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Photometry and polarimetry of Jupiter at large phase angles
ICARUS 58, 35--73 (1984)
Photometry and Polarimetry of Jupiter at Large Phase Angles II. Polarimetry of the South Tropical Zone, South Equatorial Belt, and the Polar
Regions from the Pioneer 10 and 11 Missions PETER H. SMITH AND MARTIN G. TOMASKO Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721 Received June 15, 1983; revised December 2, 1983 The imaging photopolarimeter (IPP) experiment on the Pioneer 50 and 11 missions to Jupiter measured the intensity and linear polarization of red and blue sunlight reflected from the planet over a range of phase angles inaccessible from the Earth. We give an overview of the polarization data obtained in the two Jupiter encounters at phase angles from 43° to 117° and briefly describe the photometry data from the Pioneer 15 encounter at phase angles between 34° and 80° which partially fill a gap in the phase coverage from Pioneer 10 (M. G. Tomasko, R. A. West, and N. D. Castillo, 5978, Icarus 33, 558-592). The polarimetry and photometry of the South Tropical Zone (STrZ), the north component of the South Equatorial Belt (SEBn), and a north-south cut extending to the south pole are given in detailed tables. Comparison of the data to multiple-scattering models yields several details of the distribution and single-scattering properties of the clouds and aerosols on Jupiter. The observed polarization in blue light at latitudes less than about 40 ° shows only small variations between belts and zones. Simple models indicate that the tops of the belt and zone clouds are reached at nearly the same pressure level of about 320 mb and that the polarization differences are a result of the lower cloud albedo in the belt. The optical thickness of the belt as well as the zone clouds at this level must be at least 1.5 to prevent the polarization produced by underlying gas from being seen in the data. The polarization rises abruptly toward the limb and terminator in red light, indicating a haze of positively polarizing particles with an optical thickness of a few tenths at a pressure level of about 120 rob. The polarization in both colors increases abruptly from latitudes north of 40°N and south of 48°S to values as high as 60% at high latitudes. This effect is not due to a longer slant path but must be due to a large increase in the optical thickness of the polarizing haze at high latitudes. There is some indication that the size of the haze aerosols grows with increasing latitude as well. The photometry data indicate little change in the brightness of planetary features in the year between the two Pioneer encounters. Photometric models that fit the Pioneer 50 data fit the Pioneer 15 data remarkably well with essentially the same phase functions. Using a two-cloud model, we find that our models best fit the limb darkening at 12° phase when the belt absorbers are evenly distributed in both the clouds. There is no evidence for rainbow-like bumps on the singlescattering phase functions in the range of scattering angles from 120° to 140° as might result from scattering by spherical particles.
amount of information is required also to describe the vertical distribution and the single-scattering properties of the particles. Several types of data have been used in studies aimed at determining the distribution and scattering properties of Jupiter's clouds. Observations in the ultraviolet between 2000 and 3000 ,~ from Voyager (West et al., 1981), the International Ultraviolet Explorer (Tomasko and Martinek, 1978), the OAO satellite (Wallace et al., 1972), as
I. INTRODUCTION
The optical properties and vertical distribution of aerosol and cloud particles are important in controlling many of the physical processes occurring in Jupiter's atmosphere, and so are of considerable interest. Even a glance at an image of the planet conveys the fact that a great deal of information is required to specify the horizontal distribution of the aerosols. A considerable 35
0059-5035/84 $3.00 Copyright© 1984by AcademicPress, Inc. All rightsof reproductionin any formreserved.
36
SMITH AND TOMASKO
well as various rocket flights have indicated the presence of high-level aerosols with an optical thickness of several tenths and a low albedo shortward of 3000 A. This haze is seen at pressure levels of roughly 100 mb at low latitudes rising to pressures of a few tens of millibars or less at latitudes greater than - 4 0 °. Studies in absorption bands of methane, ammonia, and the quadrupole lines of hydrogen [see Wallace and Hunten (1978) for a review] in the visible and near infrared are sensitive to deeper levels. In combination with the predictions of thermodynamic equilibrium models (see Weidenschilling and Lewis, 1973) such data often are interpreted in terms of two cloud layers. An upper cloud (presumably of ammonia crystals) is thought to have its base near 600 mb. A deeper cloud occurs with its top at a pressure of about 2 bars (Axel, 1972), or more (Sato and Hansen, 1979). Finally, observations near 5 ~m where gaseous opacity is a minimum reveal small regions with brightness temperatures of 260°K indicating the presence of significant gaps at some locations in the cloud layers (Terrile and Westphal, 1977; Marten et al., 1981). Despite the large number of high-quality observations of Jupiter, the constituent responsible for the colors of the clouds remains to be identified. In principle, measurements of the polarization of reflected sunlight as a function of phase angle a can yield constraints on the single-scattering polarizing properties of the cloud particles at the corresponding single-scattering angles (180-a) and ultimately can constrain the refractive index and composition of the particles. Interpretation of existing groundbased measurements of polarization (Lyot, 1929; Dollfus, 1957; Hall and Riley, 1969; Gehrels et al., 1969; Morozhenko and Yanovitskii, 1973) have been hampered by the small range of phase angles accessible to ground-based studies and also by the fact that the cloud particles are expected to be nonspherical. In this case laboratory measurements are required to convert con-
straints on the single-scattering phase matrix to constraints on the size, shape, and refractive index of the cloud particles. Near the limb at small phase angles, the polarization results primarily from secondorder scattering, and will be radial for a phase matrix that produces positive polarization (maximum electric vector perpendicular to the scattering plane) at intermediate scattering angles (near 90°), and tangential to the limb for a phase matrix that is negative at intermediate angles. The observations of Gehrels et al. (1969) showed very different behavior near the poles compared with the east and west limbs at low latitudes, indicating much more positively polarizing material in the polar regions. The Pioneer 10 and 11 missions to Jupiter provided the first opportunity to measure the brightness and polarization of Jupiter at phase angles larger than the maximum of about 12° obtainable from the Earth. The measurements of the brightness of a dark belt (the SEBn at 5°S-7°S) and a bright zone (the STrZ at 18°S-21°S) made by Pioneer 10 at phase angles from 12° to 150° (with a gap between 34° and 109°) were reported by Tomasko et al. (1978) (hereafter referred to as Paper I). Here we present the photometry of these regions obtained by Pioneer 11 at phase angles from 34° to 80°, partially filling the gap in coverage from Pioneer 10. Both Pioneer 10 and 11 made measurements of the degree and position angle of polarization of sunlight reflected from Jupiter (Gehrels et al., 1974; Coffeen, 1974; Baker et al., 1975). The polarimetry of the Great Red Spot has been presented by Doose (1976). The SEBn was discussed by Stoll (1980) who derived constraints on the single-scattering polarization of the cloud particles assuming the ammonia cloud top occurs near 600 mb. Here we proceed using a different approach and compare a belt and a zone as well as discuss the polarimetry of the polar regions. In Section II of this paper we present the
JOVIAN PHOTOMETRY AND POLARIMETRY
photometry data from Pioneer 11 and the polarimetry from both missions. In Section III we compare the photometric models derived from the Pioneer 10 data to the data obtained on Pioneer 11. In Section IV we compare the polarimetry of the belt, zone, and the polar regions to simple models. Section V describes more detailed models of the belt and zone polarimetry. We discuss our results in the context of other work and summarize our conclusions in a final section. I1. DATA
A. Photometry
