Time Variability in the Radio Brightness Distribution of Saturn

Icarus142, 125–147 (1999)

Article ID icar.1999.6194, available online at http://www.idealibrary.com on

Time Variability in the Radio Brightness Distribution of Saturn

Floris van der Tak,1 Imke de Pater, Adriana Silva, and Robyn Millan

Astronomy Department, University of California, 601 Campbell Hall, Berkeley, California 94720E-mail: [email protected]

Received November 20, 1997; revised June 23, 1999

We present images of Saturn at wavelengths of 0.35, 2.0, 3.6, and6.1 cm taken in 1990–1995. These include the first radio imagesof the planet’s entire southern hemisphere, which is shown to be≈5% brighter than the northern at 6.1 and 2.0 cm, and possibly at0.35 cm. The latitudinal brightness distribution varies substantiallyover time. The bright band at latitude 30◦N seen throughout the1980s at wavelengths 6.1 cm and longer by A. W. Grossman, D. O.Muhleman, and G. L. Berge (1989, Science 245, 1211–1215), by I.de Pater and J. R. Dickel (1991, Icarus 94, 474–492), and in our1990 6.1-cm image is absent in our 6.1-cm image from 1995. In-stead, this image shows a bright band around latitude≈40◦S and adark zone around the equator. An image at 2.0 cm from 1994 showsa bright band around latitudes ≈40◦N and another one around≈17◦N which displays substructure. This contrasts with the flat2.0-cm brightness distribution observed throughout the 1980s.

We model the changes in Saturn’s brightness at radio wavelengthscaused by supersaturation and humidity effects in the NH4SH andNH3-ice clouds, as well as by variations in the temperature structureof the upper troposphere. It is found that each of these processes isby itself able to change the planet’s radio brightness, but that a multi-wavelength study can disentangle their effects. The 3.6- and 6.1-cmobservations from 1990 can be reproduced by supersaturation of theNH4SH cloud, while humidity effects and supersaturation of NH3

ice are ruled out. Detailed modeling of the data from 1990 shows thatat northern midlatitudes, NH4SH condensed at the thermochemicalequilibrium temperatue of 235.5 K, while over most of the planet,condensation did not occur until T= (190± 5) K. Supersaturationmay also cause the dark equatorial region seen in 1995 at 6.1 cm.

Observations of the rings show that the west (dusk) ansa is brighterthan the east (dawn) ansa by factors of up to 2. The polarizationcharacteristics are as expected in the case of single scattering ofSaturn’s thermal emission. The magnitude of the asymmetry in-creases with increasing wavelength and with decreasing distanceto the planet, implying the effect arises in the scattered planetaryemission rather than in the rings’ thermal emission. We show thatthe east–west asymmetry may be due to multiple scattering in grav-itational (Julian–Toomre) wakes, although more detailed modelsare needed to assess this possibility.

The measured brightness of the A and inner B rings as a functionof scattering angle agrees to within≈30% with model calculationsby J. N. Cuzzi, J. B. Pollack, and A. L. Summers (1980, Icarus 44,

1 Current address: Sterrewacht, Postbus 9513, 2300 RA Leiden,Netherlands.

683–705) of scattering of Saturn’s thermal emission off ice particleswith N(r)∼ r−3 between r= 0.1 and 100 cm. In particular, the pre-dicted strong forward peak of the scattering is clearly seen in thedata. The brightness of both ansae in the outer B ring is a factorof 2 lower than that of the model and than the brightness at in-termediate scattering angles, suggesting an excess of large (radius

∼>100 cm) particles in this ring. c© 1999 Academic Press

1. INTRODUCTION

Radio observations of the giant planets probe the troposphere,nidens,er-truc-me-eastdioicalobescen-

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from the 0.5-bar level down to∼10 bar on Jupiter and Saturand to∼100 bar on Uranus and Neptune, and thereby provinformation complementary to visual and infrared observatiowhich typically probe the regime 1–1000 mbar. Radio interfometers resolve the planets, allowing one to study spatial sture in the atmospheres. In the case of Saturn, radio interferotry also serves to study the rings, which appear in emissionand west of the planet and in absorption toward it. The radata sample a different regime of ring particle sizes than optand near-infrared observations because scattered light prapproximately wavelength-sized material. Observations attimeter wavelengths sample scattering angles≈20◦–160◦ be-cause the radiation being scattered is planetary emission, wsunlight is being scattered in the optical, so that only backstered light is received on Earth. In addition, the thermal radiatof the≈95 K rings is detectable only at far-infrared and radwavelengths.

Images of Saturn at radio wavelengths have been publisby Grossmann, Muhleman, and Berge (1989; hereafter GMBand by de Pater and Dickel (1982, 1991), and extensive mohave been developed by Briggs and Sackett (1989). All thauthors found that the brightness distribution of the planet at 020 cm wavelength is to first order described by a limb-darkedisk. At the shorter wavelengths, the disk appeared featurebut at 6.1 and 20 cm, a bright band was present around lati30◦ north. In this paper, we show that the latitudinal structurethe planet changes drastically over time at all wavelengthsobservation that is consistent with the findings by Molnaret al.(1999), who present data taken in November 1995, a few moafter our most recent data set. We carry out model calculatto investigate the physical origin of these bands.

5

0019-1035/99 $30.00
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All rights of reproduction in any form reserved.

126

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VAN DER TAK ET AL.

TABLE ISummary of VLA Observations

Frequency Configuration Beam FWHM Diameter Inclination 3C 286 PhaseDate (GHz) (arcsec) (arcsec) (deg) (Jy) calibrator(s

30/08/1990 4.885 B 1.6 17.9 29.3 7.55 1911–20101/09/1990 8.415 B 1.0 17.9 29.3 5.27 1911–20115/05/1992 0.330 C 77.6× 51.6 16.9 18.4 26.4 1939–154,

2321–16327/09/1994 14.940 C 1.5 18.9 7.5 3.59 2246–12113/08/1995 4.860 A 1.5 19.0 0.1 7.40 2323–032

Note.The flux density of 3C 286 at 4.9 GHz is slightly lower in the 1995 observations than in the 1990 observationsg

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In 1995, Saturn’s rings were seen edge-on from Earth forfirst time since 1980. Since the southern hemisphere hashidden from view over that period, we present the first radioages of the entire southern hemisphere. The edge-on geomalso offers a unique opportunity to observe both hemisphof the planet simultaneously. This is ideal to reveal north–soasymmetries in the planet’s atmosphere, without having torect for different viewing geometry and obscuration by the rin

The radio emission from Saturn’s rings has been studiedtensively by Cuzziet al. (1980) and Grossman (1990). Frointerferometer observations which did not resolve the indivual rings, Cuzziet al.(1980) modeled the ring emission in detaand predicted a strong forward scattering effect for all ringsall wavelengths, although most pronounced at the longer (320 cm) wavelengths. Grossman (1990) examined observaof the ring brightness as a function of scattering angle, and fothat ring brightness indeed increases toward smaller scattephase angles at wavelengths of 6.1 and 20 cm, but not at 2.0This observation also agrees with data presented by de PateDickel (1991; hereafter dPD91). All ring-resolved observatiosupport the prediction that the C ring, despite a smaller optdepth, is as bright as the A ring, caused by the fact that the C“sees” the largest solid angle from Saturn’s disk. In this pawe provide additional data on the scattering phase functiothe ring particles at different wavelengths and ring inclinatangles. Moreover, we provide clear evidence of an east–wasymmetry in the ring brightness, a feature that was notedby dPD91 and later by Molnaret al. (1999).

2. OBSERVATIONS

2.1. Centimeter-Wave Observations

In 1990–1994, the Very Large Array (VLA)2 near Socorro,New Mexico, was used to observe Saturn at 2.0–90 cm, as s

ble I. Antenna spacings range from 680 mA configuration, from 210 m to 11.4 km in B

erated by the National Radio Astronomy Observatory, a fl Science Foundation operated under cooperative agreem

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configuration, and from 73 m to 3.4 km in the C configuratioAlso listed in Table I is the ring inclinationB at the time of observation, which is defined as the angle between the ring planeour line of sight, equal to zero when the ring plane is perpenular to the plane of the sky, i.e., when the rings are seen edgThe 6.1-cm observations in August 1995 were scheduled toincide with the ring plane crossing as seen from Earth. Howeat this epoch, the array was in its most extended configurawhich is not well suited to image objects as large as Saturnall observations, nonsidereal tracking was performed usingJPL ephemeris. At wavelengths 6.1 cm and shorter, the couum correlator was used, with a total bandwidth of 100 MHIntegration time on source was 300–330 min per observaThe flux calibrator was 3C 286, and its flux density, basedthe scale of Ottet al. (1994), is given in Table I. Calibration iaccurate to within 5%. For the 90-cm observation, a detecexperiment, we used the spectral line correlator. The sidebwere centered at 327.5 and 333.0 MHz, with sixteen 6.25-Mchannels per sideband, separated by 390.6 kHz. This spfrequency setup avoids interference with terrestrial signals.

