Jovian Stratospheric Hazes: The High Phase Angle View from Galileo

Jovian Stratospheric Hazes: The High Phase Angle View from Galileo

Icarus 139, 211–226 (1999) Article ID icar.1999.6103, available online at on Jovian Stratospheric Hazes: The High Phase An...

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Icarus 139, 211–226 (1999) Article ID icar.1999.6103, available online at on

Jovian Stratospheric Hazes: The High Phase Angle View from Galileo Kathy Rages Space Physics Research Institute, Sunnyvale, California 94087 E-mail: [email protected]

Reta Beebe New Mexico State University, Las Cruces, New Mexico 88003

and David Senske Sterling Software/Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California 91109 Received May 12, 1998; revised December 11, 1998

INTRODUCTION High phase angle Galileo images of Jupiter’s limb reveal the presence of stratospheric hazes in the equatorial region (latitude 9◦ N) and the transition zone at the southern edge of the north polar region (60◦ N). During orbit E4, images were taken in both violet and near-IR continuum filters, effectively probing Jupiter’s stratosphere at two different altitudes. A discrete layer detached from the limb is present at 60◦ N, 315◦ W, but not 20◦ further east at 60◦ N, 295◦ W. Bright streaks running roughly north–south are also present on Jupiter’s crescent at 60◦ N. No such discrete features have been seen previously in high phase angle images of the giant planets. Nor are such features seen at 9◦ N, where the haze appears to be more uniformly distributed in height and longitude. Radial intensity profiles across the limb are inverted to give vertical extinction profiles over ∼200 km in Jupiter’s stratosphere. These show that extinction in the discrete haze layer is enhanced by a factor of ∼2 over its surroundings in the violet filter, with less pronounced variation in the near-IR filter. Haze distribution models were found for both latitudes in which the near-IR images constrain the haze properties near or above the 100-mbar pressure level, where the mean particle radius is about 0.45 µm and the haze number density is near 0.15 cm−3 . In these models the violet images constrain the haze properties about 25 km higher in the atmosphere, near or above the 20-mbar pressure level, where the haze particle size is 0.32 ± 0.01 µm at 9◦ N and 0.27 ± 0.01 µm at 60◦ N. At this altitude, the haze number density increases by almost an order of magnitude between the equator and the polar transition region—from 0.1 cm−3 at 9◦ N to 0.7 cm−3 at 60◦ N. An alternative solution is possible at 60◦ N, in which the haze is placed near 1 mbar in both filters, with mean particle sizes of 0.6 µm in the violet and 1.3 µm in the near IR. °c 1999 Academic Press Key Words: Jupiter, atmosphere; atmospheres, structure.

The fact that Jupiter’s polar stratosphere contains scattering hazes is apparent from Earth-based telescopic images of the planet. When Jupiter is viewed through methane band filters, e.g., near 889-nm wavelength, the stratospheric haze forms bright caps at both poles, indicating that the haze has greater optical density and/or extends higher into the atmosphere at the poles than it does at temperate latitudes. Conversely, in the ultraviolet Jupiter’s poles are much darker than they would be if only molecular Rayleigh–Raman scattering were occurring, indicating the presence of UV absorbers in the stratosphere. Beginning with Pioneer 10 in 1973, remote sensing observations from spacecraft sent past Jupiter have added to our knowledge of the distribution and scattering properties of jovian stratospheric aerosols. The Pioneer photopolarimeters made spatially resolved observations of the intensity and polarization of sunlight scattered by Jupiter’s atmosphere at both blue and red wavelengths at seven different solar phase angles between 12◦ and 150◦ (Tomasko et al. 1978, Smith and Tomasko 1984). Jupiter is very bright at high phase angles—another indication that aerosols with particle radii of a few tenths of micrometers are present in the stratosphere. Tomasko et al. (1978) fit the Pioneer observations of low southern latitudes (both the South Tropical Zone and northern South Equatorial Belt) with models containing 0.25 optical depths of strongly forward scattering haze above the tropopause (∼100 mbar). Smith and Tomasko (1984) found similar forward scattering behavior in the polar regions, together with high positive polarization near 90◦ phase angle, which is characteristic of much smaller (Rayleigh scattering) particles.

211 0019-1035/99 $30.00 c 1999 by Academic Press Copyright ° All rights of reproduction in any form reserved.



The wide-angle camera on Voyager 2 was used to take three violet/orange image pairs of Jupiter’s ring from within solar occultation. In addition to the ring, Jupiter’s limb is clearly visible in these images as a bright line, the “twilight zone” formed by sunlight being forward scattered into the nominally dark side of the planet. (In fact, large parts of the bright line around the limb were saturated.) While these images had insufficient spatial resolution to show any details of the haze distribution as a function of altitude, West (1988) used two of the three pairs to determine the haze top pressure level (∼0.5–5 mbar, depending on latitude), and to bound the total haze optical depth (∼0.1 above 100 mbar in the violet) and mean radius (0.01–0.05 µm). The Voyager 2 photopolarimeter was also used to measure the brightness and polarization of ultraviolet (wavelength λ = 0.24 µm) light scattered from Jupiter at a number of different latitudes. From an analysis of these observations, Pryor and Hord (1991) estimate the haze production rate within Jupiter’s auroral zone is at most 6.8 × 10−12 g cm−2 s−1 . The haze loss rate is somewhat lower than this, but occurs over a wider area (poleward of ∼45◦ , while production occurs only within the auroral zone poleward of ∼60◦ ). Subsequent to the Voyager encounters, Tomasko et al. (1986) used spatially resolved spectra taken with the International Ultraviolet Explorer to constrain the properties of jovian stratospheric hazes in the equatorial region and at 40◦ N latitude. They found that at 40◦ N the stratospheric haze above the 20- to 30-mbar pressure level had an optical depth near 0.6 at λ = 0.22 µm, decreasing to about 0.3 at 0.25 µm. They inferred particle radii of a few tenths of a micrometer, number densities of 1–6 × 108 cm−2 (with the precise value depending on the particle size), and a mass loading of 20 µg cm−2 above the 50-mbar pressure level. At the equator, both the optical depth and the mass loading were an order of magnitude lower than at 40◦ N, with 3 µg cm−2 above the 150-mbar pressure level.