The imaging data from Pioneer 10 have been presented and the reductions have been described in Paper I. The instrument on Pioneer 11 was almost identical, but the trajectory was considerably different. In contrast to the very nearly equatorial trajectories of Pioneer 10 and both Voyager spacecraft, the trajectory of Pioneer 11 was at a high inclination permitting especially good views of both the south and north polar regions of Jupiter. The highest resolution images from both Pioneer encounters are shown in Fimmel et al. (1980). A typical Pioneer 11 blue and red image pair is shown in Fig. 1. While the spatial resolution is less than for images made at the same range by the subsequent Voyager mission, the Pioneer data have the advantage of having been obtained by sweeping the same channeltron detector over the entire image--a procedure that permits more accurate relative photometry than usually obtained with vidicon systems. Within about 1 hr of the closest approach to Jupiter, the imaging photopolarimeter (IPP) instrument on each Pioneer mission received a dose of energetic particle radiation sufficient to darken the glass windows over the channeltron detectors. On both missions, the size of this effect was monitored by frequent observations of an internal lamp throughout the encounter (see Paper I). Because of the different trajectory of
37
the Pioneer 11 encounter, the dose received was substantially less than that received by Pioneer 10 (Van Allen, 1976). The postpericenter Pioneer 11 photometry data have been corrected to the prepericenter system by multiplication by 1.03 and 1.05 in red and blue, respectively. Ground-based absolute photometry of Jupiter (Orton, 1975) near the time of the Pioneer 10 Jupiter encounter was used to provide an absolute calibration of the IPP on Pioneer 10. No comparable groundbased observations were made near the time of the Pioneer 11 encounter with Jupiter. However, an absolute calibration of the Pioneer 11 IPP is available from comparison of the Pioneer 11 observations of Saturn with ground-based observations of Saturn near the time of the Saturn encounter (Tomasko and Doose, 1984). In order to use the Pioneer 11 calibration at Saturn at the time of the Pioneer I 1 Jupiter encounter, the change in instrument sensitivity between the two encounters must be determined. Observations of Sirius made periodically during the interplanetary cruise can be used to monitor the changing sensitivity of the instrument to high accuracy. Figure 2 shows the average data number recorded for Sirius at gain 19 after correction for the effects of the changing spacecraft spin period and Sirius cone angle. The Pioneer 10 Sirius observations are shown on a scale displaced by one year for comparison. Both instruments experienced significant decreases in sensitivity between launch and Jupiter encounter, with a lesser rate of decline after Jupiter encounter. The abrupt decrease in sensitivity within an hour of closest approach indicated by the on-board lamp is also apparent in the figure. The values of F0, where ~'F0 is the solar flux in the Pioneer 11 passbands at Saturn's distance from the Sun, are given as 49.8 -+ 5.2 and 85.7 --- 6.8 in blue and red, respectively, in imaging mode data numbers at gain step 18 by Tomasko and Doose (1984). The corresponding values just before the Jupiter encounter at gain 13 are 47.5 - 5.3
38
SMITH AND TOMASKO
FIG. 1. (a) Pioneer 11 image C6 of Jupiter in blue light at a phase angle of 60 ° obtained from a range of 940,000 km at 18 hr 43 min UT on Dec. 2, 1974. This image was obtained in the higher resolution photometry mode. (b) Same as (a) but in red light.
JOVIAN PHOTOMETRY AND POLARIMETRY
FIG.l--Continued.
39
40
SMITH AND TOMASKO TIME (PIONEER I 0 ) ~ 1972 50
1973
1974
I
I
1975 I
1976 I
1978 I
1~,
4a
""30
PIONEER10 . . . . . PIONEER il - -
"4. "~
G 200 AIN --o .....
~
LUE
I6'~
15C> VEGA-x SIRIUS- ALL
lj
where R(h) is the relative spectral response for the respective instrument, and Rpeak is the peak responsivity. Then the ratio of the values ofF0 on the two instruments is given by F0(Pl0 F0(PI0)
19o
~
20
_
1977 I
0,-HE, S
l(h)dh
Rpeak(PI l) fF®(h)RP 1
Rpeak(PI0) fFG(X)RP~o(X)dX
The ratio of the counts on the star can be used to give the ratios of the peak responsivities from C*(P~I) = Rpeak(Pll) fF*(X)RPll(h)dh. C*(PI0) Rpeak(P10)fF*OORelo(h)dh
I
1973
I
1974
I
1975
I
1976
1977
I
I
1978
1979
TIME (PIONEER I I ) - ' - - " -
FIG. 2. The sensitivities of the Pioneer 10 and 11 IPP instruments as functions of time determined by observations of the star Sirius in the polarimetry mode (with the depolarizer in place). The plotted points are the star counts normalized to compensate for changes in the cone angle of the star and in the spin period of the spacecraft: the normalized counts are defined as the sum of the counts in all the sectors of one roll multiplied by the sine of the cone angle and divided by the spin period in seconds. The amplifier gain setting for each observation is given in the legend. All points have been converted to gain step 19 by using gain ratios determined from postlaunch observations. The time scales for the two missions have been displaced by one year as indicated. For Pioneer 11 some of the points were determined from observations of Vega adjusted for a difference of 1.49 and 1.53 magnitudes between Vega and Sirius in our blue and red channels, respectively.
and 66.8 -+ 5.8 when changes in distance, gain, Jovian radiation factors, and Sirius data numbers are taken into account. A second, completely independent, method of calibrating the Pioneer 11 IPP is available. It is possible to use the observations of Sirius on each mission as an intermediate standard to tie the calibration of the Pioneer 11 instrument to that on Pioneer 10. The value ofF0 for each instrument can be defined by F0 = RpeakfFo(h)R(h)d)t
Finally, the ratios of the star counts should be taken at the same gain step (13) where the ratio of the values of Rpeak and F0 are required. Taking the shape of the solar spectrum from Labs and Neckel (1970) gives the ratio of the Pioneer 11 divided by Pioneer I0 integrals of spectral response and solar flux as 1.417 in the blue and 1.283 in the red. With the shape of the relative spectrum of Sirius taken from Hayes and Latham (1975), we have the ratio of the Pioneer I0 to Pioneer 11 integrals of the Sirius flux times the IPP relative response as 0.718 in blue and 0.797 in the red. Combining these values gives F0(blue) = 42.4 -+ 3.6 and F0(red) = 61.6 -+ 4.0. This includes an adjustment for changes in the distance between Jupiter and the Sun. In view of the size of the uncertainty associated with each of these independent calibrations of the Pioneer I I IPP, the two approaches lead to consistent results. Forming a weighted average of these values gives F0(blue) = 44.3 _+ 3 and F0(red) = 63.5 -+ 3 for Pioneer I I at Jupiter in the imaging mode at gain 13.
41
JOVIAN PHOTOMETRY AND POLARIMETRY TABLE I PIONEER II IMAGES AND PHOTOMETRIC REDUCTION FACTORS
Image No.
Mid-time"
Phase (°)
Pixel size (km)
Lat. b
Gain
GR c
GB c
C26 C18 C6 C4 C2-CI
335:17:16 336:00:41 336:18:51 336:22:58 337:02:15
48 50 60 67 80
1127 943 433 293 168
- 12.4 - 13.8 -22.1 -27.6 -37.6
DI6 D22
338:10:20 338:21:32
37 34
915 1193
38.4 36.7
13 14 13 14 13 14 15 14 13
1.00 1.46 1.00 1.46 1.00 1.46 2.073 i.46 ! .00
1.00 1.41 1.00 1.41 1.00 1.41 1.974 1.41 1.00
a Earth receipt time of middle of image (UT) in day of year:hr:min. b Latitude o f s u b s p a c e c r a f t point. c Intensities from Pioneer 1 i imaging data were put on the same relative intensity scale by dividing the data n u m b e r s by GR in red (or GB in blue). In addition, data obtained after pericenter (images D l 6 and D22) were multiplied by 1.03 in red and 1.05 in blue to adjust for the radiation-induced darkening which occurred within 1 hr o f pericenter.
The scattering geometries of each pixel in Pioneer l l images at seven phase angles from 34° to 80° have been computed from the trajectory and housekeeping data for the flyby. The phase angles of these images, their spatial resolution, and the instrument gain settings and gain ratios appropriate for each are given in Table I, while the brightness (in data numbers normalized to prepericenter gain 13 counts) are given in Table II for the STrZ and the SEBn. Figure 3 shows a north-south scan of reflectivity (actually IIF~owhere/~0 is the cosine of the solar zenith angle) from image A28 of the Pioneer l0 encounter and image C6 from Pioneer 1I. The figure shows that the latitude limits and relative brightness of Jupiter's main belts and zones remained relatively unchanged in the one-year interval between the two encounters. A more rigorous comparison of the brightness of the planet at the times of the two encounters follows in Section III where scattering models are presented, but is not possible from a visual inspection of Fig. 3 alone because the phase angles of the two images are appreciably different. The brightness of
the Pioneer 11 images (in data numbers normalized to prepericenter gain 13 counts) are given in Table II for the STrZ and the SEBn. 1,0
'
'
,
~
I
~
I -60
,
I
I
'
~.
