B rings to derive their effective optical depth over the region of the planet they both obscure. Since each ring covers a certain fraction of this region, we have used the relative areas of the two rings to do the weighting. Thus, the effective optical depth is determined by comparing the average brightness temperature of the obscured region to the brightness temperature of the planet. We assume that the average brightness temperature of the obscured region is equal to the average of the brightness temperature of that part of the region blocked by the B ring and the portion blocked by the A ring weighted by their relative areas. Thus, if re~ is the effective optical depth of the combined A and B ring, then e-~7~.dsinIBI) =
fAe-(~'~lsinIBI) + fBe -~,J'~'lBI),
(1)
SATURN'S RINGS AT 1.30 cm where fA and fB are the fractions o f the blocked region o b s c u r e d by the A and B rings and ZA and zB are their respective optical depths. In Fig. 4, we show a comparison of this model (dashed curve) with the effective optical depths obtained from the two sets of 3.71-cm data and the 1.30cm data. In this model we have ignored the Cassini division and placed the boundary of the A and B rings in the middle of the division. We have also a s s u m e d that the optical depth of the B ring is twice that of the A ring. We have also considered models which include the effects of the Cassini division (solid curves in Fig. 4). F o r simplicity, we have a s s u m e d that the division has zero optical thickness and that T A = 1 T B . F o r this case, the effective optical d e p t h of the A and B rings and Cassini's division is given by e--r~.IsinlBI = fAe--%lsinlBI
+ A e -'"m"lBI + feD,
(2)
where fA, fB and fCD are the fractions o f the i
I
i
I
i
i/
Optical Depth of Combined A + B Ring as o 1.4 - Function of Ring Tilt Angle [B)
m +
1.2 - -
--
Includes
----
Ignores Cossini Division _ I "cA - -2 "cB
Cossini
I .0 - _ .to
Division
rs f
/ /
1975-1974
OVRO
_ j.
~:x 0 . 6 - -
.-'"
1 9 7 6 HeRO
y__
. / g r e = 1.¢
/////
0.8
=1.2
Ring Particle Size and Composition
1976
0.2
i
I
I
I0
I 20
IBI
blocked region o b s c u r e d by the A and B rings and the Cassini division. We note that for small values of B in the Cassini division model [Eq. (2)], %n = B lnfcD SO that ~'en 0 as B ~ 0. Similarly, for the model which does not include the Cassini division [Eq. (1)] %~ -~ - B lnfA + rA for small B since the optical depth of the B ring is greater than that of the A ring. Thus, for both models in the low tilt angle limit, the effective optical depth of the combined ring a p p r o a c h e s the optical depth of the least optically thick region in the rings. Interestingly enough, the points on the figure a p p e a r to agree better with the models which include the Cassini division. A formal fit of this model to the points to determine the best values o f % and TB gives TA = 0.7 - 0.2 and 7B = 1.4 + 0.1. The other model, which ignores the Cassini division, gives 7"A = 0.3 ± 0.1 and ~'B = 1.0 -+ 0.1. Neither model is significantly better than the other, since there are so few points to fit. H o w e v e r it is clear that the p r e s e n c e or absence of the Cassini division affects the formal optical depth results. It is also clear, and more relevant to the present discussion, that the optical depths o b s e r v e d in the three experiments at two wavelengths m a y be satisfactorily explained by a single optical depth model. Thus, no wavelength dep e n d e n c e of the ring optical depth is required by the 1.30 and 3.71 cm data.
ra=0 5
.~ 0 . 4 o. O
0
133
i
I 30
(degrees)
F i G . 4. O b s e r v e d o p t i c a l d e p t h s o f t h e c o m b i n e d A and B rings c o m p a r e d to models described in the t e x t .
Solid-curve models include the Cassini division and assume it to have no opacity. Dashed-curve models ignore the Cassini division and place the boundary between the A and B rings in the center of the division.
The preceeding c o m p a r i s o n of the 3.71and 1.30-cm results indicates that the scattering and absorption properties of the ring particles are virtually identical at the two wavelengths. The combination o f an appreciable optical depth and a very low ring brightness t e m p e r a t u r e indicates that the particles have a very high single scattering albedo, and our results at both wavelengths are consistent with c o n s e r v a t i v e scattering. If we adopt a simple many-particle-thick ring of isotropically scattering particles as our ring model (Schloerb et al., 1979a),
134
SCHLOERB, MUHLEMAN, AND BERGE
then we may place limits upon the particle single-scattering albedo, t~o: 0.95 < cb0 ~< 1.00. The lower limit has been chosen to be conservative (about 2or). These limits on ~0 may be interpreted in terms of the ring particle size and composition, as has been pointed out by several previous workers (e.g., Pollack, 1975). A lower limit on the ring particle size of a few centimeters is possible based upon the high radar cross section and the similarity of the visible and microwave optical depths. This lower limit is composition independent and has been combined with the measured single-scattering albedos to imply that the particles must be composed of a material which is either a very good reflector of microwaves or a very poor absorber of them. Water ice is thought to be the most likely candidate since it has very low loss at microwave frequencies