In this paper, we will derive new constraints on Jupiter’s equatorial and polar stratospheric hazes from observations made by the Solid State Imaging subsystem (SSI) on the Galileo Orbiter. We calculate vertical extinction profiles with resolution comparable to the gas scale height in Jupiter’s stratosphere and use the derived single-scattering phase functions and extinction coefficients at two wavelengths to determine possible mean particle sizes and number densities for the stratospheric haze near the equator and the north pole. GALILEO SSI DATA

Galileo has continued the types of observations made by Pioneer and Voyager. In December 1996, during orbit E4, Galileo’s SSI was used to take four images of Jupiter’s equatorial limb and four images of the limb in the transition zone between north temperate latitudes and the northern polar region. These two regions are indicated by the lines parallel to the equator in Fig. 1, which shows a pair of Hubble Space Telescope images of Jupiter taken in June 1997 using the 218-nm filter and the 893-nm methane band filter on the Wide Field Camera. Galileo made images of each region in violet (mean wavelength 417 nm) and near infrared (756 nm) filters at two high solar phase angles. Images at 157◦ phase angle were taken slightly less than one jovian day after images at 146◦ , so the two sets of images probe longitudes about 20◦ apart. The images were taken close enough to Jupiter to give spatial resolutions of ∼15 km/pixel, comparable to a scale height near the tropopause. The details of the E4 images are given in Table I. The absence of a functioning high gain antenna on the Galileo Orbiter severely limited the amount of data that could be returned to Earth, so most of the returned images were compressed using an algorithm that results in the loss of some spatial and photometric resolution. However, the derivation of meaningful

FIG. 1. Jupiter as seen by the Wide Field Camera of the Hubble Space Telescope during the last week of June 1997. The image on the left was taken with an ultraviolet filter centered near 218 nm. Jupiter’s polar caps are very dark compared to the rest of the planet, due to absorption by hazes in the stratosphere before the light can be Rayleigh scattered by the gases in Jupiter’s atmosphere. The image on the right was taken with a methane band filter centered near 889 nm. Jupiter’s relatively bright polar caps are produced by stratospheric hazes scattering sunlight outward before it can be absorbed by the methane deeper in Jupiter’s atmosphere. The bright oval area at the right edge of the 889 nm image is due to vignetting in the WFPC2 methane band filter, not to any phenomenon in Jupiter’s atmosphere.



TABLE I E4 Images of Jupiter’s Limb



Planetographic latitude


Solar phase angle

Resolution (km/pixel)

S0374827001 S0374827101 S0374828401 S0374828501 S0374884401 S0374884501 S0374885801 S0374885901

Violet Near-IR Violet Near-IR Violet Near-IR Violet Near-IR

8.5–9.5◦ N 8.5–9.5◦ N 60.2–61.5◦ N 60.5–61.7◦ N 8.8–10.1◦ N 9.0–10.3◦ N 60.6–62.2◦ N 60.6–62.2◦ N

309◦ W 310◦ W 315◦ W 316◦ W 289◦ W 289◦ W 295◦ W 296◦ W

146.9◦ 147.0◦ 145.6◦ 145.6◦ 158.4◦ 158.4◦ 157.2◦ 157.2◦

13.0 13.0 13.1 13.1 15.8 15.8 15.9 15.9

vertical extinction profiles from radial limb intensity profiles requires that the spatial resolution be of order one scale height per pixel or better. Therefore, the E4 limb images were compressed using a lossless, less efficient algorithm, and the total number

of bits radioed to Earth was minimized by sending only a small portion (window) of each image. The images are shown in Fig. 2. Equatorial images are on the left; images from 60◦ N are on the right. 146◦ phase angle images

FIG. 2. Images of the jovian limb taken by the Galileo orbiter on 20 Dec 1996 (UT) during orbit E4. The left column contains the images taken near 9◦ N; the right column contains images taken near 60◦ N. Images taken at 146◦ solar phase angle are above the horizontal line; images taken at 157◦ phase angle are below it. The first and third rows are violet images; the second and fourth rows were taken with the 756-nm filter. A relatively bright layer is visible above the limb in the right topmost image. This layer is also present in the corresponding 756-nm image and represents a discrete stratospheric haze layer. This discrete haze layer is not present in the two images at the lower right, taken 20◦ in longitude further east.



FIG. 3. Polar projections of Voyager 1 mosaicked images of Jupiter’s northern hemisphere, in (a) UV and (b) orange filters, with center-to-limb darkening removed. Lines of latitude are marked every 10◦ in (b). Note the bright lanes spiralling out from the north pole in the UV image. While these features are broader than the bright streaks seen by Galileo, the two types of features may have related origins and/or similar dynamics. The cosines of the incidence and emission angles in these images vary from (0.84, 0.88) at 30◦ N to (0.27, 0.36) at 70◦ N and (0.09, 0.17) at 80◦ N.

