Time Variability in the Radio Brightness Distribution of Saturn

Icarus 142, 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 94720 E-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, and 6.1 cm taken in 1990–1995. These include the first radio images of 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 at 0.35 cm. The latitudinal brightness distribution varies substantially over time. The bright band at latitude 30◦ N seen throughout the 1980s 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 our 1990 6.1-cm image is absent in our 6.1-cm image from 1995. Instead, this image shows a bright band around latitude ≈40◦ S and a dark zone around the equator. An image at 2.0 cm from 1994 shows a bright band around latitudes ≈40◦ N and another one around ≈17◦ N which displays substructure. This contrasts with the flat 2.0-cm brightness distribution observed throughout the 1980s. We model the changes in Saturn’s brightness at radio wavelengths caused by supersaturation and humidity effects in the NH4 SH and NH3 -ice clouds, as well as by variations in the temperature structure of the upper troposphere. It is found that each of these processes is by itself able to change the planet’s radio brightness, but that a multiwavelength study can disentangle their effects. The 3.6- and 6.1-cm observations from 1990 can be reproduced by supersaturation of the NH4 SH cloud, while humidity effects and supersaturation of NH3 ice are ruled out. Detailed modeling of the data from 1990 shows that at northern midlatitudes, NH4 SH condensed at the thermochemical equilibrium temperatue of 235.5 K, while over most of the planet, condensation did not occur until T = (190 ± 5) K. Supersaturation may also cause the dark equatorial region seen in 1995 at 6.1 cm. Observations of the rings show that the west (dusk) ansa is brighter than the east (dawn) ansa by factors of up to 2. The polarization characteristics are as expected in the case of single scattering of Saturn’s thermal emission. The magnitude of the asymmetry increases with increasing wavelength and with decreasing distance to the planet, implying the effect arises in the scattered planetary emission rather than in the rings’ thermal emission. We show that the east–west asymmetry may be due to multiple scattering in gravitational (Julian–Toomre) wakes, although more detailed models are needed to assess this possibility. The measured brightness of the A and inner B rings as a function of scattering angle agrees to within ≈30% with model calculations by J. N. Cuzzi, J. B. Pollack, and A. L. Summers (1980, Icarus 44, 1 Current address: Sterrewacht, Postbus 9513, 2300 RA Leiden, The Netherlands.

683–705) of scattering of Saturn’s thermal emission off ice particles with N(r) ∼ r−3 between r = 0.1 and 100 cm. In particular, the predicted strong forward peak of the scattering is clearly seen in the data. The brightness of both ansae in the outer B ring is a factor of 2 lower than that of the model and than the brightness at intermediate 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, from the 0.5-bar level down to ∼10 bar on Jupiter and Saturn and to ∼100 bar on Uranus and Neptune, and thereby provide information complementary to visual and infrared observations, which typically probe the regime 1–1000 mbar. Radio interferometers resolve the planets, allowing one to study spatial structure in the atmospheres. In the case of Saturn, radio interferometry also serves to study the rings, which appear in emission east and west of the planet and in absorption toward it. The radio data sample a different regime of ring particle sizes than optical and near-infrared observations because scattered light probes approximately wavelength-sized material. Observations at centimeter wavelengths sample scattering angles ≈20◦ –160◦ because the radiation being scattered is planetary emission, while sunlight is being scattered in the optical, so that only backscattered light is received on Earth. In addition, the thermal radiation of the ≈95 K rings is detectable only at far-infrared and radio wavelengths. Images of Saturn at radio wavelengths have been published by Grossmann, Muhleman, and Berge (1989; hereafter GMB89) and by de Pater and Dickel (1982, 1991), and extensive models have been developed by Briggs and Sackett (1989). All these authors found that the brightness distribution of the planet at 0.3– 20 cm wavelength is to first order described by a limb-darkened disk. At the shorter wavelengths, the disk appeared featureless, but at 6.1 and 20 cm, a bright band was present around latitude 30◦ north. In this paper, we show that the latitudinal structure of the planet changes drastically over time at all wavelengths, an observation that is consistent with the findings by Molnar et al. (1999), who present data taken in November 1995, a few months after our most recent data set. We carry out model calculations to investigate the physical origin of these bands.

125 0019-1035/99 $30.00 c 1999 by Academic Press Copyright ° All rights of reproduction in any form reserved.

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TABLE I Summary of VLA Observations Frequency (GHz)

Configuration

Date

Beam FWHM (arcsec)

Diameter (arcsec)

Inclination (deg)

3C 286 (Jy)

Phase calibrator(s)

30/08/1990 01/09/1990 15/05/1992

4.885 8.415 0.330

B B C

1.6 1.0 77.6 × 51.6

17.9 17.9 16.9

29.3 29.3 18.4

7.55 5.27 26.4

27/09/1994 13/08/1995

14.940 4.860

C A

1.5 1.5

18.9 19.0

7.5 0.1

3.59 7.40

1911–201 1911–201 1939–154, 2321–163 2246–121 2323–032

Note. The flux density of 3C 286 at 4.9 GHz is slightly lower in the 1995 observations than in the 1990 observations because this source is partially resolved in the A configuration.

In 1995, Saturn’s rings were seen edge-on from Earth for the first time since 1980. Since the southern hemisphere has been hidden from view over that period, we present the first radio images of the entire southern hemisphere. The edge-on geometry also offers a unique opportunity to observe both hemispheres of the planet simultaneously. This is ideal to reveal north–south asymmetries in the planet’s atmosphere, without having to correct for different viewing geometry and obscuration by the rings. The radio emission from Saturn’s rings has been studied extensively by Cuzzi et al. (1980) and Grossman (1990). From interferometer observations which did not resolve the individual rings, Cuzzi et al. (1980) modeled the ring emission in detail, and predicted a strong forward scattering effect for all rings at all wavelengths, although most pronounced at the longer (3.7– 20 cm) wavelengths. Grossman (1990) examined observations of the ring brightness as a function of scattering angle, and found that ring brightness indeed increases toward smaller scattering phase angles at wavelengths of 6.1 and 20 cm, but not at 2.0 cm. This observation also agrees with data presented by de Pater and Dickel (1991; hereafter dPD91). All ring-resolved observations support the prediction that the C ring, despite a smaller optical depth, is as bright as the A ring, caused by the fact that the C ring “sees” the largest solid angle from Saturn’s disk. In this paper we provide additional data on the scattering phase function of the ring particles at different wavelengths and ring inclination angles. Moreover, we provide clear evidence of an east–west asymmetry in the ring brightness, a feature that was noted first by dPD91 and later by Molnar et 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 summarized in Table I. Antenna spacings range from 680 m to 36.4 km in the A configuration, from 210 m to 11.4 km in B 2 The VLA is operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

configuration, and from 73 m to 3.4 km in the C configuration. Also listed in Table I is the ring inclination B at the time of observation, which is defined as the angle between the ring plane and our line of sight, equal to zero when the ring plane is perpendicular to the plane of the sky, i.e., when the rings are seen edge-on. The 6.1-cm observations in August 1995 were scheduled to coincide with the ring plane crossing as seen from Earth. However, at this epoch, the array was in its most extended configuration, which is not well suited to image objects as large as Saturn. For all observations, nonsidereal tracking was performed using the JPL ephemeris. At wavelengths 6.1 cm and shorter, the continuum correlator was used, with a total bandwidth of 100 MHz. Integration time on source was 300–330 min per observation. The flux calibrator was 3C 286, and its flux density, based on the scale of Ott et al. (1994), is given in Table I. Calibration is accurate to within 5%. For the 90-cm observation, a detection experiment, we used the spectral line correlator. The sidebands were centered at 327.5 and 333.0 MHz, with sixteen 6.25-MHz channels per sideband, separated by 390.6 kHz. This special frequency setup avoids interference with terrestrial signals. 2.2. Millimeter-Wave Observations Additional observations of Saturn at 0.35 cm were made with the interferometer of the Berkeley–Illinois–Maryland Association (BIMA)3 (Welch et al., 1996) near Hat Creek, California, in the six sessions in 1995 specified in Table II. Nonsidereal tracking is standard at this telescope since planets are frequently used as calibrators. The total bandwidth was 800 MHz in 512 channels in two sidebands, centered at 85.2 and 88.7 GHz. Observations of the quasar 3C 454.3 served to track the instrumental gain and phase. The last column of Table II lists the flux density adopted for 3C 454.3 to set the absolute flux density scale. The numbers are interpolations from measurements at 86 GHz, done by the BIMA staff on a monthly basis for this very purpose. Absolute flux levels are accurate to < ∼20%. After editing and calibration, the six data sets were put together, with corrections applied for the different planetary distances and 3 The BIMA array is operated by the Berkeley–Illinois–Maryland Association with partial funding from the National Science Foundation.