and has been detected in the rings spectroscopically (Pilcher et al., 1970). If a water ice composition is assumed, then we may use our lower limit on &0 to place an upper limit on the particle size. This upper limit on the particle radius is 2.4 m, assuming the absorption coefficient quoted by Janssen and Olsen (1978), and it is better than our previous upper limit of 20 m that was obtained from the 3.71-cm data. The new upper limit is comparable to that of Janssen and Olsen (1978) from observations at 8mm wavelength, h o w e v e r these measurements require a small amount of thermal emission from the rings while the 1.30-cm data are consistent with conservatively scattering particles. The amount of thermal emission required by the 8-mm observations can be made consistent with the conservative scattering result at 1.30 cm if the ring particles have a single size of about 2 m. H o w e v e r , recent estimates of the ring brightness temperature at wavelengths shorter than 8 mm (Klein e t al., 1978; Epstein et al., 1980) are not consistent with this single particle size, and a broad range of sizes may be required to explain all of the
estimates of the ring brightness temperature at millimeter and centimeter wavelengths. Conclusions
We have made observations of Saturn and the ring system at a wavelength of 1.30 cm and compared them to our previous observations at 3.71 cm. There is no evidence for any wavelength dependence of the ring particle properties or the limb darkening of the planetary disk. The ring particles are nearly conservative scatterers at both wavelengths, and the ring optical depths are the same to within the probable errors. A conservative lower limit of 0.95 has been placed on the single scattering albedo at both wavelengths. The observed difference in the bestfitting planetary radius at 1.30 and 3.71 cm, which we have interpreted in terms of limb darkening of the planet, is marginally different from the difference predicted by models of the atmosphere in which NH3 is the principal source of microwave opacity (such as those described in Klein et al., 1978). However, in view of the magnitude of the errors and the model dependence of the interpretation, it is not possible to say that we have detected a significant deviation from the model prediction. In spite of this, we find the observed discrepancy interesting since Klein et al. find that a pure NH3 model may not reproduce the shape of the spectrum between 10 and 21 cm. Clearly future, more sensitive, observations of the limb darkening of Saturn will be useful to the interpretation of the Saturn microwave spectrum. ACKNOWLEDGMENTS We are very grateful to Drs. Jack Welch, Mel Wright, Rick Forster, John Dreher, and the staff of the Hat Creek Radio Astronomy Observatory for making these observations possible and enjoyable. We appreciate Dr. Eugene Epstein making his results available to us in advance of publication. This work constitutes a portion of F.P.S.'s doctoral dissertation and was supported by NASA Grants NGR-005-002-114 and NGL-05-002-003 and by NSF Grant AST-77-00247.
S A T U R N ' S R I N G S A T 1.30 c m F.P.S. acknowledges support by NASA Grant NGL22-101-023 during the final preparation of this manuscript. REFERENCES American Ephemeris and Nautical Almanac (19731976). U.S. Govt. Printing Office, Washington, D.C. COOK, A. F., FRANKLIN, F. A., AND PALLUCONI, F. D. (1973). Saturn's rings--A survey. Icarus t8, 317337. CUZZI, J. N., AND VAN BLERKOM, D. (1974). Microwave brightness of Saturn's rings. Icarus 22, 149158. DENT, W. A., ALLER, H. D., AND OLSEN, E. T. (1974). The evolution of radio spectrum of Cassiopeia A. Astrophys. J. Lett. 188, LI I-Ll3. EPSTEIN, E. E., JANSSEN, M. A., Cuzzl, J. N., FOGARTY, W. G., AND MOTTMAN, J. (1980). Saturn's rings: 3-mm observations and derived properties. Icarus 41, 103-118. JANSSEN, M. A. (1974). Short wavelength radio observations of Saturn's rings. In The Rings of Saturn (F. D. Palluconi and G. H. Pettengill, Eds.), pp. 83-96. NASA SP 343. JANSSEN, M. A., AND OLSEN, E. T. (1978). A measurement of the brightness temperature of Saturn's rings at 8-ram wavelength. Icarus 33, 263-278. JANSSEN, M. A., GOLDEN, L. M., AND WELCH, W. J.
135
(1974). Extension of the absolute flux density scale to 22.285 GHz. Astron. Astrophys. 33, 373-377. KLEIN, M. J., AND GULKIS, S. (1978). Jupiter's atmosphere: Observations and interpretation of the microwave spectrum near 1.25-cm wavelength. Icarus 35, 44-60. KLEIN, M. J., JANSSEN, M. A. GULKIS, S., AND OLSEN, E. T. (1978). Saturn's microwave spectrum: Implications for the atmosphere and the rings. In The Saturn System (D. M. Hunten and D. Morrison, Eds.), pp. 195-216. NASA Conference Publ. 2068. PILCHER, C. B., CHAPMAN, C. R., LEBOFSKY, L. A., AND KIEEEER, H. H. (1970). Saturn's rings: Identification of water frost. Science 167, 13721373. POLLACK, J. B. (1975). The rings of Saturn. Space Sci. Rev. 18, 3-93. SCHLOERB, F. P., MUHLEMAN,O. O., AND BERGE, G. L. (1979a). Interferometric observations of Saturn and its rings at a wavelength of 3.71 cm. Icarus 39, 214-230. SCHEOERB, F. P., MUHLEMAN, D. O., AND BERGE, G. L. (1979b). An aperture synthesis study of Saturn and its rings at 3.71-cm wavelength. Icarus 39, 232250. WELCH, W. J., FORSTER, J. R., DREHER, J., HOFFMAN, W., THORNTON, D. D., AND WRIGHT, M. C. H. (1977). An interferometer for millimeter wavelengths. Astron. Astrophys. 59, 379-385.