are above the horizontal line; 157◦ images are below it. Within each phase angle block, violet images are at the top; near-IR images are at the bottom. The 146◦ images were taken from a distance of 1.29 × 106 km (18 RJ ) with a resulting spatial resolution of 13 km/pixel. The 157◦ images were taken from a distance of 1.56 × 106 km (22 RJ ), with a spatial resolution of 16 km/pixel. The gas scale height in Jupiter’s stratosphere is around 20 km, so Jupiter’s limb is resolved in both sets of images. A discrete bright layer is visible above the limb itself in the violet image taken at 60◦ N, 315◦ W (146◦ phase angle), fading out toward the south. This bright layer represents a region of enhanced stratospheric haze that is detached from the optically thick haze which forms the limb. This haze layer is also faintly present in the corresponding near-IR image of 60◦ N at 146◦ phase angle, but not 20◦ away in longitude in the images taken at 157◦ phase angle. Such localized stratospheric hazes have not been seen previously on the giant planets. Titan had a discrete stratospheric haze layer at the time of the Voyager encounters, but it appeared ubiquitous except in the north polar region. The 157◦ violet image does show at least one bright streak on the crescent at ∼290◦ W, running roughly north–south (parallel to the limb). It is possible that if a feature such as this bright streak were seen directly over the limb, it would appear as a separate haze layer. Note that the streak seen at 157◦ cannot be exactly what appeared over the limb as a separate haze layer in the

146◦ images, since the planetary rotation between the two sets of images is in the wrong direction. Bright N–S streaks are also present, although less prominent, in the 146◦ images. The streaks are several pixels wide, with a foreshortening of about 7 : 1, so they span ∼700 km, or 1◦ of longitude at 60◦ N. A larger context for the 60◦ N images is provided by Voyager 1, which observed bright “spiral” features throughout Jupiter’s north polar region (Fig. 3). On February 28, 1979, the planet was imaged in orange and UV filters as it rotated in front of Voyager’s narrow angle camera. At a range of 6.7 × 106 km a 3 × 3 mosaicking pattern was required to image the entire planet at a resolution of 62 km/pixel at the subspacecraft point at 2.7◦ N latitude. This slightly northern approach of the spacecraft provided an oblique line-of-sight to the north pole and showed longitudinal variation in the polar hazes. The data were acquired over a 10-h period spanning about 366 degrees of longitude. A Minnaert function with a coefficient of 0.6 was subtracted from the Voyager images to remove large-scale center-to-limb effects, and the resulting images were remapped into the polar projection in Fig. 3. This map shows longitudinal enhancements in UV reflectivity, perhaps similar in origin to the bright N–S streaks seen in the Galileo images, that are associated with long-lived anticyclonic storm systems in the range 35–50◦ N. These storm systems appear to be a source of haze particles that serve as markers, revealing a high-altitude polar convergence. Rates of atmospheric motion implied by the Voyager images are difficult



to interpret. Tropospheric zonal winds are small at these latitudes and nothing is known about vertical winds or gradients of the zonal winds as a function of height. Some understanding of rates of dispersion is needed to interpret the photometric properties. The viewing aspect changes rapidly with latitude and distance from the central meridian. In addition, the data is integrated over a broad band pass of 325 ± 45 nm. Despite difficulties in interpreting this data, this projection provides insight into the nature of the longitudinal variation of the high altitude hazes. IMAGE PROCESSING

Each of the limb images was photometrically calibrated using the VICAR software suite developed by the Multimission Image Processing Laboratory at JPL. Details of the Galileo SSI photometric characteristics and calibration can be found in Klaasen et al. (1997). VICAR subroutines were also used to establish the viewing geometry of each image and to determine the approximate position of Jupiter’s center relative to each image. The location of the planet center was approximate because only a small segment of the limb arc was visible in each image, so the center of curvature could not be established through direct measurement. Instead it was initially assumed that the point of maximum slope on the rising portion of each radial scan fell on an ellipsoid with an equatorial radius of 71,492 km and a polar radius of 66,854 km, corresponding to the 1-bar pressure level (Lindal et al. 1981). After the dark current subtraction carried out by VICAR, some nonzero background remained near the limb, extending out for ∼50 pixels (∼800 km) at a level of 5–8 DN. The origin of this excess background is not certain. Klaasen et al. (1997) indicate that scattered light from a bright source is present at or above the 1% level up to 20 pixels away, and this may account for most or all of the observed excess. This residual background was fit to a quadratic function of radius at locations along the 60◦ N limb where the dark region inside the terminator was visible, and interpolated values of the quadratic function were then subtracted from the specific intensities (I/F’s) on the limb and bright crescent. On the equatorial frames and along much of the limb at 60◦ N no interior dark region was visible. At these locations a constant average background was calculated and then subtracted from the limb and crescent I/F’s produced by the standard radiometric calibration. Figure 4 shows I/F as a function of radius for one scan from each of the E4 images. Note that radius decreases to the right. The bright N–S streaks noticed in some of the 60◦ N images produce “humps” in the descending portions of the corresponding I/F profiles in Fig. 4b. The maximum value of I/F in each scan is largely determined by the albedo-weighted single-scattering phase function $0 P(θ), which is a function of both wavelength and scattering angle (scattering angle θ = 180◦ − phase angle). It is clear from Fig. 4 that the behavior of $0 P(θ ) as a function of wavelength varies with latitude. At 9◦ N violet I/F’s (and therefore $0 P(θ )) are around half those seen in near-IR at the