2.2. Millimeter-Wave Observations

Additional observations of Saturn at 0.35 cm were made wthe interferometer of the Berkeley–Illinois–Maryland Assoction (BIMA)3 (Welchet al., 1996) near Hat Creek, Californiain the six sessions in 1995 specified in Table II. Nonsidetracking is standard at this telescope since planets are frequused as calibrators. The total bandwidth was 800 MHz inchannels in two sidebands, centered at 85.2 and 88.7 GHzservations of the quasar 3C 454.3 served to track the inmental gain and phase. The last column of Table II listsflux density adopted for 3C 454.3 to set the absolute flux dsity scale. The numbers are interpolations from measuremat 86 GHz, done by the BIMA staff on a monthly basis for thvery purpose. Absolute flux levels are accurate to∼<20%. Af-

a-ent

ter editing and calibration, the six data sets were put together,with corrections applied for the different planetary distances and

3The BIMA array is operated by the Berkeley–Illinois–Maryland Associationwith partial funding from the National Science Foundation.

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VARIABILITY OF SATURN’S B

TABLE IISummary of BIMA Observations

Date Configuration Time on-source Inclination 3C 454(1995) (h) (deg) (Jy)

24/3 6A 3.5 3.3 10.029/3 6B 4.7 3.0 10.001/6 6C 4.4 0.3 7.504/11 6C 4.1 −3.2 6.114/12 9H 2.5 −3.0 5.723/12 9H 0.5 −2.7 5.5

Note.The configuration code is the number of antennas (6 or 9), folloby A (extended)–C (compact). The “hybrid” (H) array employed in Decemhas short east–west and long north–south baselines. Total time on-sou19.7 h; the weighted mean ring inclination|B| is 2.5◦. The image made fromthe combined data has a beam size of 5.0′′ FWHM.

position angles. The combined data set has projected basefrom the antenna shadowing limit out to 64 kλ.

2.3. Imaging Strategy

The five data sets presented here differ considerably inrange of baseline lengths covered, while for a good compson, the images should cover the same range of spatial scInterferometric observations do not have one intrinsic angresolution, but are sensitive to a range of spatial frequenciethis paper, we are interested in brightness structure on sca0.2–5 Saturn radii, and by adjusting the weights in the Foutransforms, we have constructed the images in such a wabring out these scales, although not all observations weresensitive in the corresponding range of antenna spacings.

The standard way to make images from interferometer dusing the CLEAN deconvolution algorithm, is suitable for studing the rings, and we will use it in the second part of this paTo image the planet itself, however, this method is less appriate, because the object has a smooth brightness distribextended over many synthesized beams, while the algorattempts to find point sources. This mismatch shows up asgitudinal structure in the “deconvolved” image, which canbe real since the observations presented here span nearlysaturnian rotation.

For the VLA data from 1990 and 1994, we used the specialdeconvolution method developed by de Pater and Dickel (19An initial self-calibration used a uniform disk as a model, whsubsequent iterations used more realistic representations osaturnian system, including limb darkening and, for the 1data, a simple description of the rings. Uniform weightingthe visibility points led to synthesized beams of axial ratiosto 1.5, but analysis was performed on the images in Figwhich have been convolved to a circular beam. The sizethese convolving beams are listed in the fourth column of TabThe linear resolution is typically∼0.15RS (Table I), where the
equatorial radius of the 1-bar level,RS= 60,268 km, is fromLindal et al. (1985).
RIGHTNESS DISTRIBUTION 127

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The 1995 VLA data, being taken in the A configuration, sriously suffer from missing short antenna spacings. Only 1.of the visibility points are on projected baselines shorter th14 kλ, the first null of the visibility function. Applying a gaussian taper with a 1/e width of 200 kλ to the UV data producedan image with structure on the desired scales. However, thesitivity is too low to permit self-calibration. The “blobs” on theast side of the planet and the negative emission west of itartifacts, caused by either phase errors or deconvolution erThe maps do not have an overall slope, which would be indtive of pointing errors.

The BIMA data do not have baselines∼>100 kλ, but the cov-ered portion of the UV plane is well filled due to the combinatiof different array configurations. This allowed us to perform tFourier transform with superuniform weighting. In this schemthe weight of a visibility point is inversely proportional to the local point density as evaluated over many adjacent UV cells rathan over just one, as in ordinary uniform weighting. Compawith ordinary uniform weighting, this decreases the size ofsynthesized beam and gives better sidelobe suppression.image in Fig. 1e has a beam size of 5.0′′ FWHM.

At 90 cm, the planet is unresolved in the (77.6× 51.6)′′ beam(uniform weighting). This allowed mapping and deconvolutiin the standard way. We deleted all UV data points with an aplitude>12 Jy, which are probably due to interference becathey all appear on short antenna spacings. The first threelast four channels in each sideband were discarded becaubandpass effects. The processed data set contains baselinethe shadowing limit out to 3.8 kλ. We used nearby backgrounsources for self-calibration of the antenna phases. The resu2σ upper limit of 9.6 mJy is consistent with models by de Paand Mitchell (1993), which predict a brightness temperature400–450 K, or a flux density of 6.4–7.2 mJy for a source size(16.94× 15.23)′′.

Part I: Atmosphere

The images of Saturn’s atmosphere are studied using a matmosphere based on the assumption of thermochemical eqrium. Sections 3 and 4 argue that this assumption is a reasonfirst approximation by showing that the model reproduces bthe observed total flux density at 0.1–100 cm and the shapthe limb darkening. Section 5 presents the observed deviatfrom this basic model, and these are interpreted in Sectionlatitudinal variations in the atmospheric structure, in particuin the altitudes at which NH4SH and solid NH3 condense out.

3. BROADBAND RADIO SPECTRUM

As a first constraint on the atmospheric model, we compthe predicted total flux density of the planet at radio waveleng
to the values observed here and in previous work. The ob-served brightness temperatures were obtained by fitting Bessel

143.4

128 VAN DER TAK ET AL.

FIG. 1. VLA and BIMA images of Saturn. Contour levels are: (a) 2.7 to 166.6 by 6.3 K; (b) 4.7 to 166.2 by 6.2 K; (c) 2.6 to 181.5 by 6.9 K; (d) 15.9 to
by 15.9 K; (e) 7.1 to 148.3 by 7.1 K. Dashed contours indicate negative values. The lowest contour is drawn at approximately the 3σ noise level. The hatched area
i

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within the contour around position (0, 0) in (d) is an intensity decrease, wh

functions, i.e., the Fourier transform of a uniform disk, to oUV data. The size and shape of the disk were taken fromAstronomical Almanac, since the radii of the optical and rademission of Saturn are to within 0.6% the same. This leathe disk-averaged brightness as the only free parameter, anbest-fit values are listed in Table III. To account for the cosmmicrowave background, which is invisible to an interferome
2.7 K has been added to the result of the fitting routine. Teffect of the rings on the total brightness is discussed bel
le all other features on the disk are increases.

urtheovesd itsic

er,

Absolute calibration is the major source of uncertainty, which5% for most data sets. The 6.1-cm data from 1995 contain soshort baselines that the accuracy is closer to≈10%. Calibrationat 0.35 cm is accurate to≈20%.

The other observations listed in Table III are those from tde Pater and Mitchell (1993) collection which were takensmall ring inclination angles. The error bars of the Briggs a
heow.Sackett (1989) data have been changed to include the uncer-tainty of the absolute calibration of the old VLA system: 10%

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TABLE IIIObserved Disk Brightness Temperatures of Saturn

Wavelength Brightness Inclination Reference(cm) temperature (K) (deg)

0.10 145± 14.5 0.02 Werner and Neugebauer (1970.20 137± 11 <5 Ulich (1981)0.33 149.3± 4.1 <8 Ulich (1981)0.34 157.8± 31.6 3.03 This work1.33 132.5± 13.3 <0.25 Briggs and Sackett (1989)1.99 136.1± 6.8 <0.25 Briggs and Sackett (1989)2.00 158.9± 7.9 7.5 This work3.56 161.1± 8.1 29.3 This work6.13 180.5± 18 0.07 This work6.14 168.6± 8.4 29.3 This work6.14 173.6± 8.7 <0.25 Briggs and Sackett (1989)

20.73 219± 11 <0.25 Briggs and Sackett (1989)69.72 352± 42 <0.25 Briggs and Sackett (1989)90.78 <601.0 (2σ ) 18.4 This work

Note.To correct the total flux for emission and absorption by the rings,2.0-cm point from this work has been increased by 5.5%.

at 1.3 cm and 5% at 2.0, 6.1, and 20 cm. Figure 2 showsavailable data points atB< 10◦ as solid symbols, with mode
curves after de Pater and Mitchell (1993) and de Pater and MassieEarth’s ionosphere. The dotted curve considers solid NH3 and
ctric
(1985) superposed. The models have been calculated for zero
FIG. 2. Observed and modeled radio spectrum of Saturn. Solid symbols are data at ring inclination angleB< 10◦, open symbols are data atB> 10◦. Squares

H2O particles as additional absorbers, where we use the diele

are data presented in this paper, as is the triangle denoting our 90-cm uppliquid and solid absorbers is seen to be negligible.