Interferometry of Saturn and Its Rings at 1.30-cm Wavelength I F. P E T E R S C H L O E R B , 2 D U A N E O. M U H L E M A N , AND G L E N N L. B E R G E Division o f Geological and Planetary Sciences and Owens Valley Radio Observatory, California Institute o f Technology, Pasadena, California 91125 Received N o v e m b e r 16, 1979; revised January 15, 1980 We present interferometric observations of Saturn and its ring s y s t e m m a d e at the Hat Creek Radio A s t r o n o m y O b s e r v a t o r y at a wavelength of 1.30 cm. The data have been analyzed by both model-fitting and aperture s y n t h e s i s techniques to determine the brightness t e m p e r a t u r e and optical thickness of the ring s y s t e m and estimate the a m o u n t of planetary limb darkening. We find that the ring optical depth is close to thai o b s e r v e d at visible wavelengths, while the ring brightness t e m p e r a t u r e is only 7 _+ l°K. T h e s e observational constraints require the ring particles to be nearly c o n s e r v a t i v e scatterers at this wavelength. A conservative lower limit to the single-scattering albedo of the particles at 1.30-cm wavelength is 0.95, a n d if their composition is a s s u m e d to be water ice, then this lower limit implies an upper limit of 2.4 m for the radius of a typical ring particle. The aperture s y n t h e s i s m a p s show evidence for a small offset in the position of Saturn from that given in the American Ephemeris and NauticalAlmanac. The direction and magnitude o f this offset are consistent with that found from a similar analysis of 3.71-cm interferometric data w h i c h we have previously presented (F. P. Schloerb, D. O. M u h l e m a n , and G. L. Berge, 1979b, Icarus 39, 232-250). L i m b darkening of the planetary disk has been estimated by solving for the best-fitting disk radius in the models. The best-fitting radius is 0.998 _+ 0.004 times the nominal Saturn radius and indicates that the planet is not appreciably limb dark at 1.30 cm. Since o u r previous 3.71-cm data also indicated that the planet was not strongly limb dark (F. P. Schloerb, D. O. M u h l e m a n , and G. L. Berge, 1979a, Icarus 39, 214-230), we feel that the limb darkening is not strongly wavelength d e p e n d e n t between 1.30 and 3.71 cm. The difference b e t w e e n the best-fitting disk radii at 3.71 and 1.30 cm is +0.007 -- 0.007 times the nominal Saturn radius and suggests that the planet is more limb dark at 1.30 cm than at 3.71 cm. Models of the a t m o s p h e r e which have NHa as the principal source of microwave opacity predict that the planet will be less limb dark at 1.30 cm. H o w e v e r , the magnitude of the effect predicted by the NHa models is - 0 . 0 0 9 and only marginally different from the o b s e r v e d value. INTRODUCTION
In two previous papers (Schloerb et al., 1979a,b) we reported on an extensive set of interferometric observations of Saturn and its ring system at a wavelength of 3.71 cm. The principal conclusions of those studies were that the optical thickness of the ring s y s t e m is nearly the same at visible and m i c r o w a v e wavelengths and that the rings have a very low m i c r o w a v e brightness temperature. Our work and that of others (e.g., Pollack, 1975) have shown that the combiContribution No. 3350 of the Division of Geological and Planetary Sciences. 2 Present address: D e p a r t m e n t of Physics and Ast r o n o m y , University of M a s s a c h u s e t t s , A m h e r s t , Mass. 01003.
nation of these two constraints places severe limits on the properties of the ring particles; they must be nearly conservative scatterers at 3.71 cm and their size must be greater than a few centimeters. These properties are consistent with the bulk composition of the particles being w a t e r ice, a material which has been detected in the rings spectroscopically (Pilcher et al., 1970). If the ring particles are nearly conservative scatterers at 3.71 cm, then the ring brightness t e m p e r a t u r e at this wavelength must be due to emission by Saturn that is scattered to the E a r t h by the ring particles (Cuzzi and Van Blerkom, 1974). At shorter wavelengths w a t e r ice particles will eventually b e c o m e n o n c o n s e r v a t i v e scatterers 125 0019-1035/80/040125-115-2.00/0 Copyright © 1980by Academic Press, Inc. All rights reserved of reproduction in any form reserved.
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SCHLOERB, M U H L E M A N , AND BERGE
( o p t i c a l l y thick) a n d e m i t t h e r m a l r a d i a t i o n . W h e n this o c c u r s t h e b r i g h t n e s s t e m p e r a t u r e o f t h e rings i n c r e a s e s a b o v e t h e 3.71c m v a l u e , a n d t h e n a t u r e o f this i n c r e a s e w o u l d p r o v i d e a s e n s i t i v e c o n s t r a i n t on m o d e l s o f the ring p a r t i c l e s . In this p a p e r , we present interferometric observations w h i c h w e h a v e m a d e at a w a v e l e n g t h o f 1.30 c m in an a t t e m p t to p l a c e c o n s t r a i n t s upon the amount of thermal radiation emitt e d b y t h e ring p a r t i c l e s . N o ring r a d i a t i o n in e x c e s s o f t h e a m o u n t o b s e r v e d at 3.71 cm was observed, indicating that the partic l e s a r e n e a r l y c o n s e r v a t i v e s c a t t e r e r s at 1.30 c m as w e l l as 3.71 c m . O u r n e w observations allow a considerable