same phase angle, while at 60◦ N I/F’s in both filters are about the same at each phase angle. The rising portion of each radial intensity profile is shown with an expanded horizontal scale in Fig. 5. The discrete scattering layer near 60◦ N, 315◦ W is clearly visible as a flattening or inversion in the radial I/F profile in both the violet and near-IR images of this region (Fig. 5b). The two violet images of the equatorial region display more gradual rises in I/F across the limb than the others. In the 158◦ image (S0374884401) this behavior is too pronounced to be due only to limb darkening. Taking the 158◦ I/F profile at face value leads to a stratospheric extinction scale height of ∼300 km, a value at variance with both the extinction profiles derived from the other images and the gas scale height of 15–20 km in Jupiter’s stratosphere. At both phase angles, the equatorial violet frames were the first shuttering after the target slew. Four RIMS (a little over four minutes) were allocated for targeting, which should have been sufficient to reach the desired scan platform orientation and then for the scan platform motion to damp out, but it is possible that target acquisition required longer than expected (for example, a reference star might have been missed on one spacecraft rotation and then reacquired on a subsequent rotation) and that residual scan platform motion is responsible for the apparent smear in the 158◦ image. There is no engineering telemetry to determine if there was any problem reaching the target on time, and it is not possible to estimate the number of pixels a scan platform “jitter” might amount to because there are no data on how far the damping cycle for platform motion had proceeded before these images were shuttered. This problem should not affect the other three images in each target sequence. Examination of other image sequences (e.g., G1GSSULCUS01, a 1 × 4 mosaic of Ganymede, and G1ISGLOMON03/04, a 2 × 2 On-Chip-Mosaic of Io) demonstrates that scan platform jitter damps out in less than 8.7 s once the target is properly acquired. There was no change in pointing between the violet and near-IR frames in each sequence, and only a small shift to get from the equatorial to polar limb location. The radial smear in the 60◦ N images is also severely limited by the fact that we see features (discrete haze layers and N–S streaks) only a few pixels wide, with no measurable difference in width between the violet and near-IR images. EXTINCTION PROFILES

Radial I/F profiles at intervals of 0.1◦ along the limb have been inverted to yield vertical extinction profiles for all these images, together with the albedo-weighted single-scattering phase function $0 P(θ ) at an altitude near the intensity peak of each profile, using the limb inversion algorithm first developed for Titan (Rages and Pollack 1983) and further refined for Uranus (Pollack et al. 1987) and Neptune (Moses et al. 1995). This procedure calculates the single-scattering contribution to I/F for a set of concentric homogeneous ellipsoidal shells and estimates the multiple-scattering contribution by using the results of a plane-parallel adding–doubling code for similar scattering



FIG. 4. Specific intensity (I/F) as a function of radius for typical locations along the limb of each image, at (a) 9◦ N and (b) 60◦ N. Scans from 146◦ phase angle images are denoted by filled circles (violet) and open circles (near-IR), and scans from 157◦ phase angle images are denoted by filled squares (violet) and open squares (near-IR). Note that altitude decreases to the right.

geometries and haze distributions. For the analysis of the Galileo images, calculated limb intensity profiles were then convolved with the SSI point spread function given by Klaasen et al. (1997) before being compared with the observed radial intensity profiles. This step was required since the SSI resolution was not much less than a scale height, so several of the 5-km thick homogeneous shells contributed to each observed data point. The vertical extinction profile and the combined gas/haze singlescattering phase function were adjusted to minimize χ 2 , the sum of the squared residuals between the observed and calculated radial intensity profiles, subject to some “sanity” constraints such

as the exclusion of negative extinctions and an imposed bias against large changes in the extinction scale height across adjacent shell boundaries. Sample extinction profiles from each image are shown in Fig. 6, and the corresponding calculated I/F profiles are shown together with the observations in Figs. 7 and 8. The albedoweighted single-scattering phase functions $0 P(θ ) derived from the limb scan inversions are given in the “Observed” column of Tables II and III. These single-scattering phase functions are clearly not those of pure molecular (Rayleigh) scatterers, demonstrating conclusively that hazes with particle sizes of at least a




TABLE III $0 P(θ) for Optically Thick Haze at 60◦ N

$0 P(θ) for Optically Thick Haze at 9◦ N



Rayleigh scattering

Model 0

Model 1


1.48 2.90


2.67 5.95



Violet filter 33.1◦ 21.6◦

1.48 ± 0.05 2.95 ± 0.09

1.28 1.40


2.66 ± 0.08 5.9 ± 0.2

1.28 1.40

Model 0

Model 1

Model 2

1.89 4.22

1.85 4.24

2.13 4.96

2.16 4.77

Violet filter 1.37 2.74


1.91 ± 0.06 4.21 ± 0.12

Near-IR filter 33.1◦

Rayleigh scattering

1.26 1.39

2.01 3.68

Near-IR filter 3.03 5.73


2.15 ± 0.06 4.96 ± 0.15

1.26 1.39

2.74 3.61

FIG. 5. The rising portion of each of the I/F profiles shown in Fig. 4, using the same system of symbols. The humps in the 146◦ curves (open and filled circles) at 60◦ N (b) are caused by the discrete haze layer visible in Fig. 2.



FIG. 6. Profiles of the total (Rayleigh scattering plus haze) linear extinction coefficient as a function of altitude, derived by inverting each of the I/F profiles in Fig. 4. Altitudes are measured above an arbitrary zero point, which will be found to differ for the violet and near-IR profiles, and the four extinction profiles have been horizontally offset from one another for clarity. Each extinction profile is marked by a single symbol, following the system of symbols used in Figs. 4 and 5. The symbol is placed at the point on the extinction profile for which the albedo-weighted single-scattering phase function ($0 P(θ )) is best defined by the radial I/F profile. The shading around each curve represents the uncertainty in the extinction profile.

few tenths of a micrometer are present in addition to gas. The altitudes to which these single-scattering phase functions apply correspond to linear extinction coefficients β ≈ 4 × 10−4 km−1 , and are marked with symbols on the extinction profiles in Fig. 6. Note that the zero point of the altitude scale in Fig. 6 is arbitrary. It may (and it will be later shown that it does) vary among the individual extinction profiles shown. The discrete haze layer at 315◦ W longitude is clearly visible in Fig. 6b in the violet, and also present in the near-IR. The extinction coefficient of this discrete haze layer decreases by a factor of ∼5 between 417 and 756 nm, which is not enough to be con-

sistent with the λ−4 wavelength dependence of Rayleigh scattering. Calculations using Mie theory show that the extinction efficiency decreases by the observed factor of ∼5 for particles with radii of ∼0.1 µm. As shown in Table IV, at 60.7◦ N in the violet, the entire observed extinction in the discrete haze layer would be accounted for by molecular Rayleigh scattering at an atmospheric density of 0.02 am. At 115 K, 1 am = 436 mbar, so the discrete haze layer is no lower than the ∼8-mbar pressure level, corresponding to an altitude of at least 60 km above the tropopause and at least 75 km above the tops of the ammonia clouds (Lindal et al. 1981).