)

he

the

inclination angle, but changing this angle to 30◦ affects thebrightness of the disk by<1 K. The figure illustrates that theeffects of considering different absorbers are much larger ththose of a changing mean emission angle. The solid curve taonly absorption by gaseous NH3 into account. The model at-mosphere is in thermochemical equilibrium, with the tropspheric abundances below the clouds per mole of gas taken fBriggs and Sackett (1989): [NH3]= 5.2× 10−4 (1.9× solar N),[H2O]= 6.9× 10−3 (4.7× solar O), [CH4]= 4.2× 10−3 (3.0×solar C) and [H2S]= 4.1× 10−4 (11.0× solar S). Solar abun-dances are from Grevesse and Noels (1993) for carbon, nitroand oxygen, and from Anders and Grevesse (1989) for sulfu

The other two curves in Fig. 2 are estimates of the effecttropospheric clouds on Saturn’s radio spectrum. These calations assume wet adiabatic cloud densities, which are uplimits based on the assumption of no loss by precipitation. Tdashed curve includes absorption by the H2O and NH4SH cloudsbesides NH3 gas. The effect of these clouds is appreciable onat wavelengths∼>10 cm. At 30 cm, liquid H2O may decreasethe disk brightness by 5 K, and liquid NH4SH may absorb an-other 12 K up to a total of∼<17 K. The water abundance is mostlconstrained by the 70-cm data point, a difficult measurementcause of the strong background emission and variability of

er limit; circles are measurements by other authors. In the range 1–10 cm, theeffect of

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130 VAN DER T

constants from de Pater and Mitchell (1993). The dielectric cstant for NH3 ice at radio wavelengths was assumed to equalvalue at optical wavelengths, which is likely an overestimaAround 6 cm, NH3 ice may cause a brightness decrease of∼<6 K,which is similar to the observational uncertainty. A more pnounced effect is visible at wavelengths shortward of 0.5 cm,to absorption and scattering by NH3 ice particles in the uppetroposphere. Solid NH3 is expected to form in the giant planetatmospheres; recently, Brookeet al. (1998) obtained the firsdirect detection of NH3 ice on Jupiter using the Infrared SpaObservatory. However, it is seen from the figure that includthe ice does not appreciably improve the match to the data0.1–0.3 cm, the fit even becomes somewhat worse, which cbe due to a too high dielectric constant of NH3 ice or to the clouddensity being less than maximum due to precipitation.

Also shown in Fig. 2 are our observations atB> 10◦, as opensymbols. The measured total flux densities have been convto pure disk flux densities by correcting for emission andsorption by the rings. Correction factors are from Kleinet al.(1978), a crude model that assumes the rings to have astant surface density and an optical depthτ = 0.7 over the entirewavelength range. Application of this model typically changSaturn’s disk brightness temperature by 1–10%, dependinring inclination angle and wavelength. De Pater and Mitch(1993) show Saturn’s radio spectrum including observationall ring inclination angles, which show a large scatter, more tcan be explained by calibration problems alone. Our 2.0point illustrates this: it lies significantly above the model cureven though the point is supposed to be corrected for ringfects. The Kleinet al. model can and should be improved, uing recent high-resolution images at centimeter and millimewavelengths, as well as data obtained during the Voyagerbys. Optical depths and ring brightness temperatures havebeen determined for the A, B, and C rings separately, and shclear dependence on radial position and on wavelength (GMBdPD91; Part II below). This information was not available whKlein et al. (1978) developed their model. When the inaccracies in the ring model are removed, some spread in thepoints may remain, caused by spatial and temporal changatmospheric opacity or the temperature–pressure profile, ling to changes in Saturn’s disk-averaged brightness temperaGiven the large variations in the brightness structure seen b(see Section 5 below) and Molnaret al. (1999), it is not in-conceivable that Saturn’s disk-averaged brightness tempervaries as well.

4. LIMB DARKENING

Although the broadband spectrum provides a good first chof planetary model atmospheres, its use is limited to derivingglobal average of the distribution of microwave absorbers.terferometers can resolve this distribution and thereby provinformation on planetary meteorology. However, the long in
gration times prohibit the detection of features in the east–w
K ET AL.

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direction. What is resolved is the limb darkening, and this effwill be used here as a more stringent test of the models. Figushows scans in the east–west direction through the imagesFig. 1. (In this paper, cardinal directions refer to Saturn, nothe sky.) The error bars represent the 1σ variation in bright-ness in regions of the images without emission from the plaor from the rings. The data have been folded about the cenmeridian to increase the signal-to-noise ratio, and averagedone beam FWHM in latitude. The beam size is indicated bybar. The planetocentric latitudes of the scans have been chosavoid the various latitudinal features visible in the images, whare discussed in the next section. To convert planetocentrsub-Earth latitudes, subtract the ring inclination.

Superposed are scans through model images, which havetilted by the inclination angle and convolved with the appropriabeam. The model is that of the solid curve in Fig. 2. Interferoeters do not measure the total flux density of the source, andability of deconvolution algorithms to recover it is model depedent and limited by the size of the central hole in the UV plaFor extended, smooth objects such as planets, the accurathe recovered brightness is no better than≈5%, even with ourspecialized deconvolution method. In addition, the latitudinbrightness structure visible in Figs. 1a, c, and d obviously cnot be reproduced by a model with a uniform distributionabsorbers. If the atmosphere were globally in thermochemequilibrium, the model should match the data on average,it will be shown in Section 6.3 that at least for epoch 1990,global brightness was decreased by≈5% due to supercoolingWe accommodated the uncertainty in observed absolute briness by scaling the model curves by factors ranging from 210% from unity to match the data at the central meridian. Tmultiplicative scaling is an approximation of an exact spatFourier filtering of the model results.

Except for the 6.1-cm image from 1995, which contains resual phase errors as discussed in Section 2, the match betdata and model is excellent. The conclusion is that thermochical equilibrium provides a good starting point for more dtailed modeling. The departures from equilibrium calculatedSection 6 have only a small impact on the limb darkening curv

5. NORTH–SOUTH PROFILES

Figure 4 presents scans through the images from Fig. 1 athe central meridian, averaged over one beam FWHM in lontude. The error bars are the same as in Fig. 3. Integrationlongitude would reduce the noise in these scans by factors oto≈3 for the VLA data and up to≈2 for the BIMA data, depend-ing on latitude (cf. Tables I and II). We have not performed tintegration since the error bars are already quite small. Howewe stress that whether a feature in the scans is significant owas based not only on the scans, but on the entire image (Figsince only features visible at all longitudes are significant.

estel images as for the east–west scans, again convolved to the

raged over

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION 131

BR

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FIG. 3. Observed limb darkening curves, taken at the indicated planetocentric latitudes to avoid bright bands or absorption by the rings and ave
one beam FWHM in latitude. Superposed are slices through model images including only gaseous absorbents. The bar at the bottom left corner indicates theobservational resolution.
tionisi-

thentric

resolution of the observations, tilted by the ring inclination ascaled to the data. To have resolution constant over the graphordinate is the sine of the planetocentric latitudeλplc. In 1990and 1994, part of the back side of the planet was visible.describe this, the following analytic continuation of sin(λplc) isused as ordinate: sin(λplc− lπ )+ 2l , with the “cycle number”lthe integer part of (λplc∓π/2)/π for λplc

<> 0. For easier refer-

ence, the corresponding values ofλplc itself are given at the topof each plot.

nd, the

To

The first thing to note is the absorption by the rings atλplc=0◦–15◦S in Fig. 4a and atλplc= 10◦–50◦S in Figs. 4b and 4c. Thebrightness dip near zero latitude in Fig. 4d is not a ring absorpbut an atmospheric feature, discussed below. The A ring is vble in emission in Figs. 4b and 4c atλplc≈−90◦. The latitudinalstructure in the images is better visible in Fig. 5, which showsratio of data to (scaled) model brightness versus planetoce
latitude. This presentation also allows a more quantitative de-scription of the latitudinal structure. However, since the scaling


del imagesy

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FIG. 4. Scans through our data along the central meridian, averaged over one beam FWHM in longitude. The dotted lines are slices through moincluding only gaseous absorbents. The bar at the bottom center indicates the observational resolution. The lower ordinate is sin(λplc), which corresponds directlto position on the original image, while the upper ordinate isλplc itself for convenience. The rings are seen in absorption atλplc=−15◦ to 0◦ (a) and atλplc=−50◦
to−10◦ in (b) and (c), and in emission nearλplc≈−90◦ in (b) and (c). All other observed deviations from the model are atmospheric, as discussed in the text.
v

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cmt thet.earenoral

of the model to the data is somewhat arbitrary, the unit leindicated by the dashed line in Fig. 5, is uncertain by≈10%.The region of absorption by the rings, where the model isexpected to match the data, has been omitted from Figs. 5b5c. The ratio error bars are the data error bars divided bymodel brightness.