I
I 0
L
~
.I 50
0.8
l
0~6
~_o =~
0.4
0.2 -90
,
I -30
,
~
,
, 60
LATITUDE
FIG. 3. T h e refiectivity of a L a m b e r t surface, I/ (p.oF0), as a function of latitude along the central meridian o f image C6 at a p h a s e angle of 60 ° (see Figs. la,b) from the Pioneer I l e n c o u n t e r and from image A28 at 23 ° phase (see Paper I) from Pioneer 10. The boundaries of the principal belts and zones are seen to be similar at the times o f the two encounters. The difference in the phase angles of the two images precludes quantitative c o m p a r i s o n of the reflectivities of the planet at the times of the two encounters without detailed scattering models, but the reflectivities of the bright zones s e e m quite similar.
42
Phase
(°)
SMITH A N D TOMASKO T A B L E IIA
T A B L E liB
PIONEER 11 PHOTOMETRY STrZ
PIONEER 11 PHOTOMETRY SEBn
Roll
/z
go
A~
/red
/blue
Phase (°)
Roll
/x
~o
A~
Led
lblu¢
34
65 81 101 121 141 161 181 200
0.2064 0.3878 0.5661 0.6841 0.7028 0.6339 0.4696 0.2490
0.3961 0.6162 0.8295 0.9604 0.9833 0.8932 0.6954 0.4132
144.45 141.95 137.43 137.80 154.13 134.14 139.69 143.68
15.0 24.5 34.0 39.9 41.0 37.0 28.5 17.1
13.5 16.1 18.8 20.7 20.9 19.9 17.4 13.1
37
11 29 51 71 91 109 135 155
0.1621 0.3665 0.5550 0.6589 0.6744 0.6165 0.4036 0.1617
0.3310 0.5825 0.8204 0.9532 0.9853 0.9213 0.6717 0.3657
142.72 139.80 134.33 133.92 163.57 135.38 140.69 143.09
13.6 23.7 32.4 38.0 4L0.3 39.6 30.0 14.1
12.7 15.4 17.7 19.5 20.5 20.4 17.7 12.6
48
485 505 525 545 560 570
0.8468 0.9768 0.9854 0.8701 0.6551 0.3092
0.2030 0.5244 0.7688 0.9383 0.9878 0.8972
164.59 147.96 22.94 12.81 88.31 150.02
7.5 21.9 33.5 40.3 40.5 32.7
4.5 11.5 16.4 19.5 19.9 18.5
50
44 49 57 80 108 139
0.2916 0.5082 0.6855 0.9262 0.9909 0.8543
0.8996 0.9714 0.9870 0.8771 0.6144 0.2023
148.28 127.97 61.86 3.95 108.94 161.34
30.9 37.1 39.9 36.2 24.3 6.3
18.5 19.9 20.0 17.1 12.2 4.2
60
1026 1060 1090 1120 1150 1180 1210 1240 1250
0.8395 0.9200 0.9553 0.9573 0.9232 0.8506 0.7223 0.4704 0.2288
0.1153 0.3143 0.4715 0.6218 0.7510 0.8597 0.9466 0.9867 0.9385
146.11 3.5 2.5 130.44 12.2 7.0 104.83 19.5 10.4 65.77 26.2 13.0 36.27 32.0 15.0 17.59 40.0 17.5 4.31 39.6 19.5 82.29 "38.0 20.2 132.57 30.6 - 1%3
68
360 400 500 600 675
0.8532 0.8750 0.9095 0.9173 0.9085
0.7724 0.7268 0.6065 0.4767 0.3743
34.41 41.36 60.36 82.26 97.67
35.3 32.8 27.3 20.7 15.2
17.1 16.1 13.7 10.6 8.3
80
287 325 375 426 460 500
0.7494 0.7818 0.8063 0.8125 0.8097 0.8151
0.6862 0.6013 0.4878 0.3779 0.2983 0.2086
45.34 54.11 65.71 76.64 84.15 91.67
32.0 27.6 21.8 15.7 12.2 8.1
15.7 14.0 11.8 9.0 7.2 4.6
34
91 111 130 151 171 191 211
0.1504 0.3207 0.4601 0.5086 0.4835 0.3577 0.1658
0.4805 0.7015 0.8598 0.9201 0.8802 0.7269 0.4849
148.22 149.55 155.80 178.15 156.17 148.55 147.74
17.9 28.5 36.8 40.1 38.3 31.0 19.1
18.0 23.4 29.5 30.0 28.9 24.7 17.0
37
49 71 89 109 131 149 167
0.1764 0.3486 0.4409 0.4719 0.4158 0.2809 0.1001
0.5214 0.7509 0.8716 0.9183 0.8532 0.7006 0.4757
145.99 t47.65 154.98 179.27 154.71 149.17 147.78
21.9 33.1 38.9 41.2 38.2 30.6 20.8
20.0 25.1 28.4 30.0 27.9 24.1 18.9
480 500 520 540 555 563
0.8257 0.9651 0.9771 0.8581 0.6239 0.3059
0.1447 0.4702 0.7150 0.8999 0.9160 0.8193
174.70 137.95 74.59 64.87 103.64 135.46
5.1 20.5 33.0 40.9 40.5 32.7
4.5 15.1 23.5 29.3 29.7 24.9
52 54 62 72 91 114 146
0.2762 0.4148 0.6486 0.8008 0.9492 0.9883 0.8332
0.8085 0.8688 0.9191 0.9001 0.7835 0.5623 0.1318
134.27 125.11 95.12 68.99 56.20 135.28 176.79
31.8 36.6 40.9 40.9 35.6 24.6 4.0
23.4 26.7 29.5 29.5 25.7 18.0 3.5
1020 1070 1110 1150 1180 1200 1219 1229
0.9016 0.9913 0.9930 0.9232 0.6154 0.8970 0.5000 0.2508
0.1382 0.4156 0.6008 0.7687 0.8618 0.9058 0.9145 0.8600
169.30 162.28 13.36 24.83 38.46 56.39 89.28 117.93
4.7 17.5 27.5 36.5 41.2 42.5 40.8 33.3
4.3 12.8 19.6 25.9 29.0 30.2 29.0 25.0
360 375 400 500 600 680
0.8571 0.8714 0.8929 0.9540 0.9840 0.9892
0.7944 0.7795 0.7539 0.6429 0.5212 0.4173
17.40 15.12 11.35 5.47 33.37 79.10
38.6 38.1 36.5 30.7 24.5 18.3
27.8 27.3 26.2 21.9 17.7 13.5
287 295 325 375 426 475 525 575
0.8048 0.8181 0.8598 0.9066 0.9304 0.9398 0.9344 0.9165
0.7201 0.7031 0.6384 0.5282 0.4209 0.3086 0.1923 0.0750
5.74 7.98 16.59 31.93 49.54 69.96 90.35 106.94
33.6 35.3 32.3 25.9 19.8 13.2 7.6 2.2
20.8 23.0 22.3 17.8 13.7 9.7 5.8 2.3
48
50
60
67
80
JOVIAN PHOTOMETRY
43
AND POLARIMETRY
T A B L E III PIONEER 10 AND 11 POLARIMETRY OF JUPITER Map
Start time a
End time a
Phase (°)
Pixel size b (km)
Gain
Dist. C
Pioneer 10 01 02 03 04
337:23:33 338:02:28 338:03:23 338:07:12
338:01:07 338:02:53 338:03:56 338:07:57
43 103 141 157
1970 1080 1070 2830
--- 350 --- 28 -+ 55 --- 180
0 0 0 0
4.57 2.949 2.929 6.12
-+ .63 +- .05 +- .10 -.33
Pioneer 11 A3 A2 A1 A0 B1 B2 B3
337:01:03 337:03:10 337:04:24 337:05:17 337:06:43 337:07:03 337:07:51
337:01:42 337:04:17 337:05:07 337:05:22 337:06:52 337:07:40 337:08:52
80 98 120 150 140 104 82
2710 1140 500 340 1020 1440 2100
-+ 220 --- 330 -+ 130 -+ 6 --+ 30 _+ 220 -+ 330
2 2,3,4,5 2,3 1 2 2,3 2,3
5.91 3.06 1.91 1.61 2.85 3.60 4.80
---+ -+ -+ -+ -+
.40 .60 .23 .01 .05 .40 .60
Note. The values ofF0 for the polarimetry-mode data are 1400 in red and 1360 in blue for Pioneer 11 and 440 in blue for Pioneer 10. These values should be used with Table IV to obtain I/F from instrument counts. a All times are UT Earth receipt times of data in day of year:hr:min (Pioneer 10: 1973, Pioneer 11: 1974). b Pixel size = (Dist. - 1)(70,850 km) (7.8 × 10 -3 radians). c Distance to center of Jupiter in units of Jupiter's radius (adopted as 70,850 km).