FIG. 7. The radial I/F profiles calculated using the extinction profiles given in Fig. 6 and observed values of $0 P(θ ) given in Table II (solid line), together with the observed data points (symbols with error bars), for 9◦ N in (a) violet at 147◦ , (b) near-IR at 147◦ , (c) violet at 158◦ , and (d) near-IR at 158◦ . The symbols used for the data points correspond to those appearing on the extinction profiles in Figs. 6a and 6b.

The extinction profiles at 9◦ N and at 60◦ N, 295◦ W display only small departures from a smooth exponential increase with depth, and so the haze/gas mixing ratio in these locations varies only slowly with altitude. The striking exception to this is the violet filter profile at 9◦ N and 158◦ phase (filled square in Fig. 6a). This extinction profile flattens sharply as the line-of-sight optical depth approaches unity. This behavior is required to reproduce the slow rise and rounded peak seen in the 158◦ violet equatorial

image (Fig. 7c). The manifest difference between this extinction profile and all the others, as well as the physical difficulty of producing the 300-km extinction scale height shown, lead to the supposition of residual scan platform motion during this exposure, as outlined above. The inner portion of the I/F profile in Fig. 7a (violet, 147◦ phase) is also not fit very well by the quasi-exponential extinction profile in Fig. 6a (filled circle), so the same problem may have occurred with this image.

TABLE IV Discrete Haze Layer at 60◦ N


$0 P(θ)β (Vio) (km−1 )

$0 P(θ)β (NIR) (km−1 )

Ratio (Vio)/(NIR)

60.7◦ N 61.4◦ N

2.1 × 10−4 3.2 × 10−4

4.2 × 10−5 5.6 × 10−5

5.0 5.7

Rayleigh scattering (km-am)−1

1.07 × 10−2 (411 nm)

8.3 × 10−4 (756 nm)


The combined gas/haze single-scattering phase function at the point where the atmosphere becomes optically thick (the “main limb”) varies with latitude, as shown in Tables II and III. These single-scattering phase functions have been modeled using Mie theory to calculate the scattering from spherical haze particles in a molecular Rayleigh scattering atmosphere given by the Voyager radio occultation profile (Lindal et al. 1981). The assumption of spherical haze particles is reasonable in this case,



FIG. 8. The same as described in Fig. 7, except for 60◦ N, with $0 P(θ ) given in Table III.

since the shape of the diffraction peak is not strongly affected by particle shape, and for particle sizes less than about 1 µm, scattering angles out to ∼30◦ will lie within the diffraction peak. The haze complex refractive index and particle size distribution are essentially unconstrained by the data. In the models described below, the haze particles are nonabsorbing and have a real refractive index of 1.29, consistent with methane ice. The haze scattering properties were calculated using a Hansen–Hovenier size distribution (Hansen and Hovenier 1974) with b = 0.05. n(a) = a (1−3b)/b Exp(−a/rm b),


where rm is the cross-section weighted mean particle radius. R∞ n(a)a 3 da . (2) rm = R0∞ 2 0 n(a)a da An initial attempt was made to fit the derived phase functions for both filters at each latitude using a common haze particle size and haze/gas mixing ratio (“Model 0” in Tables II, III, V, and VI)

but this proved quite unsuccessful. A more sophisticated model was then adopted, in which the phase functions derived from the violet and near-IR images were taken to be at different altitudes, with differing mean haze particle sizes rm and number densities N , and with molecular Rayleigh scattering defined by the Voyager radio occultation pressure-temperature profile. Additional constraints were imposed by requiring that the model also fit the total extinction profile in the range between the two altitudes. The properties derived for the stratospheric haze at 9◦ N are given in Table V. Mie scattering fits indicate a mean particle radius rm near 0.32 µm and number density N ∼ 0.1 cm−3 at the altitude probed primarily in violet, which is around 16 mbar (74 km above the 1-bar level) and rm near 0.45 µm and N ∼ 0.2 cm−3 at the altitude best seen in the near-IR filter, which is near 96 mbar (44 km above the 1-bar level). These pressures are determined by assuming that any Rayleigh scattering component in the observed single scattering phase function (in this case ∼80% in violet and ∼40% in near-IR) is produced by Jupiter’s atmospheric gases (89% hydrogen, 11% helium). The gas density can then be calculated directly from the Rayleigh scattering extinction



TABLE V Characteristics of Haze Models for 9◦ N Model 0 0.39 ± 0.02 1.5+0.8 −0.5 0.22 0.62

rm (µm) N (cm−3 am−1 ) βMie /βtot (Vio) βMie /βtot (NIR) Model 1 Altitude above 1 bar level (km) Pressure (mbar) rm (µm) N (cm−3 ) vs (cm s−1 ) Sedimentation mass flux (g cm−2 s−1 )