In the 1995 6.1-cm image (Figs. 4d and 5d), the southhemisphere is brighter than the northern by≈5%. This is the
first time that the entire southern hemisphere is seen at ra
el,

otandthe

rn

wavelengths. The small part of the southern hemisphere viin 1994,λplc= 20◦–45◦S, suggests an enhanced brightnessa similar fraction (Fig. 5a) relative to the model. The 0.35-data (Fig. 5e) may show a brighter southern hemisphere, buspatial resolution is not high enough for a definite statemen

In addition, a variety of latitudinally confined features appin Figs. 4 and 5. Particularly striking is the difference betwethe two 6.1-cm images from 1990 and 1995. Such large temp
diovariations in Saturn’s radio brightness structure have not been


contrast in Fi

DAT

A/M

OD

EL

RAT

IO

FIG. 5. As in Fig. 4, but showing the ratio of the data and model scans.

g wasmre-hisas

uchi-

red

seen before. The image from 1990 (Fig. 4c) shows the briband at northern midlatitudes (λplc≈ 30◦–45◦), which was alsoseen by GMB89 and dPD91. The maximum brightness excof ≈4% over the model value occurs atλplc≈ 37◦N (Fig. 5c).Although in previous observations, the intensity of this featuhad varied over time, it had never disappeared, as in the 6.1image from 1995 in Fig. 4d. The latter image shows a bright ba(relative to the background) at 14◦N and another one at≈37◦

latitude south. This region is≈5% brighter than the rest of thesouthern hemisphere, making the total north–south brightn

g. 5d≈10%. The third feature in Fig. 5d is the dip

ht

ess

re-cmnd

ess

at the equator. The cross section of the rings at this epochonly≈100 km, so that at the observational resolution of 8200 kFWHM, even 100% absorption would not be detectable. Thefore, the feature must originate in the planetary atmosphere. T“equatorial zone” and the enhanced brightness around it walso seen by Molnaret al. (1999) in lower-sensitivity 3.6- and6.1-cm images taken in November 1995. The feature was mweaker in November than in August, which is additional evdence for variability of Saturn’s brightness distribution.

The 2.0-cm image (Fig. 4a) shows two bright bands cente◦ ◦
nearλplc≈ 17 N andλplc≈ 40 N. Comparison with the model

h

h

ey,

s

a

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e

i

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r

s

–16cesf

8).at

o

ria-

er-u-- to-cmce

eical

as

134 VAN DER T

curve indicates that the band at 40◦N has an excess brightness≈7%, while the maximum excess of≈13% occurs at 10◦N. Thisis the first time that brightness structure at 2.0 cm is seen onurn. Images at 2.0 cm from 1986–1987 (GMB89; dPD91) sha featureless planet. An image from 1982 (dPD91) may sstructure similar to the bands in our data, but at a marginal cfidence level. We note that in 1982, the 6.1-cm band at nortmidlatitudes was weaker by a factor 2–3 than in 1986.

The 2.0-cm band atλplc≈ 40◦N is unresolved in the latituddirection, as are the bands in both 6.1-cm images. The onlsolved band is the one aroundλplc≈ 17◦N in the 2.0-cm imagewhich has an asymmetric shape. This feature can be descby the combination of two unresolved components. One iλplc≈ 21◦N, of similar strength and width as the band at 40◦N.The second is brighter than the first and located atλplc≈ 12◦N,just north of the region of absorption by the rings, where6.1-cm image from 1995 also shows enhanced emission.decomposition is only meant to illustrate, and it is by no meunique.

The 3.6-cm data do not show any latitudinal structure to a leof ≈1%. Likewise, the 0.35-cm image, which probes almthe same depth into the atmosphere, shows a featureless phowever, latitudinal structure in the atmosphere such as se2.0 and 6.1 cm would not show up in this image due to the laconvolving beam.

6. MODELS OF LATITUDINAL BRIGHTNESS VARIATIONS

The model calculations shown in Figs. 2–5 are essentthose by de Pater and Mitchell (1993) and are based on amochemical equilibrium atmosphere after Romani (1986).details about the construction of such model atmospheres sPateret al. (1989). As in Fig. 2 we used the abundances deriby Briggs and Sackett (1989). All model calculations in this stion are based on opacities from gaseous NH3, H2S, and H2Oonly (solid line in Fig. 2), since the calculated upper limitsthe absorption by clouds are small at the wavelengths of inte(Section 3) and because the dielectric constants of the vaclouds are poorly known. Figure 6 shows the temperaturethe abundances of the major trace constituents versus preas well as the weighting functions at the wavelengths of ourservations. The weighting functionWλ(z) at wavelengthλ andaltitudez is defined as

Wλ(z) = e−τλ · dτλdz, (1)

whereτ is the optical depth at wavelengthλ and altitudez (τ in-creases into the atmosphere). It is seen thatWλ becomes broadeand peaks at larger pressures as the frequency differencethe NH3 lines at 23.9 GHz increases. Observations at walengthλ probe altitudes near whereWλ peaks; in the limit that
Wλ(z)= δ(z), the brightness temperature would equal the phical temperature at altitudez.
AK ET AL.

of

Sat-owowon-ern

re-

ribedat

theThisns

velst

lanet;n at

rge

allyther-Fore deed

ec-

torestiousandsure,ob-

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FIG. 6. (a) Temperature–pressure relations for model atmospheres 1(solid line), 17 (dashed line), and 22 (dotted line). (b) Solid lines: abundanof NH3 and H2S gas in thermochemical equilibrium (Model 1). The effect oNH4SH supersaturation on the NH3 abundance profile (Model 2) is shown bythe dashed line, while the dotted line illustrates the effect of humidity (Model(c) Weighting functions in the thermochemical equilibrium model (Model 1)the wavelengths of our observations.

6.1. Variations at 6.1 cm

The location of the 6.1-cm weighting function suggests twkinds of modifications to the gaseous NH3 abundance profileas possible causes of the observed latitudinal brightness vations. The first option is a rise of the base of the NH4SH solutioncloud to altitudes corresponding to temperatures below the thmochemical equilibrium value of 235.5 K. This effect, called spercooling or supersaturation, increases the opacity at the 45-bar levels (cf. dashed line in Fig. 6b) and decreases the 6.1brightness. At 0.35, 2.0, and 3.6 cm, the effect is smaller, sinWλ at these wavelengths is small at pressure levels>4 bar(Fig. 6c). Underlying a latitudinal variation of the height of thNH4SH cloud base could be the existence of a system of vertmotions, or winds, in the atmosphere. Such a wind system winferred by Bezardet al. (1984) from Voyager IRIS observa-
tions, and is generally invoked to explain changes in the optical

s

et

rne

urt-

a

u,ee)nh

theer-s.nde

Kh the

isce agentphys-aturecou-

e,en if

, al-cingved

st of

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aluesid-atic

e is

mod-useuresl to

ture

r. Inres-

ith1.4,

differences in physical temperature at 1 bar with respect to the


appearance of the planet. Variations in the NH4SH condensationheight could also arise due to local differences in the altituwhere condensation nuclei such as dust particles are preA smaller H2S abundance would also raise the NH4SH cloudbase, but this would give a higher NH3 abundance above thcloud, so that the effect on the brightness would be similar awavelengths.

Alternatively, the humidity in the NH4SH cloud could be be-low unity due to convective mixing with drier air from highealtitudes. Like supersaturation, this process is known to ocin terrestrial clouds (Pruppacher and Klett 1980). The cosponding NH3 abundance profile is illustrated by the dotted liin Fig. 6b. A lower humidity implies a lower opacity in thentire 1–5 bar range and a brightness increase at all radio wlengths. Table IV lists the calculated brightness temperatat the center of the disk for the various model atmospheWhile supersaturation (Models 2–6) can cause a significancrease in the 6.1-cm brightness without changing the 3.6brightness, modifications of the NH4SH humidity (Models 7–9)produce equal relative brightness increases at these two wlengths. The results of the calculations are shown graphicin Fig. 7.

FIG. 7. Impact of the various departures from thermochemical equilibristudied here on the radio spectrum of Saturn, illustrated by Models 1, 4, 815, and 22. Supercooling of NH4SH (short-dashed line) decreases the brightnat long wavelengths. Lowering the NH4SH humidity (dotted line) increases thbrightness at all wavelengths. Supercooling of NH3-ice (short dash–dotted linedecreases the brightness at all wavelengths but mostly toward short waveleDecreasing the NH3-ice humidity (long-dashed line) does not change the brig
ness significantly at any wavelength. The effect of a subadiabatic lapse rate (dash–dotted line) is a brightness increase which is significant at 2.0 cm onl

deent.

all

rcurre-e

ave-reses.de-cm

ave-lly

m12,ss

gths.t-

6.2. Variations at 2.0 cm

The 2.0-cm weighting function peaks close to the base ofNH3 ice cloud at 1.35 bar. Hence, local variations in the propties of the NH3 ice cloud will mostly affect the 2.0-cm brightnesIn Models 10–16, we calculate the effect of supercooling ahumidity in the solid NH3 cloud on Saturn’s brightness. Thresults are as follows. Forming the NH3 ice cloud at temper-atures below the thermochemical equilibrium value of 148decreases the brightness at all radio wavelengths, althougeffect is strongest at the shorter wavelengths, for whichWλ peaksat lower pressures. A brightness contrast of 13% at 2.0 cmachieved if condensation occurs at 115 K. This would produ4.5% decrease at 6.1 cm. Note that the differences in emerbrightness temperature are always less than the change inical temperature where condensation occurs. The temperchanges are partly cancelled since the opacity is stronglypled to temperature in regions where the NH3 abundance followsthe saturated vapor curve. The humidity of the NH3 ice cloudinfluences the brightness at all radio wavelengths by∼<2%. Inthis cloud, the NH3 abundance decreases rapidly with altitudso that basically the same temperature layer is probed, evthe humidity is as low as 20%. The humidity of the NH4SHcloud also has some influence on the brightness at 2.0 cmbeit less than at longer wavelengths (Models 7–9). Reproduthe maximum latitudinal brightness contrast of 13% obserat this wavelength requires a humidity as low as≈20%. Thiswould cause a 6.1-cm band of similar strength and a contra≈20% at 3.6 cm.