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

TABLE II Summary of BIMA Observations Date (1995)

Configuration

Time on-source (h)

Inclination (deg)

3C 454.3 (Jy)

24/3 29/3 01/6 04/11 14/12 23/12

6A 6B 6C 6C 9H 9H

3.5 4.7 4.4 4.1 2.5 0.5

3.3 3.0 0.3 −3.2 −3.0 −2.7

10.0 10.0 7.5 6.1 5.7 5.5

Note. The configuration code is the number of antennas (6 or 9), followed by A (extended)–C (compact). The “hybrid” (H) array employed in December has short east–west and long north–south baselines. Total time on-source is 19.7 h; the weighted mean ring inclination |B| is 2.5◦ . The image made from the combined data has a beam size of 5.000 FWHM.

position angles. The combined data set has projected baselines from the antenna shadowing limit out to 64 kλ. 2.3. Imaging Strategy The five data sets presented here differ considerably in the range of baseline lengths covered, while for a good comparison, the images should cover the same range of spatial scales. Interferometric observations do not have one intrinsic angular resolution, but are sensitive to a range of spatial frequencies. In this paper, we are interested in brightness structure on scales of 0.2–5 Saturn radii, and by adjusting the weights in the Fourier transforms, we have constructed the images in such a way to bring out these scales, although not all observations were most sensitive in the corresponding range of antenna spacings. The standard way to make images from interferometer data, using the CLEAN deconvolution algorithm, is suitable for studying the rings, and we will use it in the second part of this paper. To image the planet itself, however, this method is less appropriate, because the object has a smooth brightness distribution extended over many synthesized beams, while the algorithm attempts to find point sources. This mismatch shows up as longitudinal structure in the “deconvolved” image, which cannot be real since the observations presented here span nearly a full saturnian rotation. For the VLA data from 1990 and 1994, we used the specialized deconvolution method developed by de Pater and Dickel (1982). An initial self-calibration used a uniform disk as a model, while subsequent iterations used more realistic representations of the saturnian system, including limb darkening and, for the 1990 data, a simple description of the rings. Uniform weighting of the visibility points led to synthesized beams of axial ratios up to 1.5, but analysis was performed on the images in Fig. 1, which have been convolved to a circular beam. The sizes of these convolving beams are listed in the fourth column of Table I. The linear resolution is typically ∼0.15RS (Table I), where the equatorial radius of the 1-bar level, RS = 60,268 km, is from Lindal et al. (1985).

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The 1995 VLA data, being taken in the A configuration, seriously suffer from missing short antenna spacings. Only 1.7% of the visibility points are on projected baselines shorter than 14 kλ, the first null of the visibility function. Applying a gaussian taper with a 1/e width of 200 kλ to the UV data produced an image with structure on the desired scales. However, the sensitivity is too low to permit self-calibration. The “blobs” on the east side of the planet and the negative emission west of it are artifacts, caused by either phase errors or deconvolution errors. The maps do not have an overall slope, which would be indicative of pointing errors. The BIMA data do not have baselines > ∼100 kλ, but the covered portion of the UV plane is well filled due to the combination of different array configurations. This allowed us to perform the Fourier transform with superuniform weighting. In this scheme, the weight of a visibility point is inversely proportional to the local point density as evaluated over many adjacent UV cells rather than over just one, as in ordinary uniform weighting. Compared with ordinary uniform weighting, this decreases the size of the synthesized beam and gives better sidelobe suppression. The image in Fig. 1e has a beam size of 5.000 FWHM. At 90 cm, the planet is unresolved in the (77.6 × 51.6)00 beam (uniform weighting). This allowed mapping and deconvolution in the standard way. We deleted all UV data points with an amplitude >12 Jy, which are probably due to interference because they all appear on short antenna spacings. The first three and last four channels in each sideband were discarded because of bandpass effects. The processed data set contains baselines from the shadowing limit out to 3.8 kλ. We used nearby background sources for self-calibration of the antenna phases. The resulting 2σ upper limit of 9.6 mJy is consistent with models by de Pater and Mitchell (1993), which predict a brightness temperature of 400–450 K, or a flux density of 6.4–7.2 mJy for a source size of (16.94 × 15.23)00 .

Part I: Atmosphere The images of Saturn’s atmosphere are studied using a model atmosphere based on the assumption of thermochemical equilibrium. Sections 3 and 4 argue that this assumption is a reasonable first approximation by showing that the model reproduces both the observed total flux density at 0.1–100 cm and the shape of the limb darkening. Section 5 presents the observed deviations from this basic model, and these are interpreted in Section 6 as latitudinal variations in the atmospheric structure, in particular in the altitudes at which NH4 SH and solid NH3 condense out. 3. BROADBAND RADIO SPECTRUM

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

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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 143.4 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 within the contour around position (0, 0) in (d) is an intensity decrease, while all other features on the disk are increases.

functions, i.e., the Fourier transform of a uniform disk, to our UV data. The size and shape of the disk were taken from the Astronomical Almanac, since the radii of the optical and radio emission of Saturn are to within 0.6% the same. This leaves the disk-averaged brightness as the only free parameter, and its best-fit values are listed in Table III. To account for the cosmic microwave background, which is invisible to an interferometer, 2.7 K has been added to the result of the fitting routine. The effect of the rings on the total brightness is discussed below.

Absolute calibration is the major source of uncertainty, which is 5% for most data sets. The 6.1-cm data from 1995 contain so few short baselines that the accuracy is closer to ≈10%. Calibration at 0.35 cm is accurate to ≈20%. The other observations listed in Table III are those from the de Pater and Mitchell (1993) collection which were taken at small ring inclination angles. The error bars of the Briggs and Sackett (1989) data have been changed to include the uncertainty of the absolute calibration of the old VLA system: 10%

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

TABLE III Observed Disk Brightness Temperatures of Saturn Wavelength (cm)

Brightness temperature (K)

Inclination (deg)

Reference

0.10 0.20 0.33 0.34 1.33 1.99 2.00 3.56 6.13 6.14 6.14 20.73 69.72 90.78

145 ± 14.5 137 ± 11 149.3 ± 4.1 157.8 ± 31.6 132.5 ± 13.3 136.1 ± 6.8 158.9 ± 7.9 161.1 ± 8.1 180.5 ± 18 168.6 ± 8.4 173.6 ± 8.7 219 ± 11 352 ± 42 <601.0 (2σ )

0.02 <5 <8 3.03 <0.25 <0.25 7.5 29.3 0.07 29.3 <0.25 <0.25 <0.25 18.4

Werner and Neugebauer (1978) Ulich (1981) Ulich (1981) This work Briggs and Sackett (1989) Briggs and Sackett (1989) This work This work This work This work Briggs and Sackett (1989) Briggs and Sackett (1989) Briggs and Sackett (1989) This work

Note. To correct the total flux for emission and absorption by the rings, the 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 shows the available data points at B < 10◦ as solid symbols, with model curves after de Pater and Mitchell (1993) and de Pater and Massie (1985) superposed. The models have been calculated for zero

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inclination angle, but changing this angle to 30◦ affects the brightness of the disk by <1 K. The figure illustrates that the effects of considering different absorbers are much larger than those of a changing mean emission angle. The solid curve takes only absorption by gaseous NH3 into account. The model atmosphere is in thermochemical equilibrium, with the tropospheric abundances below the clouds per mole of gas taken from Briggs and Sackett (1989): [NH3 ] = 5.2 × 10−4 (1.9 × solar N), [H2 O] = 6.9 × 10−3 (4.7 × solar O), [CH4 ] = 4.2 × 10−3 (3.0 × solar C) and [H2 S] = 4.1 × 10−4 (11.0 × solar S). Solar abundances are from Grevesse and Noels (1993) for carbon, nitrogen, and oxygen, and from Anders and Grevesse (1989) for sulfur. The other two curves in Fig. 2 are estimates of the effect of tropospheric clouds on Saturn’s radio spectrum. These calculations assume wet adiabatic cloud densities, which are upper limits based on the assumption of no loss by precipitation. The dashed curve includes absorption by the H2 O and NH4 SH clouds besides NH3 gas. The effect of these clouds is appreciable only at wavelengths > ∼10 cm. At 30 cm, liquid H2 O may decrease the disk brightness by 5 K, and liquid NH4 SH may absorb another 12 K up to a total of < ∼17 K. The water abundance is mostly constrained by the 70-cm data point, a difficult measurement because of the strong background emission and variability of the Earth’s ionosphere. The dotted curve considers solid NH3 and H2 O particles as additional absorbers, where we use the dielectric

FIG. 2. Observed and modeled radio spectrum of Saturn. Solid symbols are data at ring inclination angle B < 10◦ , open symbols are data at B > 10◦ . Squares are data presented in this paper, as is the triangle denoting our 90-cm upper limit; circles are measurements by other authors. In the range 1–10 cm, the effect of liquid and solid absorbers is seen to be negligible.