74 ± 3

44 ± 2

16 ± 3 0.321 ± 0.013 0.08 ± 0.02 0.10 6. × 10−16

96 ± 10 0.45 ± 0.02 0.17 ± 0.03 0.027 9. × 10−16

coefficient and interpolated on a pressure–density profile derived from the Voyager radio occultation data. As demonstrated below for 60◦ N, an additional component of the stratospheric haze with a particle size of ∼0.01–0.03 µm may be required to reproduce the observed reflectivity of Jupiter’s equatorial region in the ultraviolet and in the methane absorption band at 889 nm. If such a separate haze component is present, these calculated pressures will be systematically high, by as much as an order of magnitude. The products of linear extinction β and albedo-weighted singlescattering phase function $0 P(θ) calculated for this model are shown as discrete points in Fig. 9, together with the products $0 P(θ )β(z) derived from the I/F profiles seen in the Galileo images (solid lines). $0 P(θ)β is used because $0 P(θ ) and β are very nearly degenerate until the slant optical depth through the atmosphere approaches unity, so only their product is reliably known for the outer parts of the extinction profile. The zero point of the altitude scale is now at the 1-bar pressure level. The correspondence between the observed and calculated values of $0 P(θ )β is very good except for the violet 158◦ profile, which is unreliable due to possible smearing. Haze contributes about half the total extinction seen in the near-IR and 15–20% of the extinction seen in violet at the altitudes being probed, but becomes the dominant source of extinction at higher altitudes, as can be seen by comparing the observed extinction curves with those expected from Rayleigh scattering alone (dashed and dotted lines in Fig. 9 corresponding to violet and near-IR, respectively). Two possible models for the haze at 60◦ N have been derived, with properties given in Table VI and resulting $0 P(θ )β profiles shown in Figs. 10 and 11. The first of these models has rm near 0.25 µm and N around 0.7 cm−3 at the altitude probed primarily in the violet (∼27 mbar or ∼65 km above the 1-bar level), which leads to approximately a 50–50 mix of haze and molecular Rayleigh scattering in the violet filter. At the altitude probed primarily by the near-IR filter (∼120 mbar or ∼40 km above the 1-bar level), rm is near 0.45 µm and N is about 0.13 cm−3 . One worrisome aspect of this model is that if the violet and near-IR extinction curves are aligned with a 25-km offset as re-

quired, the discrete haze layers in the violet and near-IR 146◦ images are offset, as shown by the vertical line passing through the peak of the near-IR layer in Fig. 10a. Aligning the discrete haze layers seen in the two filters creates its own difficulties, though. If the maxima in the discrete haze extinction in the violet and near-IR filters are assumed to be at the same altitude, the altitudes for which the single-scattering phase functions are determined (the filled and open circles) lie within 2–3 km of each other. The closer these two altitudes are, the less the atmospheric scattering properties (haze particle size, haze and gas number densities) can be expected to vary between them. But we have demonstrated that there is no acceptable fit to the observations for which the haze properties are the same at both wavelengths. If the particle size increases with decreasing altitude over the ∼25-km depth of the discrete haze layer, the extinction peak in the near-IR could appear at a somewhat lower altitude than it does in the violet, since the single-scattering extinction efficiency is a more steeply rising function of particle size near TABLE VI Characteristics of Haze Models for 60◦ N Model 0 0.23 ± 0.03 15+27 −10 0.34 0.65

rm (µm) N (cm−3 am−1 ) βMie /βtot (Vio) βMie /βtot (NIR) Model 1a Altitude above 1 bar level (km) Pressure (mbar) rm (µm) N (cm−3 ) vs (cm s−1 ) Sedimentation mass flux (g cm−2 s−1 )

66 ± 4

40.1 ± 1.5

27 ± 6 0.267 ± 0.007 0.7 ± 0.2 0.05 1.5 × 10−15

121 ± 11 0.476 ± 0.011 0.131 ± 0.015 0.024 7 × 10−16

Model 1b Altitude above 1 bar level (km) Pressure (mbar) rm (µm) N (cm−3 ) vs (cm s−1 ) Sedimentation mass flux (g cm−2 s−1 )



∼2.7 0.267 ± 0.007 and 0.02 0.7 ± 0.2 and 2 × 105 0.6 and 0.04 1.7 × 10−14 and 2 × 10−13

∼12 0.476 ± 0.011 and 0.02 0.131 ± 0.015 and 1.2 × 106 0.2 and 0.01 6 × 10−15 and 2 × 10−13

Model 2 Altitude above 1 bar level (km) Pressure (mbar) rm (µm) N (cm−3 ) vs (cm s−1 ) Sedimentation mass flux (g cm−2 s−1 )

135 ± 13

126 ± 13

1.1+0.6 −0.4

1.7+0.9 −0.6 1.32 ± 0.06 0.033 ± 0.007 4. 7 × 10−13

0.58 ± 0.05 0.101 ± 0.018 3. 1.2 × 10−13



FIG. 9. Linear extinction coefficient (β) multiplied by $0 P(θ ), for 9◦ N at (a) 147◦ phase angle and (b) 158◦ phase angle. Thick lines with shading are results derived by inverting radial I/F profiles. Those lying near filled symbols are derived from violet images, and those lying near open symbols are derived from near-IR images. The symbols themselves show the value of $0 P(θ)β calculated from the Mie scattering model in Table V and follow the same system of symbols as the previous figures. The $0 P(θ)β profiles expected from Rayleigh scattering alone are indicated by the dashed (violet) and dotted (near-IR) lines. The violet and near-IR curves have been vertically offset for clarity; violet extinction values should be read off the left-hand axes, and near-IR values off the right-hand axes. Altitudes are measured above the 1-bar pressure level and are also derived from Table V.

FIG. 10. The same as described in Fig. 9, except for 60◦ N. The Mie scattering model and altitudes are taken from Model 1a in Table VI. A vertical line has been drawn through the peak of the near-IR discrete haze layer to indicate the corresponding point on the violet extinction profile.



FIG. 11. The same as described in Fig. 10, except the Mie scattering model and altitudes are taken from Model 2 in Table VI.