Besides departures from thermochemical equilibrium, anopossible cause of brightness structure is variations in the tperature structure of the upper troposphere. In the region wNH3 ice condenses out, the temperature gradient, or lapsemay be below the wet adiabat by up to 10% because the cryact as catalysts for the conversion ofortho- to para-H2 (Massieand Hunten 1982). Lapse rates exceeding the wet adiabatic vare implausible in a convective atmosphere and are not conered here. As a first experiment, we replaced the wet adiabgradient by the values Lindalet al. (1985) derived from theVoyager 2 radio occultation data. This temperature structurindicated by the dashed line in Fig. 6a. At pressures<1.4 bar, thetemperature is seen to be enhanced relative to the previousels. The maximum difference, 12 K, occurs at the tropopa(0.1 bar). However, the computed radio brightness temperat(Table IV, Model 17) are the same as in the adiabatic mode0.1 K, because the optical depth is negligible atP< 1.4 bar.

To illustrate the effect of general changes in the temperagradient, Models 18–22 show results if the decrease in∇T fromthe adiabatic value sets in at pressures larger than 1.4 bathese models, the wet adiabatic gradient applies at high psures, while ifP< P0, the lapse rate decreases linearly waltitude to reach zero at the 0.1-bar level. Models 18–22 use2.0, 3.0, 4.0, and 5.0 bar as values ofP0. The corresponding

longy.nominal model are listed in Table IV. As an example, the dotted

136

emicale

high angular resweather conditio

VAN DER TAK ET AL.

TABLE IVBrightness Temperatures of the Center of Saturn’s Disk, Calculated for Zero Inclination Angle

Wavelength (cm) NH4SH cloud NH3 ice cloudModel 1T (K)

No. 6.1 3.6 2.0 0.35 Tbase(K) Humidity Tbase(K) Humidity (at 1 bar)

1 193.9 168.8 142.3 155.1 235.5 1.0 148.0 1.0 0.0

2 185.6 166.1 142.3 154.9 200.03 182.1 163.9 142.3 154.3 190.04 177.9 160.7 142.3 152.6 180.05 171.5 155.0 141.3 146.8 165.06 164.3 147.2 132.9 137.9 150.0

7 199.5 174.4 145.4 159.6 0.758 206.3 182.6 150.6 166.6 0.509 214.0 195.2 161.6 179.3 0.25

10 192.7 166.6 138.0 153.1 140.011 190.4 162.1 134.3 143.5 130.012 188.0 157.3 127.8 131.3 120.013 185.9 152.6 118.1 120.3 110.0

14 194.4 169.7 143.4 156.2 0.7515 194.8 170.6 144.0 157.2 0.5016 195.3 171.4 144.6 158.2 0.25

17 193.8 168.6 142.2 154.6 0.918 193.8 168.6 142.0 154.6 0.919 193.2 167.6 141.9 152.7 5.020 193.0 167.8 143.6 150.6 11.721 194.2 170.4 147.4 150.9 19.222 196.9 175.1 151.7 154.9 26.4

Note.Model 1 has a wet adiabatic temperature gradient throughout, and uses the indicated thermochequilibrium temperatures for NH4SH condensation and NH3 freezing. Model 17 uses the temperature profil
obtained by Lindalet al.(1985) from Voyager 2 data, which differs from the wet adiabatic lapse rate at pressures
l

s

y

de

e

h

tratehtnesstheleastble,ves. As

ss ateaseslanet

eeny

atom-unt,ob-gths

below 1.4 bar. Entries not listed are equal to the va

line in Fig. 6a shows the temperature structure in Model 22these models, condensation and freezing of NH3 occur at thesame temperatures as before. Small increases in the emebrightness temperatures are predicted, which become obable if the deviation from the wet adiabat sets in atP≥ 3 bar.Figure 7 shows that only at 2.0 cm a detectable effect maexpected.

We have also calculated the brightness of Saturn for Mo1–22 at wavelengths of 0.14 and 20.1 cm. These results arincluded in Table IV and Fig. 7 because no new trends appelonger or shorter wavelengths. The 0.14-cm brightness isthe same as the 0.35-cm brightness to∼<1%. This implies thatobservations at 20.1 cm are less suitable to study Saturn’satmosphere than 6.1-cm observations, since despite the hbrightness temperature (250 K vs 180 K), the received sig(in Jy) is much lower. In addition, toward longer wavelengtthe galactic background emission is stronger and the angresolution that can be obtained is lower. In contrast, imagat 0.14 cm, which has recently become possible with sevinterferometers, could give important constraints on the strucof planetary atmospheres, because of the high flux levels an

olution that can be obtained, although excens are required.

ues for Model 1.

. In

rgenterv-

be

elsnot

ar atven

deepighernals,ularingeraltured the

6.3. Comparison to Observations

The calculations presented in Table IV and Fig. 7 demonsthat several processes are able to change the planetary brigtemperature at 2.0 and/or 6.1 cm. Uniquely constrainingatmospheric structure requires simultaneous imaging at attwo wavelengths. From 1994, only 2.0-cm data are availaand our 1995 BIMA observations span 9 months, which leaonly the data sets from 1990 as suitable for detailed modelingseen from Table IV, supersaturation of the NH4SH cloud is theonly process capable of producing a large change in brightne6.1 cm and a small change at 3.6 cm. Supersaturation decrthe brightness, implying the process operates all over the pexcept at northern midlatitudes.

The central brightness temperatures in Table IV have bcalculated for inclination angleB= 0◦, but the values are verinsensitive toB, and the trends seen in the table are validany latitude. However, in constructing model images to be cpared with data, the inclination should be taken into accosince it changes the emission profile. To model the VLAservations from 1990, synthetic images at both wavelen

llentwere constructed for several values of the NH4SH condensa-tion temperature (like Models 2–6, but withB= 29.3◦). The


FIG. 8. Best fit to the 1990 data at 6.1 cm (top) and 3.6 cm (bottom). At northern midlatitudes, NH4SH forms at the thermochemical equilibrium temperatureh

en

e

rm

ob-91.

sug-

ive.ub-ec-

(235.5 K). At other latitudes, the NH4SH cloud does not form until higher in t

northern midlatitudes in these images were replaced by Modat B= 29.3◦, and the results were convolved to observatioresolution. The bright band is resolved on the longest balines, and the data constrain the position of the edges ofbright region to∼<2◦ in latitude. Figure 8 presents the modthat best matches the data. Globally, the NH4SH cloud forms at(190± 5) K, except at planetocentric latitudesλplc= 30◦–42◦,where thermochemical equilibrium applies, and the cloud fo
at a 60-km lower altitude, whereT = 235.5 K.
e atmosphere (i.e., gases are supersaturated), atT < (190± 5) K.

l 1alse-thel

s

Simultaneous observations at 2.0, 6.1, and 20 cm weretained in 1986, and presented both by GMB89 and by dPDUsing a solar composition atmosphere, the first authorsgested that the bright band atλplc≈ 30◦N at 6.1 cm togetherwith the flat brightness distribution at 2.0 cm was indicatof a lowered (75%) NH4SH humidity at northern midlatitudesHowever, the composition of Saturn’s atmosphere differs sstantially from that of the Su (Briggs and Sackett 1989; also S
tion 3), as derived from the disk-averaged radio spectrum. Using

n

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thethans. A

138 VAN DER T

the observed composition, dPD91 concluded that the brightdistribution at 2.0, 6.1, and 20 cm could be reproduced oby forming the NH4SH cloud at the 4.5- to 5.0-bar level in thband and at 2.5–3.5 bar at other latitudes, results very simto those found here. The brightness structure observed in 1at 3.6 and 6.1 cm can be explained neither by supersaturaof the NH3 ice cloud, nor by lowered humidity in the NH4SHand NH3 clouds, nor by a different temperature gradient. Thprocesses would produce either bands at both wavelengthbands at all, or even only a band at 2.0 cm, inconsistent wthe observations. The effect of absorption of solid NH3 is harderto evaluate by lack of optical constants at radio wavelengHowever, the absorptivity of solid material tends to vary slowwith wavelength, except near resonances, which, however,to lie in the infrared. Thus, latitudinal variations in the densof solid NH3 particles are unlikely to produce a bright band6.1 cm and none at 3.6 cm.

Supersaturation of the NH4SH and/or NH3-ice clouds is themost likely candidate process to explain the region of decreabrightness around the equator in the 6.1-cm image from 19However, no constraints on the gaseous NH3 abundance pro-file from other wavelengths are available, impeding a detacalculation.

Part II: Rings

7. OBSERVATIONAL RESULTS

While in the data from 1995, the rings cannot be seen due tonearly edge-on geometry, the 1990 and 1994 data clearly sthe rings both in absorption and in emission. The absorptionthe rings (the “cusp”) can be seen in Figs. 4a, 4b, and 4c, aposition where the planetocentric latitude of the absorptionture equals the ring inclination. The 1990 data show the A rin emission just south of the planet. In the 3.6-cm data, whresolve the cusp, the ring optical depth is clearly seen to decroutward (to the south). This section and the next deal with1990 and 1994 data only.