improvem e n t in t h e u p p e r limit to the size o f a t y p i c a l ice p a r t i c l e w i t h i n t h e rings to be made. OBSERVATIONS T h e o b s e r v a t i o n s w e r e m a d e at t h e U n i versity of California's Hat Creek Radio A s t r o n o m y O b s e r v a t o r y at a f r e q u e n c y o f 23 G H z (1.30-cm w a v e l e n g t h ) d u r i n g N o v e m b e r 2 - 2 2 , 1976. T h e u - v c o v e r a g e o f t h e i n t e r f e r o m e t e r w a s d e s i g n e d to p r o d u c e an aperture synthesis map of the Saturn s y s t e m . N i n e different b a s e l i n e s w e r e u s e d to o b t a i n t h e u - v c o v e r a g e s h o w n in Fig. 1. The Hat Creek interferometer (Welch et a l . , 1977) w a s u s e d in t h e w i d e - b a n d c o n t i n u u m m o d e f o r the S a t u r n o b s e r v a t i o n s . In this m o d e , t h e i n c o m i n g signal is split into t w o o r t h o g o n a l , l i n e a r p o l a r i z a t i o n s at e a c h a n t e n n a a n d all f o u r p o s s i b l e p o l a r i z a t i o n p a i r s are i n d e p e n d e n t l y c o r r e l a t e d . T h e f o u r p o s s i b l e c o n f i g u r a t i o n s p e r m i t t w o parallel-feed and two crossed-feed observat i o n s to b e m a d e s i m u l t a n e o u s l y . F o r t h e Saturn observations, the parallel feeds w e r e a r r a n g e d a l t e r n a t e l y to be e i t h e r parallel a n d p e r p e n d i c u l a r to t h e c e n t r a l m e r i d ian o f S a t u r n ( P A = - 7 °) o r p a r a l l e l a n d p e r p e n d i c u l a r to a p o s i t i o n a n g l e 45 ° a w a y f r o m t h e c e n t r a l m e r i d i a n ( P A = 38°). T h e parallel- and crossed-feed observations obt a i n e d in this w a y p e r m i t t e d all f o u r S t o k e s p a r a m e t e r s o f S a t u r n to b e m a p p e d w i t h t h e
V
FIG. 1. u-v coverage of 1976 HCRO 1.30-cm observations, u and v are the components of the interferometer baselines, expressed in wavelengths, projected onto the planet Saturn. The v axis is at a position angle of -6°7 so that it is aligned with the central meridian of Saturn. The axes intersect at u = 0, v = 0. The u axis increases to the left (east) in units of 10,000 wavelengths for Saturn at the distance of 8 AU. The v axis increases upward at the same scale. The visibility function at a point u, v is equal to its complex conjugate at - u , -v. Therefore, both values are plotted since there is information about the source at both locations. m a x i m u m s e n s i t i v i t y . N o p o l a r i z a t i o n eff e c t s w e r e o b s e r v e d , a n d w e shall o n l y present the data obtained with the parallel f e e d s in this p a p e r . T y p i c a l l y , five 200-sec Saturn integrations were vector averaged into a single 1000-sec i n t e g r a t i o n to m a k e t h e d a t a set m o r e c o m p a c t . A p p r o x i m a t e l y o n c e e v e r y 2.5 hr d u r i n g the Saturn observations, a point source of k n o w n flux d e n s i t y a n d p o s i t i o n w a s o b s e r v e d in o r d e r to c a l i b r a t e the g a i n a n d p h a s e o f the i n t e r f e r o m e t e r . T h e i n t e g r a t i o n t i m e on c a l i b r a t o r s w a s t y p i c a l l y 30 min. T h e c a l i b r a t o r s u s e d are l i s t e d in T a b l e I a l o n g w i t h t h e i r m e a s u r e d flux d e n s i t i e s . T h e flux d e n s i t y a n d p h a s e o f C A S A w e r e n o t u s e d to c a l i b r a t e t h e i n t e r f e r o m e t r i c o b s e r v a t i o n s d i r e c t l y , b u t r a t h e r t h e flux d e n s i t y v a l u e in t h e t a b l e w a s u s e d in t h e calibration of the other calibrators. Each of t h e c a l i b r a t o r s in T a b l e I is k n o w n to b e
SATURN'S RINGS AT 1.30 cm TABLE I CALIBRATORS FOR SATURN OBSERVATIONS AT 23 G H z Source
Flux density (Jansky)
CAS A ~ 3C84 3C120 3C273B
256.5 46.2 7.7 36.5
Flux d ensity from s p e c t r u m of J a n s s e n et al. (1974).
time variable, and therefore, their relative flux densities were checked m a n y times during the observing run. Since no variation was detected, their flux densities were assumed to be constant during the observations. The flux density of 3C84 was determined by using one of the 20-ft antennas to measure the relative flux densities of 3C84 and CAS A. The flux density of CAS A at 23 G H z has b e e n taken from a fit to its spectrum by Janssen et al. (1974) which includes their absolute m e a s u r e m e n t at 22.285 Ghz. The value in Table I has b e e n corrected for the decrease in the flux density of 0.6% per year (Dent et al., 1974). The flux density of 3C84 determined by the single antenna observations has also been c o r r e c t e d for the partial resolution o f CAS A by the antenna b e a m with a correction factor of 1.08 __ 0.01 (Janssen et al., 1974). The final value of the flux density of 3C84 is 46.2 _+ 2.5 Jansky, 3 and the flux densities o f the other calibrators in Table I were determined by c o m p a r ison to 3C84 using the interferometer. As can be seen from the discussion in the preceding paragraph, the flux density calibration, which is based upon the measurement of 3C84 relative to CAS A, is accurate to about 6% excluding the uncertainty in the a s s u m e d flux density o f CAS A. This 6% uncertainty is based upon the scatter of the 3C84 to CAS A m e a s u r e m e n t s and 3 1 J a n s k y = 10-26 W m -2 Hz -t.