B. Polarimetry A summary of the operation of the IPP in the polarization mode is given by Coffeen (1974). Details of the reduction procedure for Pioneer I 1 polarimetry are given by Tomasko and Smith (1982) and Tomasko and Doose (1984). The data maps were obtained by accumulating one scan line of information on each rotation of the spacecraft. The motion of the spacecraft relative to the planet over a period on the order of an hour was sufficient to sweep the scan lines from the limb of the planet to the terminator. Table III summarizes the phase angles at which polarization maps are available from the Pioneer 10 and 11 Jupiter encounters. Due to a problem that developed with the Pioneer 10 instrument, red polarization data are not available for that encounter. The imaging-mode data use another detector, and so the intensity data were not affected by this problem. Because of the motion of the spacecraft and the planet during the map, it is not possible to display the data on the planet as it appeared from the spacecraft at any one instant of time and preserve both the local
illumination conditions and the apparent locations of the pixels. Figure 4 shows one of the polarization maps displayed in a way that nevertheless gives a good feeling for the coverage on the planet. The globe outline shows the appearance of the planet from the spacecraft at a time halfway through the map. All the pixels are displayed at the latitudes at which the data were obtained. Each pixel is rotated in longitude and displayed at the same fractional longitude from the central meridian to the limb at which it was observed. Line segments are used to indicate the direction of maximum electric vector with vertical lines representing light polarized perpendicular to the scattering plane. The magnitude of the polarization is indicated by the length of the plotted line segment. In order to prevent overcrowding, only a fraction of the av~ailable blue and red data is displayed in Figs. 4a and b. In both colors the polarization is oriented essentially perpendicular to the scattering plan e everywhere in the map. This is the case generally in the Pioneer observations of Jupiter except over the Great Red Spot in red light (Doose, 1976). In both
44
SMITH AND TOMASKO
Ii
I
b
i ill J r l t i i
t jI
,~
, '
i , '
, '
ill
r
20%
T
~(
FIG. 4. Polarization map A2 obtained from Pioneer 1! at a phase angle of 98° between 3 hr 10 min and 4 hr 17 min UT on Dec. 2, 1974. The globe outline shows the appearance of the planet halfway through the map. Vertical lines represent polarization perpendicular to the local scattering plane, with the length of the line segment proportional to the degree of polarization. To avoid overcrowding, only every fourth roll of polarization data and every other sector along a roll are displayed. The data are displayed at the latitude where they were observed, but are rotated in longitude to the same fractional longitude from the central meridian to the limb in the display as that at which they were observed. The data extend all the way to the terminator. (a) In blue light. (b) In red light. colors, the polarization increases dramatically toward the terminator and toward the pole south of about 50°S. The polarization also increases toward the bright limb in both colors. At phase angles near 90 ° , the polarization is m u c h larger in blue light than in the red at low latitudes, although, at high latitudes, the opposite is true. Displays such as Fig. 4 are quite useful but are not well suited for the examination of relatively small-scale features. F o r this purpose, all the original data pixels can be displayed in a rectangular grid exactly as they were obtained. The m a p shown in Fig. 4 is displayed in this w a y in Figs. 5 and 6. Contours of constant degree of polarization are given in Fig. 5. The dramatic increase in polarization in both colors for latitudes south of 50°S is apparent. The degree of polarization in red light is r e m a r k a b l y unif o r m at low latitudes where belt and zone structure appears in ordinary images. A modest a m o u n t of contrast is seen across belts and zones in the polarization in blue light superimposed on the strong gradient of polarization caused b y the increasing
slant path through the a t m o s p h e r e a w a y f r o m the subspacecraft point. In Fig. 6, the polarizations h a v e been divided by (1//z + 1/p-0) to roughly c o m p e n s a t e for the effects of different slant paths through the atmosphere in different parts of the map. The brightness in this figure is proportional to the adjusted polarization in the map. The contrast across the belts and zones in blue light is easier to see than in Fig. 5, and the increase in polarization toward the pole remains, indicating that this is not a slant path effect in the map. Relatively little fine scale structure is apparent at different longitudes, although close examination of the entire Pioneer data set does reveal polarizations different f r o m the surrounding regions for the G r e a t Red Spot, a few large ovals, and some other locations. O v e r the equatorial and t e m p e r a t e regions the areas of higher polarization are associated with the low albedo features. This is not the case with the poles where no corresponding decrease in albedo is associated with the large increase in polarization measured. Figure 7 shows the polarization of the northern hem-
45
JOVIAN PHOTOMETRY AND POLARIMETRY a SO
70
t 60
6 z g
50
40
30
20
300
350
400
450
500
550
ROLL-
I
L
P
I
I
I
I
80-
70-
I
60-
B 6 %
50-
40-
30-
20-
300
350
450
400
500
550
ROLL-
FIG. 5. Contours of the degree of polarization in map A2 with the data not projected onto the planet but simply laid down into a rectangular grid. (a) In blue light. (b) In red light. There are data dropouts before rolls 500 and 550.
isphere of Jupiter as seen from Pioneer 11 in a projection similar to that of Fig. 3. The polarization is seen to increase dramatically toward the north pole similar to the situation in the south. Reduced intensities, degree of polarization, and angle of polarization relative to the normal to the scattering plane are given in Table IV for the STrZ and the SEBn at each map covering these latitudes, and for a north-south cut in map A2 at a phase angle of 98”. Near the center of the disk, the polarization in blue light is generally largest near 90” phase, decreasing toward both
larger and smaller phase angles. In red light, the polarization is fairly small and independent of phase near the central meridian with an abrupt rise toward the limb and terminator in maps near 90” phase. III. PHOTOMETRY
MODELS
In view of the similarity in the appearance of Jupiter at the times of the Pioneer 10 and 11 encounters seen in Fig. 3, it is interesting to compare the reflectivity of the planet at the two encounter periods in a more quantitative manner. This is especially important as a prelude to the polar-
46
SMITH AND TOMASKO
FIG. 6. Polarization map A2 displayed as an image in which the brightness is proportional to the degree of polarization divided by the quantity (1//.t + 1/p.o) to roughly correct for the different slant paths through the gas seen in different parts of the map. (a) In blue light. (b) In red light.
JOVIAN PHOTOMETRY AND POLARIMETRY
FIG.
6---Continued.