In Part I, the images were convolved with a beam matchethe resolution of the data and the expected size of features odisk. However, for the smaller features in the rings, high resotion is desirable. The 2.0-cm data had been convolved to anslightly larger beam, and the same image is used here. Howthe data sets from 1990 were smoothed considerably for thmospheric study. Figure 9 presents color representations o1990 data at the full observational resolution (see captionnumbers). Superposed on the total intensity (Stokes I) imaare contours of the linearly polarized emission (

√Q2+U2).

The polarized emission is seen to be confined to the inner Bat 3.6 cm, while at 6.1 cm, weak polarized emission fromansae of the outer B ring is detected. At both wavelengths,
polarization peaks at the ansae, where 31± 10 % of the emis-sion at 3.6 cm and 35± 10 % at 6.1 cm are polarized. The othe
AK ET AL.

essnlyeilar990tion

se, noith

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rings are weaker than the inner B ring by factors of 2–5 in toemission, and the upper limits on the polarized emission frthe other rings’ ansae are consistent with a constant polarfraction. However, along the B ring, the total intensity is approimately constant, while the polarized emission becomes wewhen moving away from the ansae. The polarization vectodirected north–south at both ansae and turns toward the eathe direction of rotation at an approximately constant rate, sthat it makes exactly one full turn over the ring system. Thobservations strongly suggest that the polarizing mechanissideways single scattering of Saturn’s thermal emission, asgested before by Grossman (1990) based on lower-sensiobservations in which only the ring ansae were detected inlarized light. In the 6.1-cm data from 1995, no polarized emisswas detectable to a 1σ upper limit of 0.76 K, consistent with theabove results. The polarized emission is at the limit of whatVLA can detect, and in the remainder of Part II, we discusstotal intensity data only.

Scans through the rings are displayed in Fig. 10, from whwe iteratively determined the brightness of the individual rinusing the ring geometry measured by the Voyager space(Cuzziet al.1984). We constructed model scans through theB, and C rings and the Cassini Division: (a) east–west, throthe ansae; (b) north–south, at 1.22 Saturn radii from the cter of the disk; (c) north–south, across the region of absorpagainst the planet (the “cusp”). The model scans were convoto (full) observational resolution and compared with the data.varying the brightness of the A, B, and C rings we obtained bfits by eye. The brightness profile across the B ring is resolvwhich was modeled as a linear decrease outward. The opdepth of the B ring also decreases outward, as can be obsefrom the shape of the 3.6 cm absorption profile in Fig. 4.

The results are summarized in Table V. In most cases, varany parameter by more than≈0.25 K gives a visibly worsefit to the data, but allowing for calibration and deconvolutierrors, 1 K should be a realistic 3σ error. This number wasestimated from the size of the “ripples” at the edges of the scin Fig. 10. The cases when the fit parameter is more uncethan 1 K are specified in the table. For the B ring, brightntemperatures at the inner and outer edges are given. AlthougCassini Division (CD) was initially assumed to have zero optidepth (and brightness), significantly better fits to the obseransa brightness profiles at all three wavelengths were obtawith a nonzero brightness temperature for the CD. This extethe observations by GMB89 and dPD91, who found a nonzoptical depth for the CD, but did not detect its emission, probabecause of the less favorable geometry of their observation

7.1. East–West Asymmetry

The left panels of Fig. 10 show east–west scans throughring ansae. It is seen that the west, or dusk, ansa is brighterthe east, or dawn, ansa, in particular at longer wavelength

rdependence on location is most readily seen from the 3.6-cmimage, which has the highest resolution. The asymmetry is most

FIG. 9. VLA images from 1990 at full resolution, in total intensity (Stokes I) (colors) and in polarized intensity (contours). Beam FWHM is (1.64× 0.91)′′at PA−9.5◦ at 6.1 cm (top) and (0.97× 0.52)′′ at PA−10.6◦ at 3.6 cm (bottom). Contour levels are at 60, 75, and 90% of the peak

√Q2 +U2: 75.7µJy/beam at

3.6 cm and 86.8µJy/beam at 6.1 cm.


FIG

.10

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1990

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prominent in the C ring, smaller but significant in the B rinand not detected in the A ring. East–west scans through theand 6.1-cm images of dPD91, taken in 1986 atB≈ 26◦, showsimilar east–west asymmetries: strongest for the C ring,absent for the A ring, and a stronger asymmetry at 6.1 tha2.0 cm. Our 2.0-cm data, taken at a much smaller ring inclinatangle (B≈ 7.5◦), do not show an east–west asymmetry. Withthe error bars, no difference in polarized emission from the tansae could be detected.

Table V shows that at 3.6 cm, the east–west asymmetry vishes at the outer edge of the B ring, but at 6.1 cm, it incluthe outer B and A rings. No east–west asymmetry is measurat 6.1 cm for the C ring, presumably because of limited anlar resolution. The highest measured value of the west-to-brightness ratio,≈2.5, occurs in the C ring at 3.6-cm wavelengt

In Section 8.2, we compare the measured ring brightnesa function of scattering angle to model calculations, and tgraph (Fig. 12) suggests that the measured asymmetry is da dim east ansa rather than to a bright west ansa. The origthe east–west asymmetry is further discussed in Section 8.

7.2. Front–Back Asymmetry

The middle and right panels of Fig. 10 show north–south scthrough the rings at 1.22 Saturn equatorial radii east and we

TABLE VMeasured Brightness Temperatures and Optical

Depths of the Rings

Ansae At 1.22Rs Cusp region

Wavelength Ring East West Front Back TB τ(N)λ

2.0 cm A 4.0 4.0 8.0 3.5 70(10) 0.12± 0.02CD 5.0 5.0B (out) 5.0 5.0 15.0(2) 10.0 <15 >0.56B (in) 10.5 10.5C 8.75 8.75 5.5 0.5 90(10) 0.08+0.02

−0.01

3.6 cm A 4.25 4.25 5.5 5.0 6(2) —CD 2.0 2.0B (out) 4.5 4.5 10.5 8.5 70(5) 0.48± 0.04

B (in) 8.0 9.0 30(5) 1.03+0.14−0.11

C 2.0 5.0 6.5 4.0 50(15) 0.65+0.20−0.15

6.1 cm A 1.5 2.5 4.0 1.25 12(2) —CD 2.0 3.0B (out) 2.0 3.0 10.0 4.5 50(10) 0.99+0.34

−0.22B (in) 7.25 9.75C 2.75 2.75 7.0 2.5 90(10) 0.41+0.08

−0.07

Note.When no value is given for the inner B ring, the outer value appliesthe entire ring. The Cassini Division (CD) is detected only at the ring ansae.measured brightness temperatures are accurate to≈1 K (3σ ), unless specifiedin parentheses. Column 7 gives the measured brightness temperature towaplanet. For the 3.6- and 6.1-cm data, the B and C rings appear in absorptithe cusp, while the A ring is in emission. At 2.0 cm, all rings are in absorptagainst the planet. The≈2 K uncertainty in the absorption depth due to latitudin
structure on the planet is not included in the listed error. The text gives detabout the optical depth calculation.

,2.0-

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rd then at

onl

the planet. These plots show another asymmetry: the near (sside of the rings is brighter than the far (north) side, implying tthe ring particles scatter preferentially in the forward directiAgain, the effect is strongest at 6.1 cm and weaker at showavelengths. The 3.6-cm data indicate that again the effemost pronounced for the B and in particular the C ring. Tnear–far asymmetry is also prominent at 2.0 cm, in contrathe east–west asymmetry. At 2.0 cm, the near–far asymmemuch stronger on the east side than on the west side. Clear fback asymmetries have also been observed at 6.1 cm by dand Grossman (1990) for the B and C rings, whereas evidfor front–back asymmetries at 2.0 cm was relatively weakring inclination angles 12.5◦–26◦. Molnaret al.(1999) detectedboth east–west and front–back asymmetry, and also foundstrength of both effects to increase toward longer waveleng

As seen in Table V, the front–back asymmetries are large6.1 cm, as mentioned above. The values given for the “froand “back” sides at 1.22RS are averaged over the east and wsides of the rings, although at the front, the west side is brigthan the east side by≈1 K at 3.6 and 6.1 cm and by up to 4 K2.0 cm (Fig. 10). No significant east–west difference existsthe “back” side.

7.3. Optical Depth

Column 7 of Table V lists the measured brightness temptures at the location of the rings in front of the planet (the “curegion). To convert these into optical depths, the contribuof the ring emission (both thermal and scattered) to the msured brightness temperature must first be subtracted. Fromradiative transfer equation in the Rayleigh–Jeans limit,

e−τ(eff)λ = TB − TR

TD − TR, (2)

where the “effective” optical depthτ (eff)λ is related to the norma

optical depthτ (N)λ by τ (eff)

λ = τ (N)λ /sinB, whereB is the ring in-

clination,TB is the observed brightness temperature, andTR isthe brightness temperature of the ring emission. For the pltary brightness temperatureTD, we adopted 170 K at 3.6 cm an180 K at 6.1 cm. At 2.0 cm, we used the average brightnessnorth and south of the cusp, 165 K, as background temperaPlanetary limb darkening was not taken into account, so thaoptical depths from the 1990 data may be slightly overestima

During the 1990 observations, the ring inclination waslarge that only the B and C rings obscured the planet, whileA ring appears in emission just south of it. This is a rare opptunity to measure the ring brightness at a scattering angle eto the ring inclination,α=B= 30◦. (The scattering angleα isdefined in the next section.) At 3.6-cm wavelength, the A-rbrightness atα= 30◦ is consistent with the value measuredthe “front” side at 1.22RS, or α≈ 60◦. At 6.1 cm, however, thecusp brightness exceeds the value at the “front” side by a fa

ails≈3 (Table V). The observation by Grossman (1990) that the ringscattering phase function strongly peaks in the forward direction

in

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142 VAN DER T

is extended by this observation toα= 30◦. Previously publishedimages were taken at smaller ring inclinations, where the rare not visible in emission at scattering angles∼<40◦. At 3.6 cm,the emission of the B and C rings at the cusp was assumeequal the value measured at the front side at 1.22RS. At 6.1 cm,we multiplied the brightness temperature of the front side bwhich is a lower limit since scattering accounts for a larger pof the flux from the inner rings.