127
does not include all o f the possible systematic effects which might occur. As a further c h e c k on the calibration, we o b s e r v e d Jupiter with the interferometer on its shortest baseline (40 ft) and c o m p a r e d it to 3C84. This observation was corrected for the partial resolution of Jupiter by the interferometer and gave a disk t e m p e r a t u r e of 146 _+ 7°K assuming the disk dimensions in the American Ephemeris and Nautical Almanac. It shall be seen in subsequent sections
that the disk t e m p e r a t u r e of Saturn is 140 _+ 2°K ( A E N A dimensions) which gives a Saturn-to-Jupiter ratio o f 0.95 _+ 0.06. This ratio is in good agreement with those of other o b s e r v e r s at this wavelength, whose values fall b e t w e e n 0.95 and 0.90 (Janssen, 1974). The disk t e m p e r a t u r e s of both planets are about 8% higher than those of other o b s e r v e r s (cf., Klein and Gulkis, 1978; Klein et al., 1978), but this difference is within the experimental errors. DATA ANALYSIS AND RESULTS
We have used both model-fitting and aperture synthesis techniques to analyze the H a t Creek (1.30 cm) data, and we have treated the data in the same manner as o u r previous 3.71-cm data obtained at the Owens Valley Radio O b s e r v a t o r y . The model-fitting analysis is identical to that p e r f o r m e d on the O w e n s Valley data by Schloerb et al. (1979a) in all of its essential characteristics. The planetary and ring dimensions of C o o k et al. (1973) were used to define the sizes o f the model c o m p o n e n t s , and the a p p a r e n t polar radius was taken to be that appropriate for a ring tilt of 15°.3. The distance to the planet and its geocentric position given in the A E N A were adopted for the observations. The data errors, which are used to weight the data in the model fit, were determined from the scatter o f the 1000-sec data points so that the various possible systematic errors that could affect the data are included in the estimation to some extent. The errors on the amplitudes and phases of the visibility function were estimated separately
128
SCHLOERB, MUHLEMAN, AND BERGE
since amplitude and phase errors are thought to be mostly independent of each other. The s y s t e m of weights used to fit the models to the H a t Creek data was designed to take into account both the relative data errors and the amount of new information about Saturn provided by each additional data point. The amplitude and phase errors on a given baseline were taken to be the same for all points on that baseline, and the inverse square of these errors provides the basic weight applied to a given data point. H o w e v e r , a further consideration of the weighting system is required since certain regions of the u - v plane were sampled more densely than others. I f the data were we!ghted only on the basis of the data errors, then these highly sampled regions would dominate the model fitting even though they might not be very sensitive to certain model parameters. In order to correct this effect, the baselines were grouped together according to their resolution and the observations on a given baseline were downweighted by the total n u m b e r of observations in that baseline's resolution group. This downweighting m a k e s each group about equally important in determining the best fitting model. The baseline groups were chosen to be: the shortest baseline, the longest n o r t h - s o u t h baseline, the intermediate n o r t h - s o u t h baseline, the e a s t - w e s t baselines whose resolutions were equivalent to or greater than the longest n o r t h - s o u t h baseline, and the e a s t - w e s t baselines whose resolutions were equivalent to the intermediate n o r t h - s o u t h baseline. The 1.30-cm aperture synthesis maps shown here were also produced in the same m a n n e r as the 3.71-cm m a p s of Schloerb e t a l . (1979b). The measured visibility function was Fourier transformed and " c l e a n e d " to produce a m a p which is free from the effects o f sidelobes of the synthesized beam. The synthesized b e a m is obtained by Fourier transforming the u - v coverage obtained by the interferometer, shown in Fig. 1, and we h a v e given a map
DIRTY BEAM
1976 tiCBO
1.30 CM
D 0 /
I
I
L
t
I
I
I
I
I
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FIG. 2. Contour map of the synthesized beam of the 1976 HCRO observations. The contour levels are 90, 70, 50, 30, 10, -10, and -30% of the peak response. The center of the beam is at the center of the map; east is to the left and north is upward. The intervals at the map boundaries are 10 arcsec for Saturn at a distance of 8 AU. of the b e a m obtained in this w a y in Fig. 2. The synthesized b e a m of the H a t Creek observations has lower sidelobes and less resolution than the counterpart from the O w e n s Valley 3.71-cm observations. The aperture synthesis maps compliment the model fitting analysis since they are free from m a n y of the assumptions which go into the models. Thus, they provide a check on the model-fitting results and permit us to search for new, unmodeled features o f the Saturn radio emission. The model-fitting results are s u m m a r i z e d in Table II. Unfortunately, we were unable to obtain useful results for all o f the models which were fit to the O w e n s Valley Saturn data since the H a t Creek data set was insensitive to the C-ring parameters. This insensitivity was primarily due to the lower ring tilt angle, which made the separation of the C ring from the other rings more difficult than it had been earlier in 1976 when the 3.71-cm observations were made. In addition, the H a t C r e e k observations
129
SATURN'S RINGS AT 1.30 cm TABLE II MODEL FITTING RESULTS FOR H C R O DATA AT 1 . 3 0 - c m WAVELENGTH
TDISK" (°K) T~ P l a n e t (°K) T~ B l o c k e d b (°K) TB A + B R i n g (°K) X Offset ( e q u a t o r i a l radii) Y Offset ( e q u a t o r i a l radii) Effective disk radius I m p r o v e m e n t in r e s i d u a l s from Model C (%)
Model A (uniform disk)
Model B
Model C
138 139.6 _+ 0 . 6 --0c
137 151.0 -+ 1.0 56.3 ± 6.2 -0c
140 150.0 ± 1.0 5 2 . 9 ± 6.1 6.0 + 1.1 0c
0c
0c
0c
1~ - 23.7
1c - 3.2
Ic 0
Model D
140 153.1 --+ 1.0 26.4 ± 5.9 6 . 8 ± 1.2 0.028 + 0.009 -0.038
+ 0.009 Ic 3.2
Model E
140 153.1 ± 1.0 2 6 . 4 ± 6.0 6.8 _+ 1.2 0.028 c -0.038 c 0.998 ± 0.004 3.2
a Ta~s k = ( h Z / 2 k ) × ( m o d e l flux d e n s i t y / s o l i d a n g l e o f d i s k w i t h A E N A d i m e n s i o n s ) . b Refers to the region of the planet blocked by both the A and B rings. c P a r a m e t e r f i x e d f o r m o d e l fit.