47
48
SMITH AND TOMASKO
ization models discussed in the following sections where the polarimetry from the two encounters is combined into a single data set to constrain scattering models, implicitly assuming that the scattering properties of the planet changed relatively little between the encounters. For the best Pioneer 10 models of the STrZ given in Table III of Paper I, the values of F0 that gave the
best fits to the photometry data were 1.043 and 1.002 times the nominal values in red and blue, respectively. When exactly the same model structures are compared to the Pioneer 11 photometry data of the STrZ, the values of F0 that minimize the residuals are 1.065 and 1.034 times the weighted average values of F0 from the two ways of calibrating the Pioneer 11 instrument at Ju-
TABLE IVA POLARIMETRY OF JUPITER STrZ
Phase
Map
Roll
/z
/z0
(°)
A~ (°)
lbJ~e (counts)
Pblue (%)
0bJue (°)
/red (counts)
/)red (%)
0red (o)
43
01
3 56 94 147 208 242 269 288 299
0.8104 0.9218 0.9684 0.9843 0.9436 0.8904 0.8297 0.7765 0.7370
0.9284 0.8707 0.8052 0.6770 0.4859 0.3568 0.2409 0.1517 0.0935
85.3 69.1 71.7 122.1 163.3 169.6 171.9 173.4 172.9
292.0 273.5 247.8 204.5 139.5 98.5 63.5 39.0 23.7
1.4 1.3 1.4 1.5 2.2 3.3 4.6 6.8 9.2
172.0 174.0 171.0 177.0 179.0 177.0 178.0 181.0 182.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
80
A3
123 127 143 151
0.3394 0.4571 0.5545 0.5988
0.9159 0.9159 0.8896 0.8749
-66.8 -44.5 -30.0 -22.3
797.0 850.0 845.0 845.5
9.3 6.9 5.9 5.5
179.0 177.0 175.0 174.0
793.0 857.0 870.0 868.0
3.3 1.8 1.3 1.1
166.0 158.0 148.0 148.0
98
A2
262 272 282 294 314 338 362 386 406 430 446 458 466
0.2784 0.3539 0.4129 0.5174 0.6153 0.6885 0.7441 0.7664 0:7945 0.8077 0.8106 0.8201 0.8186
0.9018 0.8719 0.8448 0.7775 0.6830 0.5790 0.4814 0.3843 0.3079 0.2164 0.1563 0.1127 0.0830
-20.2 -12.1 -5.4 6.9 17.9 28.1 35.3 46.4 51.9 60.5 66.3 69.8 72.6
821.0 829.0 827.0 796.0 718.0 616.5 504.0 391.5 301.5 200.0 135.5 95.0 68.5
10.1 8.4 7.5 6.6 6.2 6.4 6.8 8.5 10.0 13.8 18.1 22.0 25.4
178.0 177.0 175.0 174.0 173.0 173.0 173.0 174.0 175.0 175.0 177.0 I77.0 177.7
845.0 857.3 856.7 828.5 748.0 650.5 527.0 413.5 312.0 201.5 133.5 90.0 64.0
4.1 2.8 2.1 1.4 1.2 1.3 1.5 2.3 3.5 5.8 8.7 11.4 14.4
172.0 168.0 166.0 162.0 156.0 157.0 164.0 167.0 169.0 171.0 173.0 174.0 174.5
103
02
390 404
0.4891 0.6055
0.6610 0.5508
32.1 31.8
241.6 199.2
6.0 5.8
179.0 178.0
0.0 0.0
0.0 0.0
0.0 0.0
120
A1
600 610 620 630 640 650 660 694
0.2591 0.3531 0.4082 0.4527 0.4915 0.4897 0.5197 0.5357
0.6604 0.5428 0.4473 0.3356 0.2313 0.1860 0.1116 0.0639
24.0 30.7 36.0 42.2 47.0 50.0 52.8 54.7
782.0 703.5 599.5 453.5 315.0 248.5 144.5 86.0
10.0 8.1 8.3 9.9 12.4 15.5 20.6 25.7
173.0 171.0 171.0 172.0 172.0 174.0 175.0 176.4
831.0 753.0 643.0 484.5 333.0 262.0 149.0 86.0
4.8 3.3 3.3 4.3 6.5 9.0 13.0 17.0
171.0 166.0 164.0 165.0 167.0 169.0 171.0 173.6
JOVIAN PHOTOMETRY AND POLARIMETRY
piter, indicating that the zone got brighter by about 2% in red light and 3% in blue. These changes are, however, fairly small compared to the uncertainties in connecting
49
the calibration of the two Pioneer instruments. If the Pioneer 10 calibration transferred through the star observations to Pioneer 11 is used instead of the average of the
TABLE IVB POLARIMETRY OF JUPITER SEBn
Phase
Map
Roll
p,
/.to
(°)
Ibi.~
A~p (°)
(counts)
Pbl.e (%)
0brae (o)
/red (counts)
Pred (%)
0~a (o)
7.8 -24.9 -91.8 - 144.3 -157.2 - 164.3 - 166.6
187.0 164.5 148.5 114.7 85.0 39.5 20.0
2.0 2.0 2.2 2.4 3.5 6.9 10.6
177.0 173.0 176.0 175.0 180.0 178.0 179.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
43
O1
18 79 132 189 230 280 299
0.8902 0.9718 0.9883 0.9579 0.9027 0.7928 0.7348
0.9602 0.8625 0.7365 0.5635 0.4106 0.1987 0.1045
80
A3
70 82 94 111 139 171 207
0.2218 0.3264 0.4287 0.5078 0.5989 0.6734 0.7272
0.9880 0.9855 0.9624 0.9312 0.8767 0.8116 0.7328
-68.8 - 14.6 - 1.6 14.8 23.2 30.1 39.9
545.0 588.0 596.0 577.0 552.0 534.0 489.0
15.8 11.1 9.2 8.1 7.4 7.3 7.4
180.0 179.0 177.0 175.0 174.0 175.0 174.0
672.0 792.0 824.0 830.0 805.0 758.0 694.5
6.0 3.0 1.9 1.3 1.0 1.1 1.1
172.0 169.0 166.0 158.0 148.0 151.0 153.0
98
A2
266 290 330 370 410 450
0.2806 0.4235 0.5362 0.5930 0.6190 0.6117
0.8950 0.7728 0.5982 0.4362 0.2809 0.1300
27.1 38.4 49.8 59.5 68.5 77.1
580.0 551.0 468.0 350.0 227.0 101.0
12.6 9.9 9.6 11.6 15.5 27.0
177.0 174.0 172.0 172.0 175.0 177.0
745.5 716.0 608.0 449.0 274.0 112.0
3.5 2.3 2.3 3.3 5.7 12.8
172.0 166.0 165.0 163.0 189.0 173.0
103
02
394 408 433 451 465
0.6174 0.7142 0.8381 0.9010 0.9373
0.6204 0.5141 0.3348 0.2113 0.1179
2.9 2.4 2.8 4.6 7.8
170.4 138.8 85.2 47.6 22.5
6.0 6.3 8.4 12.6 22.1
181.0 181.0 181.0 181.0 182.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
120
A1
628 648 670 686 702
0.1658 0.1817 0.2524 0.2564 0.2379
0.5515 0.4213 0.2790 0.1871 0.1049
46.8 52.9 55.7 58.6 61.3
544.0 492.0 391.0 289.0 187.0
15.9 18.0 19. I 23.0 31.2
174.0 174.0 175.0 176.0 178.0
8.9 10.3 11.3 15.0 22.1
171.0 170.0 171.0 171.0 174.0
0.0 0.0 0.0 0.0 0.0 611.0 549.0 434.0 310.0 189.0
TABLE IVC POLARIMETRY OF JUPITER SOUTH POLAR REGION (PHASE 98°, MAP A2) Lat. (°)
/~
-85.0 -80.0 -70.0 -60.0 -50.0 -45.0
0.5571 0.5536 0.5578 0.5756 0.5945 0.5913
~
0.0427 0.1289 0.2724 0.4114 0.5320 0.5890
Atp (°)
/blue
Pblue
ObJ~e
/red
/°red
Orcd
(counts)
(%)
(°)
(counts)
(%)
(°)
-77.8 -74.4 -67.7 -58.8 -47.1 -40.5
41.0 112.0 250.0 335.0 428.0 498.0
50.6 47.6 41.7 32.7 19.6 11.5
178.0 179.0 181.0 182.0 181.0 179.0
41.4 111.0 257.0 378.0 526.0 596.0
54.7 53.1 42.7 23.3 6.3 1.3
177.0 179.0 181.0 182.0 178.0 162.0
50
SMITH AND TOMASKO
i FIG. 7. Contours of polarization in map B3 obtained at a phase angle of 82 °. The projection scheme is similar to that used for Fig. 4. The longitude of the terminator at the mid-time of the map is also drawn. (a) In blue light. (b) In red light.