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constants from de Pater and Mitchell (1993). The dielectric constant for NH3 ice at radio wavelengths was assumed to equal the value at optical wavelengths, which is likely an overestimate. Around 6 cm, NH3 ice may cause a brightness decrease of < ∼6 K, which is similar to the observational uncertainty. A more pronounced effect is visible at wavelengths shortward of 0.5 cm, due to absorption and scattering by NH3 ice particles in the upper troposphere. Solid NH3 is expected to form in the giant planets’ atmospheres; recently, Brooke et al. (1998) obtained the first direct detection of NH3 ice on Jupiter using the Infrared Space Observatory. However, it is seen from the figure that including the ice does not appreciably improve the match to the data. At 0.1–0.3 cm, the fit even becomes somewhat worse, which could be due to a too high dielectric constant of NH3 ice or to the cloud density being less than maximum due to precipitation. Also shown in Fig. 2 are our observations at B > 10◦ , as open symbols. The measured total flux densities have been converted to pure disk flux densities by correcting for emission and absorption by the rings. Correction factors are from Klein et al. (1978), a crude model that assumes the rings to have a constant surface density and an optical depth τ = 0.7 over the entire wavelength range. Application of this model typically changes Saturn’s disk brightness temperature by 1–10%, depending on ring inclination angle and wavelength. De Pater and Mitchell (1993) show Saturn’s radio spectrum including observations at all ring inclination angles, which show a large scatter, more than can be explained by calibration problems alone. Our 2.0-cm point illustrates this: it lies significantly above the model curve, even though the point is supposed to be corrected for ring effects. The Klein et al. model can and should be improved, using recent high-resolution images at centimeter and millimeter wavelengths, as well as data obtained during the Voyager flybys. Optical depths and ring brightness temperatures have now been determined for the A, B, and C rings separately, and show a clear dependence on radial position and on wavelength (GMB89; dPD91; Part II below). This information was not available when Klein et al. (1978) developed their model. When the inaccuracies in the ring model are removed, some spread in the data points may remain, caused by spatial and temporal changes in atmospheric opacity or the temperature–pressure profile, leading to changes in Saturn’s disk-averaged brightness temperature. Given the large variations in the brightness structure seen by us (see Section 5 below) and Molnar et al. (1999), it is not inconceivable that Saturn’s disk-averaged brightness temperature varies as well. 4. LIMB DARKENING

Although the broadband spectrum provides a good first check of planetary model atmospheres, its use is limited to deriving the global average of the distribution of microwave absorbers. Interferometers can resolve this distribution and thereby provide information on planetary meteorology. However, the long integration times prohibit the detection of features in the east–west

direction. What is resolved is the limb darkening, and this effect will be used here as a more stringent test of the models. Figure 3 shows scans in the east–west direction through the images from Fig. 1. (In this paper, cardinal directions refer to Saturn, not to the sky.) The error bars represent the 1σ variation in brightness in regions of the images without emission from the planet or from the rings. The data have been folded about the central meridian to increase the signal-to-noise ratio, and averaged over one beam FWHM in latitude. The beam size is indicated by the bar. The planetocentric latitudes of the scans have been chosen to avoid the various latitudinal features visible in the images, which are discussed in the next section. To convert planetocentric to sub-Earth latitudes, subtract the ring inclination. Superposed are scans through model images, which have been tilted by the inclination angle and convolved with the appropriate beam. The model is that of the solid curve in Fig. 2. Interferometers do not measure the total flux density of the source, and the ability of deconvolution algorithms to recover it is model dependent and limited by the size of the central hole in the UV plane. For extended, smooth objects such as planets, the accuracy of the recovered brightness is no better than ≈5%, even with our specialized deconvolution method. In addition, the latitudinal brightness structure visible in Figs. 1a, c, and d obviously cannot be reproduced by a model with a uniform distribution of absorbers. If the atmosphere were globally in thermochemical equilibrium, the model should match the data on average, but it will be shown in Section 6.3 that at least for epoch 1990, the global brightness was decreased by ≈5% due to supercooling. We accommodated the uncertainty in observed absolute brightness by scaling the model curves by factors ranging from 2 to 10% from unity to match the data at the central meridian. This multiplicative scaling is an approximation of an exact spatial Fourier filtering of the model results. Except for the 6.1-cm image from 1995, which contains residual phase errors as discussed in Section 2, the match between data and model is excellent. The conclusion is that thermochemical equilibrium provides a good starting point for more detailed modeling. The departures from equilibrium calculated in Section 6 have only a small impact on the limb darkening curves. 5. NORTH–SOUTH PROFILES

Figure 4 presents scans through the images from Fig. 1 along the central meridian, averaged over one beam FWHM in longitude. The error bars are the same as in Fig. 3. Integration over longitude would reduce the noise in these scans by factors of up to ≈3 for the VLA data and up to ≈2 for the BIMA data, depending on latitude (cf. Tables I and II). We have not performed this integration since the error bars are already quite small. However, we stress that whether a feature in the scans is significant or not was based not only on the scans, but on the entire image (Fig. 1), since only features visible at all longitudes are significant. The dashed lines in Fig. 4 are scans through the same model images as for the east–west scans, again convolved to the

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BRIGHTNESS (mJy beam-1)

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

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

resolution of the observations, tilted by the ring inclination and scaled to the data. To have resolution constant over the graph, the ordinate is the sine of the planetocentric latitude λplc . In 1990 and 1994, part of the back side of the planet was visible. To describe this, the following analytic continuation of sin(λplc ) is used as ordinate: sin(λplc − lπ ) + 2l, with the “cycle number” l the integer part of (λplc ∓ π/2)/π for λplc < > 0. For easier reference, the corresponding values of λplc itself are given at the top of each plot.

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

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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 model images including only gaseous absorbents. The bar at the bottom center indicates the observational resolution. The lower ordinate is sin(λplc ), which corresponds directly to position on the original image, while the upper ordinate is λplc itself for convenience. The rings are seen in absorption at λplc = −15◦ to 0◦ (a) and at λplc = −50◦ to −10◦ in (b) and (c), and in emission near λplc ≈ −90◦ in (b) and (c). All other observed deviations from the model are atmospheric, as discussed in the text.

of the model to the data is somewhat arbitrary, the unit level, indicated by the dashed line in Fig. 5, is uncertain by ≈10%. The region of absorption by the rings, where the model is not expected to match the data, has been omitted from Figs. 5b and 5c. The ratio error bars are the data error bars divided by the model brightness. In the 1995 6.1-cm image (Figs. 4d and 5d), the southern hemisphere is brighter than the northern by ≈5%. This is the first time that the entire southern hemisphere is seen at radio

wavelengths. The small part of the southern hemisphere visible in 1994, λplc = 20◦ –45◦ S, suggests an enhanced brightness by a similar fraction (Fig. 5a) relative to the model. The 0.35-cm data (Fig. 5e) may show a brighter southern hemisphere, but the spatial resolution is not high enough for a definite statement. In addition, a variety of latitudinally confined features appear in Figs. 4 and 5. Particularly striking is the difference between the two 6.1-cm images from 1990 and 1995. Such large temporal variations in Saturn’s radio brightness structure have not been

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DATA/MODEL RATIO

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

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

seen before. The image from 1990 (Fig. 4c) shows the bright band at northern midlatitudes (λplc ≈ 30◦ –45◦ ), which was also seen by GMB89 and dPD91. The maximum brightness excess of ≈4% over the model value occurs at λplc ≈ 37◦ N (Fig. 5c). Although in previous observations, the intensity of this feature had varied over time, it had never disappeared, as in the 6.1-cm image from 1995 in Fig. 4d. The latter image shows a bright band (relative to the background) at 14◦ N and another one at ≈37◦ latitude south. This region is ≈5% brighter than the rest of the southern hemisphere, making the total north–south brightness contrast in Fig. 5d ≈10%. The third feature in Fig. 5d is the dip

at the equator. The cross section of the rings at this epoch was only ≈100 km, so that at the observational resolution of 8200 km FWHM, even 100% absorption would not be detectable. Therefore, the feature must originate in the planetary atmosphere. This “equatorial zone” and the enhanced brightness around it was also seen by Molnar et al. (1999) in lower-sensitivity 3.6- and 6.1-cm images taken in November 1995. The feature was much weaker in November than in August, which is additional evidence for variability of Saturn’s brightness distribution. The 2.0-cm image (Fig. 4a) shows two bright bands centered near λplc ≈ 17◦ N and λplc ≈ 40◦ N. Comparison with the model