have somewhat less spatial resolution than those obtained at the Owens Valley, making the separation even more difficult. Thus, we are unable to extend the 3.71-cm C-ring results to the 1.30-cm wavelength. Our inability to fit models which include the C ring might raise some questions about the believability of models which include the A and B rings. Therefore, we have fit two models that do not include any radiation from the rings, Models A and B, in order to demonstrate that the ring radiation found in a model that includes the rings, Model C, is significant. Model A is a simple uniformly bright, elliptical disk with Saturn's dimensions. In Model B, we include the effect o f the ring opacity blocking the planetary emission where the rings cross the planet, but constrain the ring brightness temperature to be zero. Finally, in Model C we allow the rings to block the planet and have a nonzero brightness temperature. We note that the residuals to the model that includes all o f the effects of the rings (Model C) are significantly lower than those which do not include all o f the effects (Models A and B) and that the parameters in Model C are all much larger than their errors. The former point might be viewed skeptically since even the addition of irrele-
vant parameters to the model is expected to improve the residuals to the fit. H o w e v e r , we have verified that the improvement in the residuals is significant by comparing it to the improvement shown by other models with three or more parameters. Thus, it is quite likely that the ring radiation in Model C is a real detection. We can also demonstrate our sensitivity to the ring features in a way that is independent o f any model by producing an aperture synthesis map of the ring system. In Fig. 3a we show a map o f the Saturn data which has had the response o f a uniformly bright disk removed from it. The brightness temperature of the disk was adopted to be 140°K since this was the value obtained in Model A. (The brightness temperature is appropriate for the dimensions o f Cook et al. (1973) which were used to do the disk subtraction.) The map shows residual features in the region where the rings cross in front o f the planet and at the positions of the ansae. The negative feature (dashed contours) that appears at the position where the rings cross the planet is due to the opacity of the rings and indicates that they reduce the planetary brightness at that poisition. The positive features at the positions of the ansae are direct detections of
130
SCHLOERB, MUHLEMAN, AND BERGE --
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FIG. 3. (a) CLEAN 1.30-cm aperture synthesis map of Saturn with the response to a uniformly bright, 140°Kdisk removed from the center of the map. The disk dimensions are 20.62 x 18.66 arcsec at a Saturn distance of 8 AU. (b) CLEAN map of the residuals to Model C in Table II. (c) CLEAN map of the residuals to Model D, which includes a position offset from the AENA ephemeris. Model D parameters are given in Table II. All of the above maps have the same dimensions and contours. East is to the left and north is upward; the intervals at the map edge are 10 arcsec for Saturn at a distance of 8 AU. The CLEAN beam HPBW is 8 arcsec E-W and 15 arcsec N-S. The deflections in the maps are in units of brightness temperature averaged over the CLEAN beam. The contour values are: 5, 4, 3, 2, -2, -3, -4, and -5°K. Dashed contours represent negative values. the ring r a d i a t i o n a n d f u r t h e r i n d i c a t e that the ring r a d i a t i o n d e t e c t e d in M o d e l C is a real effect. T h e detailed differences b e t w e e n the d a t a a n d M o d e l C m a y be e x a m i n e d b y cons t r u c t i n g an a p e r t u r e s y n t h e s i s m a p of the r e s i d u a l s to M o d e l C. A r e s i d u a l s m a p is produced by Fourier transforming and " c l e a n i n g " the v e c t o r difference b e t w e e n the data a n d the visibility f u n c t i o n o f M o d e l C, a n d this m a p is s h o w n in Fig. 3b. T h e m a p s h o w s a significant n e g a t i v e f e a t u r e o n the e a s t e r n limb o f the p l a n e t a n d small p o s i t i v e f e a t u r e s o n the w e s t e r n a n s a a n d n o r t h e r n limb. This d i s t r i b u t i o n of r e s i d u a l
f e a t u r e s is similar to that f o u n d in the a n a l o g o u s 3.71-cm m a p a n d is p r o b a b l y due to a n e r r o r in the A E N A e p h e m e r i s . T o c h e c k the m a g n i t u d e of this error, we have fit M o d e l D to the data. M o d e l D allows the b r i g h t n e s s r e g i o n s of M o d e l C to be offset from the n o m i n a l A E N A p o s i t i o n a n d s o l v e s for the b e s t fitting offset a n d n e w b r i g h t n e s s t e m p e r a t u r e s at that position. T h e offset v a l u e s in T a b l e II are e x p r e s s e d in u n i t s o f p l a n e t a r y radii since the fit was d o n e after d i s t a n c e n o r m a l i z a t i o n o f the data. I f we use the t y p i c a l d i s t a n c e a n d p o s i t i o n angle o f S a t u r n at the time o f the o b s e r v a t i o n s to d e t e r m i n e the offsets in
SATURN'S RINGS AT 1.30 cm right ascension and declination, then the values are (best p o s i t i o n - - A E N A ) : ARA
=
0.31 _+ 0.08 arcsec,
ADEC = - 0 . 3 2 + 0.08 arcsec.
131
of Saturn is not k n o w n to sufficient precision and since changing the radius is only an approximation to limb darkening. On the other hand, a c o m p a r i s o n of the effective radii determined at 1.30 and 3.71 cm m a y be used to see whether the planetary limb darkening is wavelength dependent, since the uncertainties in the method should affect both sets of data in about the same way. The 3.71-cm effective radius has been determined by a fit of the 1976 Owens Valley data to the identical model used for the 1.30-cm data. Its value of 1.005 _+ 0.003 times the radius of Saturn is 20- larger than the 1.30-cm effective radius, indicating that the planet is marginally less limb dark at 3.71 cm than at 1.30 cm. Interestingly enough, even though the o b s e r v e d variation is only marginally significant, it is in the opposite sense to that e x p e c t e d by models o f the a t m o s p h e r e in which NH3 is the dominant source of opacity at these wavelengths (E. Olsen, private communication). H o w e v e r , the difference between the 3.71- and 1.30-cm effective radii that is e x p e c t e d by the NH3 models is only - 0 . 0 0 9 (as determined by the change in the first zero crossing of the visibility function). Thus, since the o b s e r v e d difference is +0.007 _+ 0.007, it is probably not possible to say that we have detected a significant deviation from the model prediction.