two independent calibration methods, one would conclude that the zone got darker (by 3% in the red and 4% in the blue) instead of brighter in the year between the two encounters. A similar comparison for the SEBn (based on the average of the two methods of evaluating F0 for Pioneer 11) indicates that this belt got brighter by some 8% in red light and 11% in blue between the two encounters. Even these differences are less than the differences between the two techniques for calibrating the Pioneer 11 instrument, so it is difficult to rule out the possibility that the belt remained roughly the same brightness between the two encounters and the zone actually got somewhat darker. In any case, the reflectivity of the STrZ seems to have changed relatively little between the two encounters, with the best estimate being an increase of about 2% in red light and 3% in blue. The SEBn got brighter relative to the STrZ by some 6% in the red and 8% in the blue in the year between the encounters. The general quality of the fits of models using the phase functions derived from the Pioneer 10 data to the Pioneer 11 imaging data is shown in Fig. 8. Also shown are models in which the single-scattering phase functions of the clouds are changed to have
a local bump similar to that produced by a rainbow for spherical particles (see Fig. 9) at scattering angles from 120° to 140°. Phase functions with bumps in this range of scattering angles make the fits to the observed data somewhat worse than the standard Henyey-Greenstein functions of Paper I. On the other hand, more gradual changes in the phase functions in the range of scattering angles from 80° to 140° (see Fig. 10) are more difficult to distinguish because of the relatively low values of any of these singlescattering phase functions in this range and the large contribution of multiple scattering compared to single scattering in the intensities observed at this range of phase angles. In general, phase functions with deeper minima than the double H enyey-G reenstein functions given in Paper I fit slightly worse, and ones that are even flatter in this range fit about as well or marginally better. All of the smooth phase functions give models that are a few percent too dark at 67° phase compared to the observations. However, because the models fit well at 60° and 80° phase, the required feature on the phase function would have to be very narrow and very high to account for the observed effect. It seems more likely that the discrepancy is the result of uncertainties in the scattering geometries assigned to the
JOVIAN PHOTOMETRY AND POLARIMETRY pixels in this image which contained only a very limited portion of the limb. The photometry models have an additional use regarding the polarization data. The data in the polarization mode use an aperture nominally 256 times larger in area and a different effective integration time per pixel than the imaging-mode data, and data in the two modes generally are not available at exactly the same phase. The data in the polarimetry mode can be calibrated in terms of intensity level by comparisons with models which fit the imagingmode data. Comparison with the STrz models of Table III of Paper I yields values for F0 in the polarimetry mode on Pioneer I 1 at gain step 2 of F0(red) = 1400 and F0(blue) = 1360. The uncertainties in these values are about 6.5% in the blue and 5.0% in the red primarily due to the uncertainties in the reference ground-based photometry. Examination of the Pioneer I0 polarization-mode data in blue light indicates that these data obtained at gain step 0 must be multiplied by 3.09 to put them on the same scale as the Pioneer 11 polarization-mode observations. An additional uncertainty is present in the intensity scales of Pioneer 10 polarization maps 02, 03, and 04 because these data were obtained while the Pioneer 10 instrument sensitivity was decreasing with time due to exposure to the large energetic particle flux, and calibration lamp data were not obtained at sufficient time resolution to follow the decrease at these times (see Paper I). IV. OVERVIEWOF POLARIMETRY COMPARED TO A REFLECTING-LAYER MODEL
A. Comparison o f the STrZ and SEBn A simple model with few free parameters has great virtue as a general introduction to a complex subject. For this reason, we begin the analysis of the Jupiter polarimetry
51
with the analysis of a single high-quality polarization map at a phase angle of 98° using a simple reflecting-layer (RL) model. The model consists of a polarizing Rayleighscattering layer--not necessarily pure gas--above a depolarizing Lambert surface. The free parameters are the optical thickness and single-scattering albedo of the Rayleigh layer and the reflectivity of the " c l o u d " surface. While it is known from the outset that the model does not match the photometry at all phase angles, it does fairly well at a single phase angle. Other phase angles would need different effective cloud reflectivities to reproduce the effect of the actual cloud phase function. In addition, while such a model is known to fail in reproducing ground-based observations of the center-to-limb variations (CTLV) in the intensity in molecular absorption bands, the intensity of light emerging from the atmosphere at small phase depends on scattering properties at moderately large scattering optical depths (z - 10). The observed polarization at large phase, on the other hand, is formed essentially in single scattering and depends on the polarizing properties of the atmosphere above the level with optical depth -½. Unfortunately, because the gas layer above Jupiter's clouds is known to contain a thin haze, the gas optical depth in the RL model overestimates the actual pressure level at the cloud tops. Section V explores the question of the actual cloud heights with a model that explicitly includes the haze. Since the Rayleigh-scattering optical depth of the gas is much larger in blue light than red, the blue data are expected to be more sensitive to the location of the cloud top and will be discussed first. Figure 6a shows a small but definite increase in the polarization of belts compared to zones in blue light. This effect could be caused by two mechanisms. The higher belt polarization is due at least partially to the fact that the belts have a darker underlying cloud and so a smaller dilution of the polarized light scattered from the Rayleigh region by unpolarized light scattered from the de-
60
I
I
I
I//I
I
PHASE=36°
I
I//
I
I
PHASE=58*
I
PHASE=48* -
40
20 LATITUDES
T
1 I00
>l--
Z LtJ l-Z
l
I
60
~, 0.95 0.95
a ILl
-18"
I 140
TO
-'21 °
I 180
I// I 220 60
7"1
I
HAZE:
//
I I00 ROLL I
I
GAS :
"rM ~H 0,25 0 . 7 5 0 . 2 5 O,75
(~R 0.997 0.879
I 140
I z, 180 560
I
//
520
I
480
I
I
CLC~JOS:
TR 0.04 0.08
OJ¢ 0.997 0.997
gT fl 92 0 . 8 0 0.9~8 - 0 . 7 0 RZ 3
F, 62.7 62.5
- -
40
-
20
I I
I
60
I k . ,,,
I00
I
140
I
J//
I100
I000
SO0
I
,,~
600
I
300
I
400
500
ROLL
b
~
30
I
I
I
I //I
PHASE=38*
I
I
I ~tl
I
I
520
480
~ASE=48
*
20 l
I0
~M = 0 . 9 9 5 T H = 0 125 gH = 0 7 5
__
>... I.-
I I00
Z
wR : 0 . 9 8 9 l"q = O. 16 Fo = 4 7 . 2
1
I
140
180
we gl fl gz
= 0.99,5 = 0 80 = 0969 = -0.80
I/,,
I
220 60
I-7,'
I
laJ
3
rn
I
!;"
I
I "~''
I
I
I00 ROLL
140
I
I
I
I,/I
180 560
/11
I
I
LATITUDES-18°T0-21 ° _
30
•
~".----~,~
.
I0
PHASE=50 ° k P H A S E = 6 0 ~ I
I
I\.
I
60
I00
140"
I100
PHASE= 67 ° "4 ./
I
100"6 500 ROLL
I
600
PHASE=80°'~ /.,1
500
I
!_
400
500
"
FIG. 8. (a) Pioneer l I photometry of the South Tropical Zone at 7 phase angles in red light as marked. The bright limb is toward the left and the terminator is on the right side in each panel. The model shown by the solid line uses a double Henyey-Greenstein phase function with the indicated parameters (taken from Paper I). The cloud particle phase function for the model shown by the dashed lines uses a similar phase function except for a local bump between scattering angles of 120° and 140° shown in Fig. 10 as "RZ3." (b) Same as (a) but in blue light and showing only the double HenyeyGreenstein phase function taken from Paper I with the indicated parameters. (c) Same as (b) but for the SEBn in red light. (d) Same as (b) but for the SEBn in blue light. 52
JOVIAN PHOTOMETRY AND POLARIMETRY 60
I
I
I
I
I
PHASE=36 °
I
I
I
53 I
PHASE=38 °
.