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curve indicates that the band at 40◦ N has an excess brightness of ≈7%, while the maximum excess of ≈13% occurs at 10◦ N. This is the first time that brightness structure at 2.0 cm is seen on Saturn. Images at 2.0 cm from 1986–1987 (GMB89; dPD91) show a featureless planet. An image from 1982 (dPD91) may show structure similar to the bands in our data, but at a marginal confidence level. We note that in 1982, the 6.1-cm band at northern midlatitudes was weaker by a factor 2–3 than in 1986. The 2.0-cm band at λplc ≈ 40◦ N is unresolved in the latitude direction, as are the bands in both 6.1-cm images. The only resolved band is the one around λplc ≈ 17◦ N in the 2.0-cm image, which has an asymmetric shape. This feature can be described by the combination of two unresolved components. One is at λplc ≈ 21◦ N, of similar strength and width as the band at 40◦ N. The second is brighter than the first and located at λplc ≈ 12◦ N, just north of the region of absorption by the rings, where the 6.1-cm image from 1995 also shows enhanced emission. This decomposition is only meant to illustrate, and it is by no means unique. The 3.6-cm data do not show any latitudinal structure to a level of ≈1%. Likewise, the 0.35-cm image, which probes almost the same depth into the atmosphere, shows a featureless planet; however, latitudinal structure in the atmosphere such as seen at 2.0 and 6.1 cm would not show up in this image due to the large convolving beam. 6. MODELS OF LATITUDINAL BRIGHTNESS VARIATIONS

The model calculations shown in Figs. 2–5 are essentially those by de Pater and Mitchell (1993) and are based on a thermochemical equilibrium atmosphere after Romani (1986). For details about the construction of such model atmospheres see de Pater et al. (1989). As in Fig. 2 we used the abundances derived by Briggs and Sackett (1989). All model calculations in this section are based on opacities from gaseous NH3 , H2 S, and H2 O only (solid line in Fig. 2), since the calculated upper limits to the absorption by clouds are small at the wavelengths of interest (Section 3) and because the dielectric constants of the various clouds are poorly known. Figure 6 shows the temperature and the abundances of the major trace constituents versus pressure, as well as the weighting functions at the wavelengths of our observations. The weighting function Wλ (z) at wavelength λ and altitude z is defined as Wλ (z) = e−τ λ ·

dτλ , dz

(1)

where τ is the optical depth at wavelength λ and altitude z (τ increases into the atmosphere). It is seen that Wλ becomes broader and peaks at larger pressures as the frequency difference with the NH3 lines at 23.9 GHz increases. Observations at wavelength λ probe altitudes near where Wλ peaks; in the limit that Wλ (z) = δ(z), the brightness temperature would equal the physical temperature at altitude z.

FIG. 6. (a) Temperature–pressure relations for model atmospheres 1–16 (solid line), 17 (dashed line), and 22 (dotted line). (b) Solid lines: abundances of NH3 and H2 S gas in thermochemical equilibrium (Model 1). The effect of NH4 SH supersaturation on the NH3 abundance profile (Model 2) is shown by the dashed line, while the dotted line illustrates the effect of humidity (Model 8). (c) Weighting functions in the thermochemical equilibrium model (Model 1) at the wavelengths of our observations.

6.1. Variations at 6.1 cm The location of the 6.1-cm weighting function suggests two kinds of modifications to the gaseous NH3 abundance profile as possible causes of the observed latitudinal brightness variations. The first option is a rise of the base of the NH4 SH solution cloud to altitudes corresponding to temperatures below the thermochemical equilibrium value of 235.5 K. This effect, called supercooling or supersaturation, increases the opacity at the 4- to 5-bar levels (cf. dashed line in Fig. 6b) and decreases the 6.1-cm brightness. At 0.35, 2.0, and 3.6 cm, the effect is smaller, since Wλ at these wavelengths is small at pressure levels >4 bar (Fig. 6c). Underlying a latitudinal variation of the height of the NH4 SH cloud base could be the existence of a system of vertical motions, or winds, in the atmosphere. Such a wind system was inferred by B´ezard et al. (1984) from Voyager IRIS observations, and is generally invoked to explain changes in the optical

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

appearance of the planet. Variations in the NH4 SH condensation height could also arise due to local differences in the altitude where condensation nuclei such as dust particles are present. A smaller H2 S abundance would also raise the NH4 SH cloud base, but this would give a higher NH3 abundance above the cloud, so that the effect on the brightness would be similar at all wavelengths. Alternatively, the humidity in the NH4 SH cloud could be below unity due to convective mixing with drier air from higher altitudes. Like supersaturation, this process is known to occur in terrestrial clouds (Pruppacher and Klett 1980). The corresponding NH3 abundance profile is illustrated by the dotted line in Fig. 6b. A lower humidity implies a lower opacity in the entire 1–5 bar range and a brightness increase at all radio wavelengths. Table IV lists the calculated brightness temperatures at the center of the disk for the various model atmospheres. While supersaturation (Models 2–6) can cause a significant decrease in the 6.1-cm brightness without changing the 3.6-cm brightness, modifications of the NH4 SH humidity (Models 7–9) produce equal relative brightness increases at these two wavelengths. The results of the calculations are shown graphically in Fig. 7.

FIG. 7. Impact of the various departures from thermochemical equilibrium studied here on the radio spectrum of Saturn, illustrated by Models 1, 4, 8, 12, 15, and 22. Supercooling of NH4 SH (short-dashed line) decreases the brightness at long wavelengths. Lowering the NH4 SH humidity (dotted line) increases the brightness at all wavelengths. Supercooling of NH3 -ice (short dash–dotted line) decreases the brightness at all wavelengths but mostly toward short wavelengths. Decreasing the NH3 -ice humidity (long-dashed line) does not change the brightness significantly at any wavelength. The effect of a subadiabatic lapse rate (long dash–dotted line) is a brightness increase which is significant at 2.0 cm only.

135

6.2. Variations at 2.0 cm The 2.0-cm weighting function peaks close to the base of the NH3 ice cloud at 1.35 bar. Hence, local variations in the properties of the NH3 ice cloud will mostly affect the 2.0-cm brightness. In Models 10–16, we calculate the effect of supercooling and humidity in the solid NH3 cloud on Saturn’s brightness. The results are as follows. Forming the NH3 ice cloud at temperatures below the thermochemical equilibrium value of 148 K decreases the brightness at all radio wavelengths, although the effect is strongest at the shorter wavelengths, for which Wλ peaks at lower pressures. A brightness contrast of 13% at 2.0 cm is achieved if condensation occurs at 115 K. This would produce a 4.5% decrease at 6.1 cm. Note that the differences in emergent brightness temperature are always less than the change in physical temperature where condensation occurs. The temperature changes are partly cancelled since the opacity is strongly coupled to temperature in regions where the NH3 abundance follows the saturated vapor curve. The humidity of the NH3 ice cloud influences the brightness at all radio wavelengths by < ∼2%. In this cloud, the NH3 abundance decreases rapidly with altitude, so that basically the same temperature layer is probed, even if the humidity is as low as 20%. The humidity of the NH4 SH cloud also has some influence on the brightness at 2.0 cm, albeit less than at longer wavelengths (Models 7–9). Reproducing the maximum latitudinal brightness contrast of 13% observed at this wavelength requires a humidity as low as ≈20%. This would cause a 6.1-cm band of similar strength and a contrast of ≈20% at 3.6 cm. Besides departures from thermochemical equilibrium, another possible cause of brightness structure is variations in the temperature structure of the upper troposphere. In the region where NH3 ice condenses out, the temperature gradient, or lapse rate, may be below the wet adiabat by up to 10% because the crystals act as catalysts for the conversion of ortho- to para-H2 (Massie and Hunten 1982). Lapse rates exceeding the wet adiabatic value are implausible in a convective atmosphere and are not considered here. As a first experiment, we replaced the wet adiabatic gradient by the values Lindal et al. (1985) derived from the Voyager 2 radio occultation data. This temperature structure is indicated by the dashed line in Fig. 6a. At pressures <1.4 bar, the temperature is seen to be enhanced relative to the previous models. The maximum difference, 12 K, occurs at the tropopause (0.1 bar). However, the computed radio brightness temperatures (Table IV, Model 17) are the same as in the adiabatic model to 0.1 K, because the optical depth is negligible at P < 1.4 bar. To illustrate the effect of general changes in the temperature gradient, Models 18–22 show results if the decrease in ∇T from the adiabatic value sets in at pressures larger than 1.4 bar. In these models, the wet adiabatic gradient applies at high pressures, while if P < P0 , the lapse rate decreases linearly with altitude to reach zero at the 0.1-bar level. Models 18–22 use 1.4, 2.0, 3.0, 4.0, and 5.0 bar as values of P0 . The corresponding differences in physical temperature at 1 bar with respect to the nominal model are listed in Table IV. As an example, the dotted

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TABLE IV Brightness Temperatures of the Center of Saturn’s Disk, Calculated for Zero Inclination Angle Wavelength (cm)

NH4 SH cloud

NH3 ice cloud

Model No.