X Mie = 2πrm /λ = 0.8 (for rm = 0.1 µm and λ = 0.756 µm) than for X Mie = 1.5 (for λ = 0.417 µm). However, this would not be enough to cause the near-IR peak to correspond to the violet minimum, as it does in Fig. 10a. Model 1a requires an actual decrease in the altitude of the discrete haze layer between the location probed in the violet filter and that probed in the nearIR, corresponding to horizontal distances of a few hundred to 1000 km. More seriously, this model produces too little scattering in the 890-nm methane band and too little absorption in the UV to be consistent with observations. This has been previously shown by Tomasko et al. (1986), who found aerosols with radii of 0.2– 0.5 µm at pressures from 10 to 50 mbar, similar to this model, but required mass loadings of 20 µg cm−2 above 50 mbar, three orders of magnitude greater than those derived here. The problem is further illustrated in Fig. 12, which shows limb-to-terminator I/F profiles at 60◦ N in the two HST images shown in Fig. 1. Predicted I/F’s for haze Model 1 are shown as open circles; Model 1 permits too much methane absorption at 889 nm and does not absorb nearly enough at 218 nm, even if the imaginary part of the UV refractive index is pushed to the improbably high value of 0.3. These problems can both be alleviated if a second haze component is introduced to replace the atmospheric gas as the source of most of the Rayleigh scattering. The filled circles in Fig. 12 show the predicted I/F’s if ∼5 × 107 cm−3 am−1 of 0.02-µm haze is added to Model 1, producing about 90% of the Rayleigh scattering originally attributed to gas. The pressure levels probed therefore decrease to ∼3 and ∼12 mbar in violet and near-IR, respectively. This is Model 1b in Table VI.

The second haze model (Model 2 in Table VI) fits the data somewhat less well than the first. It places the haze much higher in the atmosphere, where Rayleigh scattering contributes essentially nothing to the total extinction. In this model rm ≈ 0.6µm and N ≈ 0.10 cm−3 at ∼1.1 mbar (violet) and rm ≈ 1.3 µm and N ≈ 0.03 cm−3 at ∼1.7 mbar (near-IR). These two pressure levels, which correspond to the points at which the line-of-sight optical depth becomes ∼1 in each filter, lie 135 and 126 km above the 1-bar level, respectively. The smaller offset between the altitudes probed in violet and near-IR in Model 2 means that the discrete haze layer is better aligned between the two filters than it was for Model 1, and there is no need to introduce any additional haze component to fit the UV and methane absorption data, since our results now apply to a much higher altitude. However, it is not immediately clear how such large haze particles could be produced at or transported to such high altitudes, or how the haze particle size could increase by a factor of more than two within an altitude range of 9 km. (Note that these particle sizes represent a separate minimum in χ 2 , not the high end of a continuum of possible solutions. No acceptable solutions were found for violet particle sizes between 0.35 and 0.5 µm, or for near-IR particle sizes between 0.5 and 1.0 µm.) It should be noted that the haze particles in Model 2 are large enough to place the 34◦ scattering angle points outside the diffraction peak, so spherical particles may not be adequate to represent the single-scattering phase function of (presumably) hydrazine or hydrocarbon ice crystals. Some caution is also in order regarding the assumption of longitudinal homogeneity (i.e., the optically thick haze has the same properties at



FIG. 12. Limb-to-terminator I/F profiles at 60◦ N at (a) 218 nm and (b) 890 nm from the HST images shown in Fig. 1, together with calculated I/F values for two different haze models. The observed I/F profiles are indicated by the solid line with stippled error bounds. Calculated I/F’s for 60◦ N haze Model 1a (defined in Table VI) are shown as open circles, assuming a complex haze refractive index of 1.29 − 0.3i at 218 nm and 1.29 − 0.0i at 890 nm. The filled circles show I/F’s calculated for Model 1b, which assumes that 90% of the scattering attributed to gas in Model 1a is actually due to a second haze component with a mean particle size of 0.02 µm and a mixing ratio of 5 × 107 cm−3 am−1 . The UV haze refractive index for Model 1b is 1.29 − 0.01i.

315◦ W and 295◦ W, corresponding to the observations at 146◦ and 157◦ phase angle). We have seen that this is not true ∼100 km above the optically thick layer, where a detached haze layer is only intermittantly present. If the optically thick haze varies in particle size or number density by tens of percent over 20◦ of longitude, then the available data are insufficient to say much more than that stratospheric hazes are present, and their particle sizes are larger than those of Rayleigh scatterers (rm ≥ 0.1 µm).

However, as shown in Fig. 8, the derived extinction profiles and single-scattering phase functions consistently reproduce the overall radial intensity profiles for ∼1000 km inside the limb, corresponding to unforeshortened distances of thousands of kilometers (10◦ in longitude) over which there are no pronounced changes in the stratospheric haze. In contrast, the longitudinal features seen in the high phase angle images are an order of magnitude narrower and produce only small-scale variations in the


radial intensity profiles, which have little effect on the derived extinction profiles and phase functions. Since there appear to be no systematic changes in the haze properties between 285◦ W and 295◦ W (from the 157◦ phase angle images) or between 315◦ W and 305◦ W (from the 146◦ phase angle images) it is unlikely that the haze changes substantially between 305◦ W and 295◦ W.


same solution may apply, at least in the ultraviolet. The possibilities of such a model are shown in Fig. 13, which shows a typical fractal aggregate phase function at the wavelength corresponding to the strongest near-infrared methane band and the variation in extinction efficiency with wavelength (both supplied by Pascal Rannou, private communication), together with the corresponding quantities for spherical particles of similar