I
PHASE=48 =
40
20 --I" LATI'~UDES-~0
T
60
I O0
TO-8"
140
;
i
180
20
>v-
I
z w
z ,.-.,
I//
HAZE: "rH gH 60 -•. 0.7'5 0.95 0.25
I
I
/t
GAS: °JR TR 0.53 0.04
I 60 ROLL I
I
I
I O0
140
I
CLOUDS: toe gl 0.991 0.80
I
II
fl g2 0.938-0.65
540
500
I
I
F= 73.!-
--'I
n-" 4O
20
40
80
120
1200
I I00
400
500
600
300
400
500
ROLL
d
3O
I
I
I
I
// I
PHASE=36*
I
I
I//
I
PHASE=38 °
I
PHASE=48 °
20
l
IOi 0
I 60
LATITUDES--5* T O - - 8 * I I t i oo 140 180
z w i_z l I I LLJ ~_ TOP GAS : Z) wR "rR -.I 30 0.90 0102
,;,I
20
// t HAZE : WN rH
I // GAS : ~R TR
0197 0 I~ 5
0193
0ll6
I 60 ROLL
I i oo
I CLOUD : ~C gl
I ,,/ I 140 540
I
0.97
0.80
I f=
//I 9Z
01979 --0.75
FO 526
I 500
I - -
20
I0 17/ 60
I O0
140
I I O0
1000
PH/SE=67°I 500
ROLL FIG. 8---Continued.
600
// 1 300
I 400
54
SMITH AND TOMASKO ,<---PHASE ANGLE a
140 I00 TIT . .
T >l-_z
2.C
60 .
.
20 IT't
+I
WATER DROPLETS
ICE PLATES
STrZ RED
g, =0.80 f =0.938
60 90 120 150 30
610 910 1210 1510 "310 610 910 120 150 180
SCATTERING ANGLE ( ° ) ~
F16.9. (left) Solid curve: the double Henyey-Greenstein phase function from Paper I for the STrZ in red light on a linear scale. Dashed line: the bump introduced for the model shown by the dashed line in Fig. 8a. The Pioneer 10 data used to derive the solid curve were obtained at the phase angles marked by arrows at the top of the figure and by vertical lines on the curve. The locations of the Pioneer 11 data are marked at the bottom of the figure. Phase functions for ice plates and water droplets as measured in one polarization state by Liou et al. (1976) are also shown. Note the similarity between the HenyeyGreenstein function and the curve for "ice plates." *---PHASE ANGLE a 180
polarizing base cloud. Additionally, the polarization in the belt may be changed by a different effective thickness of the polarizing region above the belt clouds. We will apply the reflecting-layer model to estimate the change in cloud heights necessary to explain the observed polarization differences between the zone and belt. Starting with the STrZ and the singlescattering albedo of the overlying medium (primarily Rayleigh-scattering gas) set to 1.00, it is possible to find values of cloud reflectivity and optical thickness of the overlying Rayleigh-scattering medium (0.762 and 0.11, respectively) that match the brightness and positive polarization observed at the center of the disk. It happens that the observed increase in polarization toward the limb and teminator is closely fit also, as shown by the short-dash curve in Fig. ll. This gives some confidence in the simple model since no adjustments were made to force this agreement. The addition of a modest amount of absorption in the gas above the cloud (e.g., reducing the singlescattering albedo from 1.00 to 0.90) makes
Ill
140
I00
60
20
TlI . . . .
TIlT
2.0
g,: 0.80 T
1.0
o_ 0.0
RZ3
-I.0
RZ2~\ O- = J.28
-2.0
30
6'0
/
/ \
90
/
120
150
180
SCATTERING ANGLE ( ° ) - ~
FIG. 10. Phase functions (on a log scale) used in models of the Pioneer i 1 photometry of the STrZ in red light (at the scattering angles marked by arrows along the bottom of the figure) together with the standard deviations of the fits. The phase functions containing the modifications labeled RZ1 and RZ2 fit about as well as the standard Henyey-Greenstein function alone, while the modification which includes a bump similar to a rainbow for spherical particles (labeled RZ3) fits somewhat worse. The RZ3 fit to the data is shown in Fig. 8a.
JOVIAN PHOTOMETRY AND POLARIMETRY 60
/ /
/
/
,/ /
40
\
/
i./. SEBn
..~ -
-STrZ
~-ec (u
-a._.,Ik ....
.
.
.
.
. . . .
• ....
"'-"
3;o . . . .
. . . .
4;o . . . .
Spacecraft Roll N u m b e r ~
FIG. l 1. Observed degree of linear polarization in map A2 at a phase angle of 98° in blue light. The triangles are the observed points for the latitude of the STrZ and the circles are for the SEBn. The bright limb is on the left side and the terminator is toward the right. The short-dash curve is for a model consisting of an optical depth of 0.11 of conservative Rayleigh scatterers above a Lambert surface of reflectivity 0.762 computed at the scattering geometries of the STrZ. The solid curve shows the effect of changing only the scattering geometries in the model to those appropriate for the SEBn data points. The dot-dash curve shows the effect of also changing the reflectivity of the Lambert surface to reproduce the observed brightness of the SEBn. The polarization that would be observed from such a model if the Lambert surface were placed at a pressure level of 2 bars in the belt is shown by the long-dash curve.
55
particles compensates for the different amounts of gas above the clouds. This seems unlikely. At this point it is interesting to consider the polarization which the model would predict if the ammonia cloud were absent over the belt so that the cloud top occurred at a pressure level as great as 2 bars. This possibility has been suggested by Owen and Terrile (1981) among others based on the high brightness temperature of the belts as seen as 5 /zm in the infrared. The upper curve in Fig. 11 shows that nearly 30% positive polarization results from 2 bars of gas for blue light (corresponding to a Rayleigh optical depth of -½). Under this assumption, any of the so-called "hot spots" seen in the infrared should also show up as strong polarization features in the equatorial regions. None have been observed. This implies that the upper (ammonia) cloud layer exists at nearly the same pres-
PRESSURE (rnb)
0
,
15
200 ,
,
400 600 REFLIECTIVITY'0.51,~/70.55'
_
a negligible difference for such a thin gas layer. The next step is to repeat the procedure for the SEBn. The solid curve in Fig. I1 shows the result of changing only the scattering geometries and leaving the gas layer thickness and the albedo of the underlying cloud the same as for the STrZ. The dotdash curve shows the effect of lowering the cloud reflectivity to 0.55 to fit the measured belt intensities. No changes are necessary to the cloud heights in order to obtain a good fit. The relationship between the optical thickness of the overlying Rayleigh layer and the polarization of the belt and zone at the center of the disk is shown in Fig. 12. The clouds in the two regions could be at appreciably different levels only if the intrinsic polarization produced by the cloud
SEBn
_/.~).x,~ _
_
800
/0,;,,
--/~jo.az
,////__ ~,~:f_,~.
-
2 ~ 5 ./
0
r
i 0.05
STrZ
i o.lo BLUE
OPTICAL
i 0.15
0.20
DEPTH
FIG. 12. The polarization at the center of the disk in the STrZ and the SEBn in blue light as a function of the optical thickness of a conservative Rayleigh-scattering medium above a Lambert surface of various reflectivities as labeled (98° phase). If the Rayleigh-scattering medium is assumed to be pure gas, the total pressure at the Lambert surface is indicated along the top of the figure. The observed polarizations at the center of the disk in these two regions are indicated by the horizontal lines. Notice that the different polarizations observed for the two regions occur for nearly the same amount of gas above the STrZ and SEBn clouds when the different reflectivity of the clouds in these regions is taken into account.