6.1

3.6

2.0

0.35

Tbase (K)

Humidity

Tbase (K)

Humidity

1T (K) (at 1 bar)

1

193.9

168.8

142.3

155.1

235.5

1.0

148.0

1.0

0.0

2 3 4 5 6

185.6 182.1 177.9 171.5 164.3

166.1 163.9 160.7 155.0 147.2

142.3 142.3 142.3 141.3 132.9

154.9 154.3 152.6 146.8 137.9

200.0 190.0 180.0 165.0 150.0

7 8 9

199.5 206.3 214.0

174.4 182.6 195.2

145.4 150.6 161.6

159.6 166.6 179.3

10 11 12 13

192.7 190.4 188.0 185.9

166.6 162.1 157.3 152.6

138.0 134.3 127.8 118.1

153.1 143.5 131.3 120.3

14 15 16

194.4 194.8 195.3

169.7 170.6 171.4

143.4 144.0 144.6

156.2 157.2 158.2

17 18 19 20 21 22

193.8 193.8 193.2 193.0 194.2 196.9

168.6 168.6 167.6 167.8 170.4 175.1

142.2 142.0 141.9 143.6 147.4 151.7

154.6 154.6 152.7 150.6 150.9 154.9

0.75 0.50 0.25 140.0 130.0 120.0 110.0 0.75 0.50 0.25 0.9 0.9 5.0 11.7 19.2 26.4

Note. Model 1 has a wet adiabatic temperature gradient throughout, and uses the indicated thermochemical equilibrium temperatures for NH4 SH condensation and NH3 freezing. Model 17 uses the temperature profile obtained by Lindal et al. (1985) from Voyager 2 data, which differs from the wet adiabatic lapse rate at pressures below 1.4 bar. Entries not listed are equal to the values for Model 1.

line in Fig. 6a shows the temperature structure in Model 22. In these models, condensation and freezing of NH3 occur at the same temperatures as before. Small increases in the emergent brightness temperatures are predicted, which become observable if the deviation from the wet adiabat sets in at P ≥ 3 bar. Figure 7 shows that only at 2.0 cm a detectable effect may be expected. We have also calculated the brightness of Saturn for Models 1–22 at wavelengths of 0.14 and 20.1 cm. These results are not included in Table IV and Fig. 7 because no new trends appear at longer or shorter wavelengths. The 0.14-cm brightness is even the same as the 0.35-cm brightness to < ∼1%. This implies that observations at 20.1 cm are less suitable to study Saturn’s deep atmosphere than 6.1-cm observations, since despite the higher brightness temperature (250 K vs 180 K), the received signal (in Jy) is much lower. In addition, toward longer wavelengths, the galactic background emission is stronger and the angular resolution that can be obtained is lower. In contrast, imaging at 0.14 cm, which has recently become possible with several interferometers, could give important constraints on the structure of planetary atmospheres, because of the high flux levels and the high angular resolution that can be obtained, although excellent weather conditions are required.

6.3. Comparison to Observations The calculations presented in Table IV and Fig. 7 demonstrate that several processes are able to change the planetary brightness temperature at 2.0 and/or 6.1 cm. Uniquely constraining the atmospheric structure requires simultaneous imaging at at least two wavelengths. From 1994, only 2.0-cm data are available, and our 1995 BIMA observations span 9 months, which leaves only the data sets from 1990 as suitable for detailed modeling. As seen from Table IV, supersaturation of the NH4 SH cloud is the only process capable of producing a large change in brightness at 6.1 cm and a small change at 3.6 cm. Supersaturation decreases the brightness, implying the process operates all over the planet except at northern midlatitudes. The central brightness temperatures in Table IV have been calculated for inclination angle B = 0◦ , but the values are very insensitive to B, and the trends seen in the table are valid at any latitude. However, in constructing model images to be compared with data, the inclination should be taken into account, since it changes the emission profile. To model the VLA observations from 1990, synthetic images at both wavelengths were constructed for several values of the NH4 SH condensation temperature (like Models 2–6, but with B = 29.3◦ ). The

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

137

FIG. 8. Best fit to the 1990 data at 6.1 cm (top) and 3.6 cm (bottom). At northern midlatitudes, NH4 SH forms at the thermochemical equilibrium temperature (235.5 K). At other latitudes, the NH4 SH cloud does not form until higher in the atmosphere (i.e., gases are supersaturated), at T < (190 ± 5) K.

northern midlatitudes in these images were replaced by Model 1 at B = 29.3◦ , and the results were convolved to observational resolution. The bright band is resolved on the longest baselines, and the data constrain the position of the edges of the ◦ bright region to < ∼2 in latitude. Figure 8 presents the model that best matches the data. Globally, the NH4 SH cloud forms at (190 ± 5) K, except at planetocentric latitudes λplc = 30◦ –42◦ , where thermochemical equilibrium applies, and the cloud forms at a 60-km lower altitude, where T = 235.5 K.

Simultaneous observations at 2.0, 6.1, and 20 cm were obtained in 1986, and presented both by GMB89 and by dPD91. Using a solar composition atmosphere, the first authors suggested that the bright band at λplc ≈ 30◦ N at 6.1 cm together with the flat brightness distribution at 2.0 cm was indicative of a lowered (75%) NH4 SH humidity at northern midlatitudes. However, the composition of Saturn’s atmosphere differs substantially from that of the Su (Briggs and Sackett 1989; also Section 3), as derived from the disk-averaged radio spectrum. Using

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the observed composition, dPD91 concluded that the brightness distribution at 2.0, 6.1, and 20 cm could be reproduced only by forming the NH4 SH cloud at the 4.5- to 5.0-bar level in the band and at 2.5–3.5 bar at other latitudes, results very similar to those found here. The brightness structure observed in 1990 at 3.6 and 6.1 cm can be explained neither by supersaturation of the NH3 ice cloud, nor by lowered humidity in the NH4 SH and NH3 clouds, nor by a different temperature gradient. These processes would produce either bands at both wavelengths, no bands at all, or even only a band at 2.0 cm, inconsistent with the observations. The effect of absorption of solid NH3 is harder to evaluate by lack of optical constants at radio wavelengths. However, the absorptivity of solid material tends to vary slowly with wavelength, except near resonances, which, however, tend to lie in the infrared. Thus, latitudinal variations in the density of solid NH3 particles are unlikely to produce a bright band at 6.1 cm and none at 3.6 cm. Supersaturation of the NH4 SH and/or NH3 -ice clouds is the most likely candidate process to explain the region of decreased brightness around the equator in the 6.1-cm image from 1995. However, no constraints on the gaseous NH3 abundance profile from other wavelengths are available, impeding a detailed calculation.

Part II: Rings 7. OBSERVATIONAL RESULTS

While in the data from 1995, the rings cannot be seen due to the nearly edge-on geometry, the 1990 and 1994 data clearly show the rings both in absorption and in emission. The absorption by the rings (the “cusp”) can be seen in Figs. 4a, 4b, and 4c, at the position where the planetocentric latitude of the absorption feature equals the ring inclination. The 1990 data show the A ring in emission just south of the planet. In the 3.6-cm data, which resolve the cusp, the ring optical depth is clearly seen to decrease outward (to the south). This section and the next deal with the 1990 and 1994 data only. In Part I, the images were convolved with a beam matched to the resolution of the data and the expected size of features on the disk. However, for the smaller features in the rings, high resolution is desirable. The 2.0-cm data had been convolved to an only slightly larger beam, and the same image is used here. However, the data sets from 1990 were smoothed considerably for the atmospheric study. Figure 9 presents color representations of the 1990 data at the full observational resolution (see caption for numbers). Superposed on the total intensity (Stokes p I) images are contours of the linearly polarized emission ( Q 2 + U 2 ). The polarized emission is seen to be confined to the inner B ring at 3.6 cm, while at 6.1 cm, weak polarized emission from the ansae of the outer B ring is detected. At both wavelengths, the polarization peaks at the ansae, where 31 ± 10 % of the emission at 3.6 cm and 35 ± 10 % at 6.1 cm are polarized. The other