Due to the small ring inclination in the 2.0-cm data, the curegion is not entirely resolved. By assuming that the scattephase function does not have a minimum in the forward dition, we constrained the cusp brightness temperature of theto be at least equal to the value measured at 1.22RS on the nearside. For this reason, only a lower limit for the optical depththe B ring is given in the table.

The measured optical depths are in the last column of TabThe errors were determined by propagating the errors onring brightness through Eq. (2). The optical depth is smalfor the C ring, largest for the B ring, and intermediate forA ring. At 3.6 cm, the optical depth of the B ring is founto decrease outward, as implied immediately by the absorpprofile in Fig. 4b. The data are consistent with an increase inoptical depth of a given ring with increasing wavelength. Omeasurement of the A-ring brightness temperature at 6.1at α= 30◦ is crucial for this agreement. The contribution froscattering to the measured brightness temperature rises rawith wavelength, and leads, if ignored, to an underestimatthe optical depth. This is why both GMB89 and dPD91 fouthe optical depth to decrease toward longer wavelengths.

8. RING MODELS

8.1. East–West Asymmetry

The magnitude of the east–west asymmetry increases witcreasing wavelength, it appears to be strongest in the innerpart of the rings, and it may be more pronounced at large ringclination angles. These observations suggest that the asymmarises in scattered light, not in thermal emission from nonuformly distributed particles. Scattering is most important at lowavelengths, where the planet is brighter, and close to the plwhere Saturn fills the largest solid angle as seen from the rThe integrations are≈8 h, which is comparable to the Kepleriaorbital periods of 6.4 h for the C ring to 13.1 h for the A rinThis rules out large-scale azimuthal variations in the partdensity as explanation for the east–west asymmetry. In addisuch asymmetries could not persist due to Keplerian shearwest side is the evening side of the rings, where the partmay be expected to be warmer than on the east or morningas a result of irradiation by the Sun. However, this effect shobe stronger toward shorter wavelengths, opposite to what isserved. Similarly, the evening side of the planet may be war
than the morning side, causing uneven illumination of the rinbut again the resulting asymmetry should be strongest at s
AK ET AL.

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wavelengths. In addition, the diurnal irradiation by the Sun islikely to cause thermal effects at pressure levels∼>1 bar, wherethe radio emission originates (Fig. 6c). A warped ring placould produce the observed asymmetry because the ansaebe seen at slightly different scattering angles, but such a wwould have been observed before in the optical. East–west ametries have been seen at optical and near-infrared wavelenbut only in the A ring (Doneset al.1993), where we do not detecthem.

What cannot be ruled out is unresolved density variations wazimuth. The reflection off a moderately opaque slab by multscattering exceeds the transmission through it by factors upfew, and a combination of such slabs, if suitably oriented, colead to an east–west asymmetry such as observed. One pophysical interpretation of this idea is provided by gravitationwakes, which are 10- to 100-m-sized density enhancementhind large ring particles which, because of Keplerian shear,at an angle to the orbit. The theory of such structure was deoped by Julian and Toomre (1966) for the case of galactic diand has recently been applied to Saturn’s rings by Salo (11995) in dynamical simulations, in which a maximum denscontrast of∼25% and a trail angle of 20◦–25◦were found. Doneset al. (1993) proposed a connection between the wakes andazimuthal asymmetry seen at optical wavelengths in the A ra relation to the east–west asymmetry at radio wavelengthsalso suggested by Molnaret al. (1999).

Consider a pair of gravitational wakes trailing large ring pticles at the two ring ansae, as drawn schematically in Fig.If the wakes have sufficient optical depth, multiple scatterbecomes important, so that the intensity in the beam reflethrough multiple scattering is not the same as in the transted beam. Assuming isotropic scattering, an angle of incideof 60◦, and a single-scattering albedo of unity, the reflectionR(summed over all orders) is brighter than the transmissionT by50–100% for reasonable choices of optical depthτ and a cosineof the exit angleµ (van de Hulst 1980, pp. 256–257). For eample, ifτ = 1 andµ= 0.3, R= 0.664 andT = 0.402, which iscomparable to the typical observed brightness contrast betwthe east and west ansae. Higher optical depths produce a lcontrast, but this is not realistic in the case of Saturn’s ringsTable V). To achieve a higher contrast at given optical depthexit angle must be small: ifτ = 1 andµ= 0.1, R= 0.772 andT = 0.319, a contrast close to the maximum observed valu2.5. A grazing exit angle can also act to keep the same conat lower optical depth: ifτ = 0.5 andµ= 0.1, R= 0.671 andT = 0.445. A small exit angle corresponds to a large trail agle of the wakes. Our observations thus suggest that eithewake–interwake density contrast or the trail angle is somewlarger than in the simulations by Salo (1995).

The calculations by van de Hulst (1980) do not includedependence on wavelength, but the observed increase ieast–west asymmetry toward longer wavelengths can be ac

gs,hortmodated in our model by an optical depth that increases withincreasing wavelength, as is observed (Section 7.3, Table V).

indicatedre


FIG. 11. Schematic top view of Saturn and its rings. The slanted rectangles represent gravitational wakes trailing large ring particles, which areby heavy dots. The ring rotates differentially in the direction indicate by the arrow on top. The beam received on Earth from the west ansa arises fromflection
through multiple scattering in the wake, while on the east side, the light is transmitted through an otherwise similar wake. At small ring inclinationangles, a mixture
t

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of reflected and transmitted light is received on Earth from both ansae (do

Observations at 20.1 cm could further test this interpretatsince the optical depth of the rings should go down at slarge wavelengths. Alternatively, the ring inclination might pla role, because our 2.0-cm image was taken at an inclinatioonly 7.5◦. In the multiple-scattering interpretation, the asymmtry is expected to vanish at small inclination angles, becausthis case, a mixture of reflected and transmitted light is receon Earth. This situation is illustrated by the dotted rectangleFig. 11.

The above discussion assumed illumination of the slab bpoint source, which is not a good approximation for SaturC ring, seen from which the planet fills almost half the sComputations for the other limiting case, isotropic illumintion, can be found on pages 258–259 of van de Hulst (19where a Lambert surface is added. For a grazing exit aµ= 0.1 andτ = 1, R= 0.698 andT = 0.302, very similar tothe result for a thin beam. However, forµ= 0.5, R≈ T , whilefor µ= 0.7, T > R, so that the model would break down. Caculations that include the exact geometry of scattering byrings are clearly needed. Another caveat for the wake modthat in the simulations by Salo (1995), the density enhancemis strongest in the A ring, weaker in the B ring, and absenthe C ring, opposite to the trends in the radio data. Detacalculations are needed to establish if this apparent discancy is a radiative transfer effect or that mechanisms otherwakes must be sought as explanations for the east–west a
metry.
ted rectangle) and the E–W asymmetry is expected to disappear.

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8.2. Scattering Profile

Cuzziet al.(1980) give detailed predictions for the brightneof Saturn’s rings at radio wavelengths. The model assumdifferential size distribution∝a−3, with cutoffs at particle radiia= 0.1 and 100 cm. The rings are taken to consist of mvertical layers of particles composed of pure water ice witHenyey–Greenstein scattering phase function (see BohrenHuffman 1983). The only structure in the model is the optidepth changing from ring to ring; no east–west asymmetrpredicted. Comparison of this model to the data is performeterms of the scattering angleα, which is calculated from

cosα = cosB cosθ, (3)

and hence is a combination of the ring inclinationB and theazimuthθ , defined to be zero at the sub-Earth point and increing counterclockwise as seen from the ecliptic north pole,in the direction of the rotation. With this definition,α= 0◦ is“new” phase or forward scatter, andα= 180◦ is “full” phase orbackscatter. Optical studies generally adopt the opposite (Doneset al. 1993) because unlike at radio wavelengths, wis scattered is sunlight so that only backscattered light caobserved from Earth. The Cuzziet al.model predicts a generaincrease in the brightness temperature with decreasing scing angle, in particular at angles<50◦. The maximum inten-
sity occurs in the purely forward direction, which is, however,

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144 VAN DER T

unobservable. Neither the active (radar) nor the passivecrowave observations used to constrain the model resolvedindividual rings, so that a close match to the observationssented in this paper, which do resolve them, is not expectedmodel our 2.0-cm observations, we simply take the averagthe model values for 0.83 and 3.71 cm given by Cuzziet al.