This offset is consistent with that determined in June 1976 at 3.71 c m by Schloerb et al. (1979b) and supports our claim to have detected a small error in the A E N A position since the two e x p e r i m e n t s are totally independent of each o t h e r ? A m a p of the residuals to Model D is shown in Fig. 3c. Although one feature greater than 10remains on the planet, its position on the region of the planet blocked by the rings m a k e s it unlikely to be due to incorrect modeling of the brightness t e m p e r a t u r e regions in Model D. Thus, this single negative lobe must be due to either an unmodeled feature or noise. Since the feature is less than 20- and was not seen in the 3.71-cm maps, it is reasonable to interpret it as noise, and our fit to Model D, therefore, has probably r e m o v e d all of the features of the Saturn radio emission that are detectable given the signal to noise on our data. Finally, we have searched for the effects of limb darkening in our data by solving for the best-fitting disk radius (effective radius) in our models by an analysis of variance method (Schloerb et al., 1979a). The effective radius of Saturn at 1.30 cm is 0.998 _+ DISCUSSION 0.004 times the nominal radius for a model which has been fit with the position offset Ring Brightness Temperature and Optical determined in Model D. This new model, Depth Model E, is also given in Table II, and the The ring brightness t e m p e r a t u r e and optieffective radius result might be taken to cal depth results of Model D are shown in indicate that the planet is not appreciably Table III. The ring brightness t e m p e r a t u r e s limb dark at 1.30 cm. Such a direct interprein this table are normalized by the brighttation of the effective radius is probably not ness t e m p e r a t u r e of the planet since the warranted, however, since the true radius interferometer m a k e s an accurate relative m e a s u r e m e n t of the quantities and since the 4 Pioneer Saturn data have recently been used to produce a new Saturn ephemeris, JPL DE-108 planet is the illuminating source o f the (Miles Standish, private communication). The difscattered radiation from the rings. The optiference between the DE-108 and AENA Ephemercal depths listed in Table I I I refer to the ides agrees with our determination of the position average ring optical depth o v e r the region offset from AENA in June 1976 at 3.71 cm and o f the planet blocked by either the A or B November 1976 at 1.30 cm to within the probable errors (-0.1 arcsec). rings. T h e s e values are model dependent
SCHLOERB, MUHLEMAN, AND BERGE
132
T A B L E III COMPARISON OF 1.30- AND 3.71-cm RING RESULTS
Data Set
Wavelength (cm)
B
fBa
TA+Bb
TB A + B ring TBp l a n ~ (%)
1976 H C R O 1976 OVRO 1973-1974 OVRO
1.30 3.71 3.71
-15°.3 -200.8 - 260.5
0.63 0.68 0.95
0.54 _+ 0.I0 0.66 _+ 0.10 0.97 _+ 0.16
4.4 _+ 0.8 4.2 +_ 0.7 3.1 _+ 0.7
a Fraction of area on planet blocked by the A and B rings that is blocked by B ring. b Optical depth of the combined A and B rings.
since they treat the A and B rings and the Cassini division as a single ring of uniform optical depth. We will consider the effects of variations in optical depth within this ring later in the discussion. The calculation of the value allows for the diffusely scattered component of the ring brightness from this area by assuming that the brightness of the rings is uniform and equal to that determined from the ansae by the models. We have also fit a model identical to Model D to the 3.71-cm data obtained in 1976 and included these results in Table III. Finally, the values for the 3.71-cm data obtained in 1973-1974 which have been included in the table were derived from a model like Model C in this paper since we had no aperture synthesis data to suggest the presence of a position offset. A comparison of the 3.71- and 1.30-cm ring brightness temperatures shows that they are identical within the errors. We further note that the 1.30-cm ring brightness temperature is even more consistent with the 3.71-cm models which included the C ring, h o w e v e r we have not used these results to make comparisons between the two wavelengths since the models are not identical. The lack of any increase in the ring brightness temperature between the two wavelengths indicates that no thermal radiation is required to explain the brightness temperature value at 1.30 cm. The interpretation of the optical depths in Table III is less straightforward than that of the ring brightness temperatures since the A and B rings blocked different relative
areas of the planet during the three sets o f observations. The simplest comparison that can be made is between the 1976 3.71- and 1.30-cm optical depths since the relative areas blocked by the two rings are similar. The solutions for the effective opacity of the combined A and B rings in the two data sets are only lot apart, suggesting that the opacity of the rings is the same at the two wavelengths. This conclusion receives more support if we compare the results of all three experiments to a simple model of the variation of the effective optical depth of the combined A and B rings with ring tilt angle (B). In order to make such a model, we must decide how to weight the individual optical depths of the A and B rings to derive their effective optical depth over the region of the planet they both obscure. Since each ring covers a certain fraction of this region, we have used the relative areas of the two rings to do the weighting. Thus, the effective optical depth is determined by comparing the average brightness temperature of the obscured region to the brightness temperature of the planet. We assume that the average brightness temperature of the obscured region is equal to the average of the brightness temperature of that part of the region blocked by the B ring and the portion blocked by the A ring weighted by their relative areas. Thus, if re~ is the effective optical depth of the combined A and B ring, then e-~7~.dsinIBI) =
fAe-(~'~lsinIBI) + fBe -~,J'~'lBI),
(1)
SATURN'S RINGS AT 1.30 cm where fA and fB are the fractions o f the blocked region o b s c u r e d by the A and B rings and ZA and zB are their respective optical depths. In Fig. 4, we show a comparison of this model (dashed curve) with the effective optical depths obtained from the two sets of 3.71-cm data and the 1.30cm data. In this model we have ignored the Cassini division and placed the boundary of the A and B rings in the middle of the division. We have also a s s u m e d that the optical depth of the B ring is twice that of the A ring. We have also considered models which include the effects of the Cassini division (solid curves in Fig. 4). F o r simplicity, we have a s s u m e d that the division has zero optical thickness and that T A = 1 T B . F o r this case, the effective optical d e p t h of the A and B rings and Cassini's division is given by e--r~.IsinlBI = fAe--%lsinlBI
+ A e -'"m"lBI + feD,
(2)
where fA, fB and fCD are the fractions o f the i
I
i
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i
i/
Optical Depth of Combined A + B Ring as o 1.4 - Function of Ring Tilt Angle [B)
m +
1.2 - -
--
Includes
----
Ignores Cossini Division _ I "cA - -2 "cB
Cossini
I .0 - _ .to
Division
rs f
/ /
1975-1974
OVRO
_ j.