rings are weaker than the inner B ring by factors of 2–5 in total emission, and the upper limits on the polarized emission from the other rings’ ansae are consistent with a constant polarized fraction. However, along the B ring, the total intensity is approximately constant, while the polarized emission becomes weaker when moving away from the ansae. The polarization vector is directed north–south at both ansae and turns toward the east in the direction of rotation at an approximately constant rate, such that it makes exactly one full turn over the ring system. These observations strongly suggest that the polarizing mechanism is sideways single scattering of Saturn’s thermal emission, as suggested before by Grossman (1990) based on lower-sensitivity observations in which only the ring ansae were detected in polarized light. In the 6.1-cm data from 1995, no polarized emission was detectable to a 1σ upper limit of 0.76 K, consistent with the above results. The polarized emission is at the limit of what the VLA can detect, and in the remainder of Part II, we discuss the total intensity data only. Scans through the rings are displayed in Fig. 10, from which we iteratively determined the brightness of the individual rings using the ring geometry measured by the Voyager spacecraft (Cuzzi et al. 1984). We constructed model scans through the A, B, and C rings and the Cassini Division: (a) east–west, through the ansae; (b) north–south, at 1.22 Saturn radii from the center of the disk; (c) north–south, across the region of absorption against the planet (the “cusp”). The model scans were convolved to (full) observational resolution and compared with the data. By varying the brightness of the A, B, and C rings we obtained best fits by eye. The brightness profile across the B ring is resolved, which was modeled as a linear decrease outward. The optical depth of the B ring also decreases outward, as can be observed from the shape of the 3.6 cm absorption profile in Fig. 4. The results are summarized in Table V. In most cases, varying any parameter by more than ≈0.25 K gives a visibly worse fit to the data, but allowing for calibration and deconvolution errors, 1 K should be a realistic 3σ error. This number was estimated from the size of the “ripples” at the edges of the scans in Fig. 10. The cases when the fit parameter is more uncertain than 1 K are specified in the table. For the B ring, brightness temperatures at the inner and outer edges are given. Although the Cassini Division (CD) was initially assumed to have zero optical depth (and brightness), significantly better fits to the observed ansa brightness profiles at all three wavelengths were obtained with a nonzero brightness temperature for the CD. This extends the observations by GMB89 and dPD91, who found a nonzero optical depth for the CD, but did not detect its emission, probably because of the less favorable geometry of their observations. 7.1. East–West Asymmetry The left panels of Fig. 10 show east–west scans through the ring ansae. It is seen that the west, or dusk, ansa is brighter than the east, or dawn, ansa, in particular at longer wavelengths. A dependence on location is most readily seen from the 3.6-cm image, which has the highest resolution. The asymmetry is most

00 FIG. 9. VLA images from 1990 at full resolution, in total intensity (Stokes I) (colors) and in polarized intensity (contours). Beam p FWHM is (1.64 × 0.91) at PA −9.5◦ at 6.1 cm (top) and (0.97 × 0.52)00 at PA −10.6◦ at 3.6 cm (bottom). Contour levels are at 60, 75, and 90% of the peak Q 2 + U 2 : 75.7 µJy/beam at 3.6 cm and 86.8 µJy/beam at 6.1 cm.

FIG. 10. Slices through the 1990 6.1-cm (top row) and 3.6-cm (middle row) and 1994 2.0-cm (bottom row) total intensity data at full resolution. Left column: east–west, through the ring ansae. Middle column: north–south, at 1.22Rs east of the planet. Right column: north–south, at 1.22Rs west of the planet.

140 VAN DER TAK ET AL.

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VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

prominent in the C ring, smaller but significant in the B ring, and not detected in the A ring. East–west scans through the 2.0and 6.1-cm images of dPD91, taken in 1986 at B ≈ 26◦ , show similar east–west asymmetries: strongest for the C ring, and absent for the A ring, and a stronger asymmetry at 6.1 than at 2.0 cm. Our 2.0-cm data, taken at a much smaller ring inclination angle (B ≈ 7.5◦ ), do not show an east–west asymmetry. Within the error bars, no difference in polarized emission from the two ansae could be detected. Table V shows that at 3.6 cm, the east–west asymmetry vanishes at the outer edge of the B ring, but at 6.1 cm, it includes the outer B and A rings. No east–west asymmetry is measurable at 6.1 cm for the C ring, presumably because of limited angular resolution. The highest measured value of the west-to-east brightness ratio, ≈2.5, occurs in the C ring at 3.6-cm wavelength. In Section 8.2, we compare the measured ring brightness as a function of scattering angle to model calculations, and this graph (Fig. 12) suggests that the measured asymmetry is due to a dim east ansa rather than to a bright west ansa. The origin of the east–west asymmetry is further discussed in Section 8.1. 7.2. Front–Back Asymmetry

the planet. These plots show another asymmetry: the near (south) side of the rings is brighter than the far (north) side, implying that the ring particles scatter preferentially in the forward direction. Again, the effect is strongest at 6.1 cm and weaker at shorter wavelengths. The 3.6-cm data indicate that again the effect is most pronounced for the B and in particular the C ring. The near–far asymmetry is also prominent at 2.0 cm, in contrast to the east–west asymmetry. At 2.0 cm, the near–far asymmetry is much stronger on the east side than on the west side. Clear front– back asymmetries have also been observed at 6.1 cm by dPD91 and Grossman (1990) for the B and C rings, whereas evidence for front–back asymmetries at 2.0 cm was relatively weak at ring inclination angles 12.5◦ –26◦ . Molnar et al. (1999) detected both east–west and front–back asymmetry, and also found the strength of both effects to increase toward longer wavelengths. As seen in Table V, the front–back asymmetries are largest at 6.1 cm, as mentioned above. The values given for the “front” and “back” sides at 1.22RS are averaged over the east and west sides of the rings, although at the front, the west side is brighter than the east side by ≈1 K at 3.6 and 6.1 cm and by up to 4 K at 2.0 cm (Fig. 10). No significant east–west difference exists on the “back” side.

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

7.3. Optical Depth

TABLE V Measured Brightness Temperatures and Optical Depths of the Rings Ansae

At 1.22Rs

Wavelength

Ring

East

West

2.0 cm

A CD B (out) B (in) C

4.0 5.0 5.0 10.5 8.75

4.0 8.0 5.0 5.0 15.0(2) 10.5 8.75 5.5

A CD B (out) B (in) C

4.25 2.0 4.5 8.0 2.0

4.25 5.5 2.0 4.5 10.5 9.0 5.0 6.5

A CD B (out) B (in) C

1.5 2.0 2.0 7.25 2.75

2.5 4.0 3.0 3.0 10.0 9.75 2.75 7.0

3.6 cm

6.1 cm

Front

Cusp region (N)

τλ

Back

TB

3.5

70(10)

0.12 ± 0.02

10.0

<15

>0.56

0.5

90(10)

5.0

6(2)

8.5 4.0

Column 7 of Table V lists the measured brightness temperatures at the location of the rings in front of the planet (the “cusp” region). To convert these into optical depths, the contribution of the ring emission (both thermal and scattered) to the measured brightness temperature must first be subtracted. From the radiative transfer equation in the Rayleigh–Jeans limit,

0.08+0.02 −0.01 —

70(5) 0.48 ± 0.04 30(5) 1.03+0.14 −0.11 50(15) 0.65+0.20 −0.15

1.25

12(2)

—

4.5

50(10)

0.99+0.34 −0.22

2.5

90(10)

0.41+0.08 −0.07

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

(eff)

e−τλ

=

TB − TR , TD − TR

(2)

where the “effective” optical depth τλ(eff) is related to the normal optical depth τλ(N) by τλ(eff) = τλ(N) /sinB, where B is the ring inclination, TB is the observed brightness temperature, and TR is the brightness temperature of the ring emission. For the planetary brightness temperature TD , we adopted 170 K at 3.6 cm and 180 K at 6.1 cm. At 2.0 cm, we used the average brightness just north and south of the cusp, 165 K, as background temperature. Planetary limb darkening was not taken into account, so that the optical depths from the 1990 data may be slightly overestimated. During the 1990 observations, the ring inclination was so large that only the B and C rings obscured the planet, while the A ring appears in emission just south of it. This is a rare opportunity to measure the ring brightness at a scattering angle equal to the ring inclination, α = B = 30◦ . (The scattering angle α is defined in the next section.) At 3.6-cm wavelength, the A-ring brightness at α = 30◦ is consistent with the value measured at the “front” side at 1.22RS , or α ≈ 60◦ . At 6.1 cm, however, the cusp brightness exceeds the value at the “front” side by a factor ≈3 (Table V). The observation by Grossman (1990) that the ring scattering phase function strongly peaks in the forward direction