Figure 12 compares the brightness temperatures frommodel with the measurements from Table V. Even thoughattempt has been made to normalize calculations and obs
tions to each other, the data and model values are seen to agreethat the phase function at this wavelength is even more forward to≈30%. It is seen that the general brightness level of each ringpeaked than in the Cuzziet al.models.
FIG. 12. Measured ring brightness east of the planet (solid squares)superposed as dotted lines. Top to bottom: C, inner B, outer B, and A rings

AK ET AL.

mi-there-. To

of

thenorva-

in the model is consistent with the observed value, which limthe amount of silicate impurities in the ice to<10% by volume,as found earlier by Grossman (1990). The model predicts ain optical depth of the rings as the wavelength increases fr0.3 to 6 cm, in agreement with the observations (Table V).addition, the model reproduces the observed brightness incrtoward smaller scattering angles, especially for the A and inB rings. At 6.1 cm, however, the observed A-ring brightnessα= 30◦ is significantly higher than predicted, which sugges

and, if different, west (open squares), with model calculations by Cuzziet al. (1980). Left to right: 2.0-, 3.6-, and 6.1-cm wavelengths.

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The monotonic increase in brightness temperature withcreasing scattering angle is inconsistent with the observedtern in the outer B ring (Fig. 12, third row from the top), whethe ansae are weaker than the intermediate scattering angladdition, the model predicts a higher optical depth for the ouB ring than the inner, while the opposite is observed (Fig.Table V). This suggests that the scattering phase function isthe same for all rings. While the scattering properties of the riin the optical probe variations in the surface roughness ofparticles and the presence or absence of a regolith layer (Det al. 1989, Doneset al. 1993), the scattering phase functioat radio wavelengths depends on the particle size distributThe dependence on particle shape is much smaller and mafurther constrained when more sensitive polarization dataavailable, in which all rings are detected over a range of stering angles. The exponent of the size distribution adoptedCuzziet al. (1980) was later derived from the Voyager 1 radoccultation data by Zebkeret al. (1985) and by Showalter andNicholson (1990) from the Voyager 2 stellar occultation daBoth data sets indicated variations in the maximum particledius by factors up to 5, which are on a scale of 20 km foroptical data and 1200 km for the radio data. The data discusin this paper have a resolution of only about 9000 km, butcontrast to the Voyager data include the B ring, which is topaque to be studied in absorption. The brightness dip insideways direction (α= 90◦) observed by the VLA in the outeB ring suggests an excess of large particles compared withdistribution assumed by Cuzziet al.The cross section for backward and forward scattering increases sharply for particle sgreater than the wavelength. Our observed profile in the oB ring indicates stronger backward and forward scattering tthe Cuzziet al.model predicts, suggesting the presence of la(∼>100 cm) particles. The Voyager data indicated maximum pticle radii ranging from 80 to 240 cm derived from the radio daand ranging from 140 to 1190 cm derived from the optical d(Zebkeret al. 1985, Showalter and Nicholson 1990), althouthese values refer to selected regions in the A and C rings.few optical occultation data that could be obtained through thring seemed to suggest that the particles in the B ring are lathan in the A and C rings (Showalter and Nicholson 1990),qualitative agreement with the results found here. More detamodels would be useful to quantify the constraints on the sdistributions in the various rings imposed by the current data

9. CONCLUSIONS

This paper discusses radio interferometric images of Satobtained over the years 1990–1995 with the BIMA and VLtelescopes at wavelengths of 0.35, 2.0, 3.6, and 6.1 cm (Taband II). The data are used for a study of both the atmosphand the rings. For the 1990 data, we used the versatility of inferometers to present two images per data set. Both are Fo
transformed from the UV data, but with a different range in atenna spacings emphasized, since the structures the author

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interested in on the planet are on larger scales than structof interest in the rings. For the 2.0-cm data from 1994, a sinimage is sufficient to describe atmosphere and rings; the 1data, being taken close to ring plane crossing, cannot be useinvestigations of the rings. The paper is subdivided into partsthe atmosphere and the rings; we continue this division forconclusions.

9.1. Atmosphere

For all five data sets, the measured total brightness is csistent with thermochemical equilibrium models by Briggs aSackett (1989) and de Pater and Mitchell (1993), as are lidarkening curves. The southern hemisphere of the planebrighter than the northern by≈5%, both in a 2.0-cm image from1994 and in a 6.1-cm image from 1995. This is the first timthe entire southern hemisphere is seen at radio wavelengA 0.35-cm image from 1995 shows marginal evidence forsouthern brightening. On smaller spatial scales, the data sthe latitudinal brightness distribution to vary significantly wittime, both at 2.0 cm and at 6.1 cm. In 6.1-cm observations fr1982–1986 (de Pater and Dickel 1982, GMB89, dPD91), a briband appeared around latitude 30◦N, while an image from 1995instead shows a band at latitude≈40◦S and a dark region aroundthe equator. Instead of the flat 2.0-cm brightness structure in1980s, two bands are visible in 1994, at latitudes≈40◦N and≈17◦N. The second of these appears slightly resolved.

We calculated the brightness of Saturn’s atmosphere incase of departure from thermochemical equilibrium in tNH4SH and NH3-ice clouds, as well as for a range of temperture gradients in the upper troposphere. The results are presein detail in Table IV and Fig. 7 and can be summarized as flows. Supersaturation of the NH4SH solution cloud decreases th6.1-cm brightness most, while the relative change at 3.6 cmabout twice as small. There is no change at 2.0 cm and onsmall one at 0.35 cm unless the supercooling extends all theup to the base of the NH3 ice cloud at 150 K. Supersaturationof the NH3 ice cloud has a pronounced effect at 0.35, 2.0, a3.6 cm, while the relative brightness change at 6.1 cm is oabout half that at other wavelengths. Lowering the humiditythe NH4SH cloud increases the brightness temperature at alldio wavelengths significantly, and by practically equal amounIn contrast, lowering the humidity of the NH3 ice cloud pro-duces no observable change in atmospheric brightness atwavelength. Changing the temperature gradient in the uptroposphere can produce an observable brightness increa2.0 cm and a smaller increase at 3.6 cm.

The implication of these results is that observed brightnevariations at a single wavelength cannot be unambiguouslyterpreted. However, the physical processes considered all hadifferent relative effect at different wavelengths. This enablesto assign the 6.1-cm band from 1990 combined with the fl3.6-cm appearance to a very specific physical structure (
n-s areFig. 8). Over most of the planet, NH4SH is supersaturated anddoes not condense untilT < 190± 5 K. Only at northern


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midlatitudes, where the bright band is seen, does the NH4SHcloud form at the thermochemical equilibrium temperature235.5 K. Humidity variations and supersaturation of the N3

ice cloud cannot reproduce the brightness structure observe1990. The effect of absorption by solid NH3 is harder to evalu-ate by lack of optical constants, but it is unlikely that this effecould produce a bright band at 6.1 cm but none at 3.6 cm.

The physical structure of the giant planets’ atmospheresits time variation is of great interest. Using the models presenin this paper, the range of processes occurring in the condetion region of Saturn can be well constrained by simultanemonitoring at at least two radio wavelengths. The VLA, in cofigurations matched to the size of features on the disk, isideal instrument to carry out such a study.

9.2. Rings

The rings are visible in our 1990 and 1994 data in emissas well as in absorption against the planet. The linearly poized emission,∼>30% of the total light, peaks at the ansae aappears confined to the B ring, as expected if most light is sinscattered planetary emission. From the images, the brightof the rings at scattering anglesα≈ 45◦, 90◦, and 135◦ is mea-sured (Table V). We confirm the nonzero optical depth ofCassini Division first seen by GMB89, and present the firstidence for emission from this region. In addition, the large riinclination in 1990 allowed us to measure the A-ring brighness at a small scattering angle,α≈ 30◦, for the first time. It isfound that the forward scattered component of the ring emissincreases strongly with wavelength. This has important conquences for the calculation of the ring optical depth, whichfound to increase with increasing wavelength, contrary to pvious work.

We confirm that the west ansa is brighter than the eastas first noted by dPD91. The effect becomes stronger wincreasing wavelength and with decreasing distance to thenet, implying an origin in scattered planetary emission ratthan in thermal emission from the rings themselves. Multiscattering in gravitational wakes appears to satisfy all obvational constraints, but more detailed models that includeexact scattering geometry are needed. The measured ring brness as a function of scattering angle is reproduced to≈30%by the calculations by Cuzziet al. (1980) for the A and in-ner B rings (Fig. 12), except in the outer B ring, where wattribute the discrepancies to an excess of large (∼>meter-sized)particles.

ACKNOWLEDGMENTS

The authors are grateful to Joop Hovenier and Carsten Dominik for usdiscussions, Elias Brinks for assistance in preparing the 90-cm observatand Mel Wright for help in reducing the BIMA data. We also thank MaHofstadter and Larry Molnar for helpful comments on the manuscript. Twork was supported over the years through grants to the University of Califoat Berkeley by NASA, NSF, and CALSPACE, most recently by NASA GranNAGW-4659 and NAG 5-4202 and NSF Grant AST 9613998. Additional tra

of

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andtednsa-us

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ionlar-d

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support came from Jack Lissauer through NASA Grant NAGW-6544 to the SUniversity of New York at Stony Brook.

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Time Variability in the Radio Brightness Distribution of Saturn

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