Plugging the particle radii, number densities, and altitudes of Model 1a into the expression for sedimentation velocity v at low Reynolds number given in Kasten (1968) gives sedimentation mass fluxes of 1.5 × 10−15 g cm−2 s−1 at 27 mbar and 7 × 10−16 g cm−2 s−1 at 120 mbar. For a steady state, the two mass fluxes should be comparable. As is, they differ by only a factor of two, and a detailed microphysical analysis would have to account for a distribution of particle sizes at each altitude, as well as other mechanisms for haze particle transport, such as eddy diffusion. These could increase the mass fluxes by a factor of 10 or more, depending on the vigor of eddy diffusion. If eddy diffusion is negligible, the other factors mentioned might act to decrease the mass fluxes by factors of ∼2–5, but could not decrease them by the factor of 1000 required to produce the mass loading needed to satisfy the UV and methane absorption data in the absence of a separate population of small particles. West et al. (1986) cite a photochemical production rate of 9 × 108 molecules cm−2 s−1 for hydrazine, or 5 × 10−14 g cm−2 s−1 , with production concentrated near a pressure of 65 mbar at low latitudes. They also cite a production rate of 7.5 × 108 molecules cm−2 s−1 , or 4 × 10−14 g cm−2 s−1 for C2 hydrocarbons. So there would be no problem with manufacturing the aerosols in Model 1a as rapidly as they are removed by sedimentation. To the contrary, other mechanisms for particle removal would have to dominate. For Model 1b, the large haze particles have sedimentation mass fluxes of 1.7 × 10−14 g cm−2 s−1 at 2.7 mbar and 6 × 10−15 g cm−2 s−1 at 12 mbar, but the total sedimentation mass flux is dominated by the 0.02-µm particles, which have fluxes near 2 × 10−13 g cm−2 s−1 at both altitudes. This exceeds West et al.’s combined photochemical production rate for both hydrazine and C2 hydrocarbons by a factor of two. The sedimentation mass fluxes in Model 2 also exceed estimated photochemical production rates: 1.2 × 10−13 g cm−2 s−1 at 1.1 mbar and 7. × 10−13 g cm−2 s−1 at 1.7 mbar. The need for a second haze component in Model 1 is reminiscent of the situation in Titan’s atmosphere, where Courtin et al. (1991) found it necessary to include a population of 0.05-µm absorbing particles in addition to Mie scatterers with radii of a few tenths of a micrometer, in order to reproduce Titan’s atmospheric scattering properties in both the UV and the visible-IR. Rannou et al. (1995) subsequently found that the small UV absorbers could be eliminated if the larger haze particles were modeled as “bunch of grapes” fractal aggregates with fractal dimension Df ≈ 2. The jovian stratospheric hazes are also expected to be solids with some kind of nonspherical shape, so the

FIG. 13. Generic differences between fractal aggregate scatterers and spherical scatterers. (a) The single-scattering phase function of a fractal aggregate composed of 400 0.02-µm monomers with a fractal dimension Df = 2 (solid line) and that of 0.35-µm radius spherical scatterers (dashed line) at a wavelength of 889 nm. (b) The extinction efficiencies of both the fractal aggregate and the spherical scatterers as functions of wavelength, normalized to the respective values at 889 nm. The complex refractive index was 1.3 − 0.0i at all wavelengths except 218 nm, where it was 1.3 − 0.01i. In general, fractal aggregates with sizes of a few tenths of a micrometer display more backscattering and a much larger increase in extinction in the UV than spherical particles of comparable size.



size. Both phase functions and the extinction efficiencies longward of 300 nm were calculated for conservatively scattering particles with refractive index 1.3. The extinction at 218 nm was calculated for an imaginary refractive index of 0.01. The fractal aggregate was made up of 400 spherical monomers of 0.02-µm radius, aggregated with Df = 2. The Mie scatterers had radii of 0.35 µm. Note that this is slightly less than the mean size of the aggregate

vations and data analysis in this publication was provided by NASA through Grant GO-06509.01-95A, submitted to the Space Telescope Science Institute, which is operated by Association of Universities for Research in Astronomy, Incorporated, under NASA Contract NAS5-26555. David Godfrey and Colin Harris of Imperial College, London, were instrumental in the creation of the Voyager polar map. Pascal Rannou has kindly supplied fractal aggregate phase functions.

dag = r0 Nm1/Df ,

Courtin, R., R. Wegener, C. P. McKay, J. Caldwell, K. H. Fricke, F. Raulin, and P. Bruston 1991. UV spectroscopy of Titan’s atmosphere, planetary organic chemistry and prebiological synthesis II. Interpretation of new IUE observations in the 220–335 nm range. Icarus 90, 43–56. Hansen, J. E., and J. W. Hovenier 1974. Interpretation of the polarization of Venus. J. Atmos. Sci. 31, 1137–1159. Kasten, F. 1968. Falling speed of aerosol particles. J. Appl. Meteorol. 7, 944–947.


where r0 and Nm are, respectively, the monomer size and the number of monomers in the aggregate particle. The “apparent size” of the aggregate decreases slightly with decreasing wavelength as the individual monomers become more “visible” at shorter wavelengths. The extinction efficiency increases dramatically in the UV for similar reasons. Such an increase in the UV extinction efficiency would likely cause scattering and absorption by fractal aggregates to remain competitive with Rayleigh scattering without the need for a separate population of UV absorbers. Also, the monomers are more visible in backscattering, where the aggregate phase function is a factor of 2–3 larger than that of the Mie scatterers. This may help to reconcile the Galileo observations with those made at low phase angles in near-infrared methane bands. Aggregated fractal scatterers should also help resolve the apparent conflict between high phase angle photometry and polarimetry near 90◦ phase (Smith and Tomasko 1984). The next step in elucidating the properties of the jovian stratospheric hazes will be to apply detailed microphysical modeling of haze production, growth, and transport to the extinction profiles and haze models derived from the Galileo high phase angle images. What is required to keep a population of small haze particles such as those in Model 1b from growing or becoming incorporated in the larger haze particles which must also be present? What kind of production mechanisms are needed to produce such a bimodal haze distribution? Is it even possible? Can the need for the small haze particles be eliminated through the use of fractal aggregate scatterers? Is it possible to maintain a population of ∼1-µm particles at pressures of only ∼1 mbar? These are some of the questions which now need to be addressed. ACKNOWLEDGMENTS The Galileo images were obtained by the Galileo Project and the Galileo Mission Support team at the Jet Propulsion Laboratory. Support for their analysis was provided through the Galileo Project. Funding for the HST obser-


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