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is extended by this observation to α = 30◦ . Previously published images were taken at smaller ring inclinations, where the rings ◦ are not visible in emission at scattering angles < ∼40 . At 3.6 cm, the emission of the B and C rings at the cusp was assumed to equal the value measured at the front side at 1.22RS . At 6.1 cm, we multiplied the brightness temperature of the front side by 3, which is a lower limit since scattering accounts for a larger part of the flux from the inner rings. Due to the small ring inclination in the 2.0-cm data, the cusp region is not entirely resolved. By assuming that the scattering phase function does not have a minimum in the forward direction, we constrained the cusp brightness temperature of the rings to be at least equal to the value measured at 1.22RS on the near side. For this reason, only a lower limit for the optical depth of the B ring is given in the table. The measured optical depths are in the last column of Table V. The errors were determined by propagating the errors on the ring brightness through Eq. (2). The optical depth is smallest for the C ring, largest for the B ring, and intermediate for the A ring. At 3.6 cm, the optical depth of the B ring is found to decrease outward, as implied immediately by the absorption profile in Fig. 4b. The data are consistent with an increase in the optical depth of a given ring with increasing wavelength. Our measurement of the A-ring brightness temperature at 6.1 cm at α = 30◦ is crucial for this agreement. The contribution from scattering to the measured brightness temperature rises rapidly with wavelength, and leads, if ignored, to an underestimate of the optical depth. This is why both GMB89 and dPD91 found the optical depth to decrease toward longer wavelengths. 8. RING MODELS

8.1. East–West Asymmetry The magnitude of the east–west asymmetry increases with increasing wavelength, it appears to be strongest in the innermost part of the rings, and it may be more pronounced at large ring inclination angles. These observations suggest that the asymmetry arises in scattered light, not in thermal emission from nonuniformly distributed particles. Scattering is most important at long wavelengths, where the planet is brighter, and close to the planet, where Saturn fills the largest solid angle as seen from the rings. The integrations are ≈8 h, which is comparable to the Keplerian orbital periods of 6.4 h for the C ring to 13.1 h for the A ring. This rules out large-scale azimuthal variations in the particle density as explanation for the east–west asymmetry. In addition, such asymmetries could not persist due to Keplerian shear. The west side is the evening side of the rings, where the particles may be expected to be warmer than on the east or morning side as a result of irradiation by the Sun. However, this effect should be stronger toward shorter wavelengths, opposite to what is observed. Similarly, the evening side of the planet may be warmer than the morning side, causing uneven illumination of the rings, but again the resulting asymmetry should be strongest at short

wavelengths. In addition, the diurnal irradiation by the Sun is unlikely to cause thermal effects at pressure levels > ∼1 bar, where the radio emission originates (Fig. 6c). A warped ring plane could produce the observed asymmetry because the ansae would be seen at slightly different scattering angles, but such a warp would have been observed before in the optical. East–west asymmetries have been seen at optical and near-infrared wavelengths, but only in the A ring (Dones et al. 1993), where we do not detect them. What cannot be ruled out is unresolved density variations with azimuth. The reflection off a moderately opaque slab by multiple scattering exceeds the transmission through it by factors up to a few, and a combination of such slabs, if suitably oriented, could lead to an east–west asymmetry such as observed. One possible physical interpretation of this idea is provided by gravitational wakes, which are 10- to 100-m-sized density enhancements behind large ring particles which, because of Keplerian shear, trail at an angle to the orbit. The theory of such structure was developed by Julian and Toomre (1966) for the case of galactic disks, and has recently been applied to Saturn’s rings by Salo (1992, 1995) in dynamical simulations, in which a maximum density contrast of ∼25% and a trail angle of 20◦ –25◦ were found. Dones et al. (1993) proposed a connection between the wakes and the azimuthal asymmetry seen at optical wavelengths in the A ring; a relation to the east–west asymmetry at radio wavelengths was also suggested by Molnar et al. (1999). Consider a pair of gravitational wakes trailing large ring particles at the two ring ansae, as drawn schematically in Fig. 11. If the wakes have sufficient optical depth, multiple scattering becomes important, so that the intensity in the beam reflected through multiple scattering is not the same as in the transmitted beam. Assuming isotropic scattering, an angle of incidence of 60◦ , and a single-scattering albedo of unity, the reflection R (summed over all orders) is brighter than the transmission T by 50–100% for reasonable choices of optical depth τ and a cosine of the exit angle µ (van de Hulst 1980, pp. 256–257). For example, if τ = 1 and µ = 0.3, R = 0.664 and T = 0.402, which is comparable to the typical observed brightness contrast between the east and west ansae. Higher optical depths produce a larger contrast, but this is not realistic in the case of Saturn’s rings (see Table V). To achieve a higher contrast at given optical depth the exit angle must be small: if τ = 1 and µ = 0.1, R = 0.772 and T = 0.319, a contrast close to the maximum observed value of 2.5. A grazing exit angle can also act to keep the same contrast at lower optical depth: if τ = 0.5 and µ = 0.1, R = 0.671 and T = 0.445. A small exit angle corresponds to a large trail angle of the wakes. Our observations thus suggest that either the wake–interwake density contrast or the trail angle is somewhat larger than in the simulations by Salo (1995). The calculations by van de Hulst (1980) do not include a dependence on wavelength, but the observed increase in the east–west asymmetry toward longer wavelengths can be accommodated in our model by an optical depth that increases with increasing wavelength, as is observed (Section 7.3, Table V).

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FIG. 11. Schematic top view of Saturn and its rings. The slanted rectangles represent gravitational wakes trailing large ring particles, which are indicated by 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 from reflection through multiple scattering in the wake, while on the east side, the light is transmitted through an otherwise similar wake. At small ring inclination angles, a mixture of reflected and transmitted light is received on Earth from both ansae (dotted rectangle) and the E–W asymmetry is expected to disappear.

Observations at 20.1 cm could further test this interpretation, since the optical depth of the rings should go down at such large wavelengths. Alternatively, the ring inclination might play a role, because our 2.0-cm image was taken at an inclination of only 7.5◦ . In the multiple-scattering interpretation, the asymmetry is expected to vanish at small inclination angles, because in this case, a mixture of reflected and transmitted light is received on Earth. This situation is illustrated by the dotted rectangle in Fig. 11. The above discussion assumed illumination of the slab by a point source, which is not a good approximation for Saturn’s C ring, seen from which the planet fills almost half the sky. Computations for the other limiting case, isotropic illumination, can be found on pages 258–259 of van de Hulst (1980), where a Lambert surface is added. For a grazing exit angle µ = 0.1 and τ = 1, R = 0.698 and T = 0.302, very similar to the result for a thin beam. However, for µ = 0.5, R ≈ T , while for µ = 0.7, T > R, so that the model would break down. Calculations that include the exact geometry of scattering by the rings are clearly needed. Another caveat for the wake model is that in the simulations by Salo (1995), the density enhancement is strongest in the A ring, weaker in the B ring, and absent in the C ring, opposite to the trends in the radio data. Detailed calculations are needed to establish if this apparent discrepancy is a radiative transfer effect or that mechanisms other than wakes must be sought as explanations for the east–west asymmetry.

8.2. Scattering Profile Cuzzi et al. (1980) give detailed predictions for the brightness of Saturn’s rings at radio wavelengths. The model assumes a differential size distribution ∝ a −3 , with cutoffs at particle radii a = 0.1 and 100 cm. The rings are taken to consist of many vertical layers of particles composed of pure water ice with a Henyey–Greenstein scattering phase function (see Bohren and Huffman 1983). The only structure in the model is the optical depth changing from ring to ring; no east–west asymmetry is predicted. Comparison of this model to the data is performed in terms of the scattering angle α, which is calculated from cos α = cos B cos θ,

(3)

and hence is a combination of the ring inclination B and the azimuth θ , defined to be zero at the sub-Earth point and increasing counterclockwise as seen from the ecliptic north pole, i.e., in the direction of the rotation. With this definition, α = 0◦ is “new” phase or forward scatter, and α = 180◦ is “full” phase or backscatter. Optical studies generally adopt the opposite (e.g., Dones et al. 1993) because unlike at radio wavelengths, what is scattered is sunlight so that only backscattered light can be observed from Earth. The Cuzzi et al. model predicts a general increase in the brightness temperature with decreasing scattering angle, in particular at angles <50◦ . The maximum intensity occurs in the purely forward direction, which is, however,

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unobservable. Neither the active (radar) nor the passive microwave observations used to constrain the model resolved the individual rings, so that a close match to the observations presented in this paper, which do resolve them, is not expected. To model our 2.0-cm observations, we simply take the average of the model values for 0.83 and 3.71 cm given by Cuzzi et al. Figure 12 compares the brightness temperatures from the model with the measurements from Table V. Even though no attempt has been made to normalize calculations and observations to each other, the data and model values are seen to agree to ≈30%. It is seen that the general brightness level of each ring

in the model is consistent with the observed value, which limits the amount of silicate impurities in the ice to <10% by volume, as found earlier by Grossman (1990). The model predicts a rise in optical depth of the rings as the wavelength increases from 0.3 to 6 cm, in agreement with the observations (Table V). In addition, the model reproduces the observed brightness increase toward smaller scattering angles, especially for the A and inner B rings. At 6.1 cm, however, the observed A-ring brightness at α = 30◦ is significantly higher than predicted, which suggests that the phase function at this wavelength is even more forward peaked than in the Cuzzi et al. models.