~:x 0 . 6 - -
.-'"
1 9 7 6 HeRO
y__
. / g r e = 1.¢
/////
0.8
=1.2
Ring Particle Size and Composition
1976
0.2
i
I
I
I0
I 20
IBI
blocked region o b s c u r e d by the A and B rings and the Cassini division. We note that for small values of B in the Cassini division model [Eq. (2)], %n = B lnfcD SO that ~'en 0 as B ~ 0. Similarly, for the model which does not include the Cassini division [Eq. (1)] %~ -~ - B lnfA + rA for small B since the optical depth of the B ring is greater than that of the A ring. Thus, for both models in the low tilt angle limit, the effective optical depth of the combined ring a p p r o a c h e s the optical depth of the least optically thick region in the rings. Interestingly enough, the points on the figure a p p e a r to agree better with the models which include the Cassini division. A formal fit of this model to the points to determine the best values o f % and TB gives TA = 0.7 - 0.2 and 7B = 1.4 + 0.1. The other model, which ignores the Cassini division, gives 7"A = 0.3 ± 0.1 and ~'B = 1.0 -+ 0.1. Neither model is significantly better than the other, since there are so few points to fit. H o w e v e r it is clear that the p r e s e n c e or absence of the Cassini division affects the formal optical depth results. It is also clear, and more relevant to the present discussion, that the optical depths o b s e r v e d in the three experiments at two wavelengths m a y be satisfactorily explained by a single optical depth model. Thus, no wavelength dep e n d e n c e of the ring optical depth is required by the 1.30 and 3.71 cm data.
ra=0 5
.~ 0 . 4 o. O
0
133
i
I 30
(degrees)
F i G . 4. O b s e r v e d o p t i c a l d e p t h s o f t h e c o m b i n e d A and B rings c o m p a r e d to models described in the t e x t .
Solid-curve models include the Cassini division and assume it to have no opacity. Dashed-curve models ignore the Cassini division and place the boundary between the A and B rings in the center of the division.
The preceeding c o m p a r i s o n of the 3.71and 1.30-cm results indicates that the scattering and absorption properties of the ring particles are virtually identical at the two wavelengths. The combination o f an appreciable optical depth and a very low ring brightness t e m p e r a t u r e indicates that the particles have a very high single scattering albedo, and our results at both wavelengths are consistent with c o n s e r v a t i v e scattering. If we adopt a simple many-particle-thick ring of isotropically scattering particles as our ring model (Schloerb et al., 1979a),
134
SCHLOERB, MUHLEMAN, AND BERGE
then we may place limits upon the particle single-scattering albedo, t~o: 0.95 < cb0 ~< 1.00. The lower limit has been chosen to be conservative (about 2or). These limits on ~0 may be interpreted in terms of the ring particle size and composition, as has been pointed out by several previous workers (e.g., Pollack, 1975). A lower limit on the ring particle size of a few centimeters is possible based upon the high radar cross section and the similarity of the visible and microwave optical depths. This lower limit is composition independent and has been combined with the measured single-scattering albedos to imply that the particles must be composed of a material which is either a very good reflector of microwaves or a very poor absorber of them. Water ice is thought to be the most likely candidate since it has very low loss at microwave frequencies and has been detected in the rings spectroscopically (Pilcher et al., 1970). If a water ice composition is assumed, then we may use our lower limit on &0 to place an upper limit on the particle size. This upper limit on the particle radius is 2.4 m, assuming the absorption coefficient quoted by Janssen and Olsen (1978), and it is better than our previous upper limit of 20 m that was obtained from the 3.71-cm data. The new upper limit is comparable to that of Janssen and Olsen (1978) from observations at 8mm wavelength, h o w e v e r these measurements require a small amount of thermal emission from the rings while the 1.30-cm data are consistent with conservatively scattering particles. The amount of thermal emission required by the 8-mm observations can be made consistent with the conservative scattering result at 1.30 cm if the ring particles have a single size of about 2 m. H o w e v e r , recent estimates of the ring brightness temperature at wavelengths shorter than 8 mm (Klein e t al., 1978; Epstein et al., 1980) are not consistent with this single particle size, and a broad range of sizes may be required to explain all of the
estimates of the ring brightness temperature at millimeter and centimeter wavelengths. Conclusions
We have made observations of Saturn and the ring system at a wavelength of 1.30 cm and compared them to our previous observations at 3.71 cm. There is no evidence for any wavelength dependence of the ring particle properties or the limb darkening of the planetary disk. The ring particles are nearly conservative scatterers at both wavelengths, and the ring optical depths are the same to within the probable errors. A conservative lower limit of 0.95 has been placed on the single scattering albedo at both wavelengths. The observed difference in the bestfitting planetary radius at 1.30 and 3.71 cm, which we have interpreted in terms of limb darkening of the planet, is marginally different from the difference predicted by models of the atmosphere in which NH3 is the principal source of microwave opacity (such as those described in Klein et al., 1978). However, in view of the magnitude of the errors and the model dependence of the interpretation, it is not possible to say that we have detected a significant deviation from the model prediction. In spite of this, we find the observed discrepancy interesting since Klein et al. find that a pure NH3 model may not reproduce the shape of the spectrum between 10 and 21 cm. Clearly future, more sensitive, observations of the limb darkening of Saturn will be useful to the interpretation of the Saturn microwave spectrum. ACKNOWLEDGMENTS We are very grateful to Drs. Jack Welch, Mel Wright, Rick Forster, John Dreher, and the staff of the Hat Creek Radio Astronomy Observatory for making these observations possible and enjoyable. We appreciate Dr. Eugene Epstein making his results available to us in advance of publication. This work constitutes a portion of F.P.S.'s doctoral dissertation and was supported by NASA Grants NGR-005-002-114 and NGL-05-002-003 and by NSF Grant AST-77-00247.
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