FIG. 12. Measured ring brightness east of the planet (solid squares) and, if different, west (open squares), with model calculations by Cuzzi et al. (1980) superposed as dotted lines. Top to bottom: C, inner B, outer B, and A rings. Left to right: 2.0-, 3.6-, and 6.1-cm wavelengths.

VARIABILITY OF SATURN’S BRIGHTNESS DISTRIBUTION

The monotonic increase in brightness temperature with increasing scattering angle is inconsistent with the observed pattern in the outer B ring (Fig. 12, third row from the top), where the ansae are weaker than the intermediate scattering angles. In addition, the model predicts a higher optical depth for the outer B ring than the inner, while the opposite is observed (Fig. 4b, Table V). This suggests that the scattering phase function is not the same for all rings. While the scattering properties of the rings in the optical probe variations in the surface roughness of the particles and the presence or absence of a regolith layer (Doyle et al. 1989, Dones et al. 1993), the scattering phase function at radio wavelengths depends on the particle size distribution. The dependence on particle shape is much smaller and may be further constrained when more sensitive polarization data are available, in which all rings are detected over a range of scattering angles. The exponent of the size distribution adopted by Cuzzi et al. (1980) was later derived from the Voyager 1 radio occultation data by Zebker et al. (1985) and by Showalter and Nicholson (1990) from the Voyager 2 stellar occultation data. Both data sets indicated variations in the maximum particle radius by factors up to 5, which are on a scale of 20 km for the optical data and 1200 km for the radio data. The data discussed in this paper have a resolution of only about 9000 km, but in contrast to the Voyager data include the B ring, which is too opaque to be studied in absorption. The brightness dip in the sideways direction (α = 90◦ ) observed by the VLA in the outer B ring suggests an excess of large particles compared with the distribution assumed by Cuzzi et al. The cross section for backward and forward scattering increases sharply for particle sizes greater than the wavelength. Our observed profile in the outer B ring indicates stronger backward and forward scattering than the Cuzzi et al. model predicts, suggesting the presence of large (> ∼100 cm) particles. The Voyager data indicated maximum particle radii ranging from 80 to 240 cm derived from the radio data and ranging from 140 to 1190 cm derived from the optical data (Zebker et al. 1985, Showalter and Nicholson 1990), although these values refer to selected regions in the A and C rings. The few optical occultation data that could be obtained through the B ring seemed to suggest that the particles in the B ring are larger than in the A and C rings (Showalter and Nicholson 1990), in qualitative agreement with the results found here. More detailed models would be useful to quantify the constraints on the size distributions in the various rings imposed by the current data set. 9. CONCLUSIONS

This paper discusses radio interferometric images of Saturn, obtained over the years 1990–1995 with the BIMA and VLA telescopes at wavelengths of 0.35, 2.0, 3.6, and 6.1 cm (Tables I and II). The data are used for a study of both the atmosphere and the rings. For the 1990 data, we used the versatility of interferometers to present two images per data set. Both are Fourier transformed from the UV data, but with a different range in antenna spacings emphasized, since the structures the authors are

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interested in on the planet are on larger scales than structures of interest in the rings. For the 2.0-cm data from 1994, a single image is sufficient to describe atmosphere and rings; the 1995 data, being taken close to ring plane crossing, cannot be used for investigations of the rings. The paper is subdivided into parts on the atmosphere and the rings; we continue this division for the conclusions. 9.1. Atmosphere For all five data sets, the measured total brightness is consistent with thermochemical equilibrium models by Briggs and Sackett (1989) and de Pater and Mitchell (1993), as are limb darkening curves. The southern hemisphere of the planet is brighter than the northern by ≈5%, both in a 2.0-cm image from 1994 and in a 6.1-cm image from 1995. This is the first time the entire southern hemisphere is seen at radio wavelengths. A 0.35-cm image from 1995 shows marginal evidence for a southern brightening. On smaller spatial scales, the data show the latitudinal brightness distribution to vary significantly with time, both at 2.0 cm and at 6.1 cm. In 6.1-cm observations from 1982–1986 (de Pater and Dickel 1982, GMB89, dPD91), a bright band appeared around latitude 30◦ N, while an image from 1995 instead shows a band at latitude ≈40◦ S and a dark region around the equator. Instead of the flat 2.0-cm brightness structure in the 1980s, 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 in the case of departure from thermochemical equilibrium in the NH4 SH and NH3 -ice clouds, as well as for a range of temperature gradients in the upper troposphere. The results are presented in detail in Table IV and Fig. 7 and can be summarized as follows. Supersaturation of the NH4 SH solution cloud decreases the 6.1-cm brightness most, while the relative change at 3.6 cm is about twice as small. There is no change at 2.0 cm and only a small one at 0.35 cm unless the supercooling extends all the way up to the base of the NH3 ice cloud at 150 K. Supersaturation of the NH3 ice cloud has a pronounced effect at 0.35, 2.0, and 3.6 cm, while the relative brightness change at 6.1 cm is only about half that at other wavelengths. Lowering the humidity of the NH4 SH cloud increases the brightness temperature at all radio wavelengths significantly, and by practically equal amounts. In contrast, lowering the humidity of the NH3 ice cloud produces no observable change in atmospheric brightness at any wavelength. Changing the temperature gradient in the upper troposphere can produce an observable brightness increase at 2.0 cm and a smaller increase at 3.6 cm. The implication of these results is that observed brightness variations at a single wavelength cannot be unambiguously interpreted. However, the physical processes considered all have a different relative effect at different wavelengths. This enables us to assign the 6.1-cm band from 1990 combined with the flat 3.6-cm appearance to a very specific physical structure (see Fig. 8). Over most of the planet, NH4 SH is supersaturated and does not condense until T < 190 ± 5 K. Only at northern

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midlatitudes, where the bright band is seen, does the NH4 SH cloud form at the thermochemical equilibrium temperature of 235.5 K. Humidity variations and supersaturation of the NH3 ice cloud cannot reproduce the brightness structure observed in 1990. The effect of absorption by solid NH3 is harder to evaluate by lack of optical constants, but it is unlikely that this effect could produce a bright band at 6.1 cm but none at 3.6 cm. The physical structure of the giant planets’ atmospheres and its time variation is of great interest. Using the models presented in this paper, the range of processes occurring in the condensation region of Saturn can be well constrained by simultaneous monitoring at at least two radio wavelengths. The VLA, in configurations matched to the size of features on the disk, is the ideal instrument to carry out such a study.

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

9.2. Rings

Cuzzi, J. N., J. J. Lissauer, L. W. Esposito, J. B. Holberg, E. A. Marouf, and G. L. Tyler 1984. Saturn’s rings: Properties and processes. In Planetary Rings (R. Greenberg and A. Brahic, Eds.), pp. 73–199. Univ. of Arizona Press, Tucson.

The rings are visible in our 1990 and 1994 data in emission as well as in absorption against the planet. The linearly polarized emission, > ∼30% of the total light, peaks at the ansae and appears confined to the B ring, as expected if most light is singly scattered planetary emission. From the images, the brightness of the rings at scattering angles α ≈ 45◦ , 90◦ , and 135◦ is measured (Table V). We confirm the nonzero optical depth of the Cassini Division first seen by GMB89, and present the first evidence for emission from this region. In addition, the large ring inclination in 1990 allowed us to measure the A-ring brightness at a small scattering angle, α ≈ 30◦ , for the first time. It is found that the forward scattered component of the ring emission increases strongly with wavelength. This has important consequences for the calculation of the ring optical depth, which is found to increase with increasing wavelength, contrary to previous work. We confirm that the west ansa is brighter than the eastern, as first noted by dPD91. The effect becomes stronger with increasing wavelength and with decreasing distance to the planet, implying an origin in scattered planetary emission rather than in thermal emission from the rings themselves. Multiple scattering in gravitational wakes appears to satisfy all observational constraints, but more detailed models that include the exact scattering geometry are needed. The measured ring brightness as a function of scattering angle is reproduced to ≈30% by the calculations by Cuzzi et al. (1980) for the A and inner B rings (Fig. 12), except in the outer B ring, where we attribute the discrepancies to an excess of large (> ∼meter-sized) particles.

ACKNOWLEDGMENTS The authors are grateful to Joop Hovenier and Carsten Dominik for useful discussions, Elias Brinks for assistance in preparing the 90-cm observations, and Mel Wright for help in reducing the BIMA data. We also thank Mark Hofstadter and Larry Molnar for helpful comments on the manuscript. This work was supported over the years through grants to the University of California at Berkeley by NASA, NSF, and CALSPACE, most recently by NASA Grants NAGW-4659 and NAG 5-4202 and NSF Grant AST 9613998. Additional travel

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