SMITH AND TOMASKO
56
SPACECRAFT ROLL
FIG. 13. Similar to Fig. 11 but in red light. The models indicated by the solid curves are for the indicated optical depths of conservative Rayleigh scatterers above Lambert clouds with the labeled reflectivities. Note the need for a progressively greater optical depth of the positively polarizing medium to reproduce the observations as the limb and terminator are approached.
sure level throughout the equatorial and temperate regions, but that it nevertheless can have a high diffuse transmission at 5 pm. This conciusion will be discussed further in Section VI. By applying the same technique to the analysis of the red observations, it is possible to compare the ratio of optical thicknesses computed at the two wavelengths to that for a pure Rayleigh-scattering gas. The comparison will be significantly different from the pure gas case if haze aerosols are important. Actually, we would predict that haze aerosols should be relatively important in red light since they are thought to have optical depths (scaled for isotropic scattering) of several hundredths (see Paper I), comparable to the Rayleigh-scattering optical depth of the gas above the clouds in red light. Starting again with the STrZ and setting the cloud reflectivity to 0.71 to match the intensity, the optical depth of polarizing material necessary to match the polarization at the center of the
scan is 0.02. However, as is seen in Fig 13, the center-to-limb variation is incorrect. Because of the extremely small optical .depths of the polarizing layer, the scattering model is now very sensitive to slight polarizing effects of the base cloud layer. It may well be that there is a small negative polarization produced in the base cloud which would require a thicker Rayleigh layer and, consequently, produce a larger increase in polarization from the center of the planet toward the limbs. An indication of the thickness of the Rayleigh layer above the cloud top comes from the optical depth necessary to fit the polarization at the limb. This is seen to be on the order of 0.04. The SEBn is similar: the polarization is slightly higher and the reflectivity is a little less (0.64) such that the same optical thickness is required. There is some evidence that the cloud polarization needs to be slightly negative in the belt also to match the center-tolimb variations. Again an optical depth of 0.04 is needed to match the large limb polarizations. The red data suggest that two types of polarizers are necessary: (a) an optical depth of about 0.04 of Rayleigh-scattering material above the base cloud to produce the large increase in polarization at the limb and terminator; (b) a slightly negatively polarizing base cloud to reduce the polarization at the disk center to the observed value and to shape the center-to-limb variation properly. From the thickness of the top layer in red and blue a rough estimate of the optical thicknesses of haze and gas in this region can be made. The ratio of gas optical depths is known from Rayleigh theory; therefore,
= (2)4 = cC?J4
= 4.48
where b and r signify blue and red. The haze particles are known to be strongly forward scattering (Paper I). If we assume that
JOVIAN PHOTOMETRY AND POLARIMETRY 50 ~0
40
40
50
60
70
80
90
/x (b.)
.mr~"/i'/k A ,
30
~'~'xJ a.A
I 20
+~:
x/
-'~"
x-'¢
a-z'jr'~ /x,x' c~ I0 NORTH REDLX
,.,.,-"
50
/÷-+-+ p
xs
BLUE~/
g
RED ÷.+ | o~o
-
50
+/ S
p~t~"°" BLUE o.o~
~0
/?
50
/ /
.~0 to
SOUTH
-30
(0.1
+/+'÷ i4~+-+-+/
-40
l
-50
i
-60
-70
-dO
0 -90
LATITUDE
FIG. 14. T h e a v e r a g e p o l a r i z a t i o n in a 20 ° w i d e interval in l o n g i t u d e a s a f u n c t i o n o f l a t i t u d e in m a p A2 at a p h a s e a n g l e o f 98 ° in r e d a n d blue light as m a r k e d . (b) S a m e as (a) b u t for t h e n o r t h e r n h e m i s p h e r e in m a p B3 at a p h a s e a n g l e o f 82 °.
the haze particles are large enough to have about the same cross section in red and blue light, "/'haze = "J'haze r = T b aze,
then '/'haze =
1.3r[otal-
0.3"rbotal •
Substituting the total optical depths found above we find the haze to be equivalent in terms of polarization to an optical depth of 0.02 of Rayleigh-scattering gas. The actual optical depth of the haze can be estimated by dividing by 1 - g, where g is the asymmetry parameter found to be about 0.75 in Paper I. Therefore, the haze optical depth is estimated to be about 0.08 or a little greater if the haze particles produce singlescattering polarizations that are somewhat less than occur in Rayleigh scattering. The optical depth of the gas above the cloud in the blue is 0.11 - 0.02 = 0.09 which corresponds to a pressure at the cloud tops of 360 mb. Because of the number of assumptions made to obtain this value, we expect a more meaningful pressure to come from the more detailed models in the next section.
57
Even so, based on a simple reflectinglayer model applied to both a belt and zone in the red and blue we can draw several preliminary conclusions. The belt and zone cloud tops are at nearly the same pressure on the order of 360 mb. They both have an optical depth of about 0.1 of strongly polarizing haze mixed into the clear gas. And finally, on the basis of the center-to-limb variations the particles in the base cloud are seen to produce slightly negative polarization in red light and are fairly neutral in the blue. The increased polarization of a few percent observed in the belt relative to the zone in the blue can be entirely accounted for by the increased absorption in the base cloud which reduces its depolarizing influence. In no circumstances can the belt cloud top be as deep as 2 bars.
B. The Polar Regions The remarkably high polarizations observed in the polar regions can also be compared with the reflecting-layer model. Table IVC and Fig. 14a show the averaged polarizations and scattering geometries in 2 × 20° latitude-longitude bins for a north-south scan from latitude 40°S to the south pole in map A2 at a phase angle of 98 °. If the planet behaves as a Lambert surface, the range of reflectivities in this scan is fairly narrow, varying only from 0.6 to 0.7 in either color. In these preliminary models we assume that the reflectivity of the base cloud can be approximated as a Lambert surface of reflectivity 0.63 in the blue and 0.67 in the red (the average values in each color) independent of latitude. The larger polarizations in the polar regions will require thicker polarizing layers above the base cloud than the equatorial regions, and therefore the singlescattering albedo of any gas-aerosol mixture above the Lambert surface will be more important. In order that the intensities continue to fit the observations independent of the choice of optical depth of the polarizing layer, the single-scattering albedo of this region is chosen to give the observed brightness in the semi-infinite
SMITH AND TOMASKO
58
1 O,g E x
B D
008
5
006
_
./
O.l-
2
\x,
J ‘%
:
. 0°4. 002.-0
POLAR CAP+
i .
UV DARKENING i &j,..:.:: :.'r
MAGN%
POLE
LAMBERT SURFACE 0 01 -40
-50
-60
-70
-80
-90
LATITUDE
FIG. 15. The optical thickness of a Rayleigh-polarizing layer above a Lambert cloud necessary to fit the data in Fig. 14a as a function of latitude in blue or red light as marked. The latitudes of the onset of polar darkening in the ultraviolet and the bright polar hood in the strong near-infrared methane bands as well as the latitude of Jupiter’s magnetic pole are indicated for reference.
limit. This means that whether the upper layer is thin, so that the Lambert surface dominates, or thick enough to reflect the majority of the light, the calculated intensity is essentially unchanged. We use values in the blue and red of 0.964 and 0.983 for the single-scattering albedos of the upper layer. By calculating a series of models with the optical thickness of the upper layer as the remaining free parameter, it is possible to assign an optical depth to each latitude bin such that the observed polarization at that latitude is reproduced by the model. The plot of optical thickness of the Rayleigh region in each color as a function of latitude for the south polar region is shown in Fig. 15. Because the optical thicknesses shown in Fig. 15 are the equivalent Rayleigh-scattering optical depths of haze plus gas in each color, the interpretation of the figure is somewhat complex, and more detailed analyses are required to extract separate constraints on haze thickness and polariz-
ing properties as a function of latitude in each color. Nevertheless, because the haze aerosols are known to be highly polarizing at low latitudes from the increase in polarization toward the limb and terminator in red light, the large increases in polarization toward the poles shown in Fig. 15 for red light can only result from a greater optical thickness of the haze aerosols at high latitude. The figure shows the required red optical thickness of the haze reaching a value as large as 0.5 by 75”s latitude. A haze this thick produces about as much polarization as can be obtained from highly polarizing particles even if they have an arbitrarily large optical depth. The decrease in polarization toward still higher latitudes could be due to an increase in particle size rather than a true decrease in haze thickness. The Rayleigh-equivalent thickness of the aerosols in blue light must be estimated by subtracting the Rayleigh optical depth of the gas above the clouds from the values given in Fig. 15. Because the planet has been observed to become very dark in the ultraviolet for latitudes nearer to the pole than 48”s (West et al., 1981), it is natural to associate the increased polarization at high latitudes with an increased thickness of polarizing aerosols rather than an increased pressure level for the cloud top. (Note that the Rayleigh-equivalent optical depth of 0.5 in red light would require the atmosphere to be clear to a pressure level greater than 9 bars in the polar regions-a situation precluded by the observations of low albedo in the ultraviolet and high albedo in strong methane bands near the poles.) If the cloud top is assumed to occur at the same level at high latitudes as in the STrZ and SEBn, we can subtract about 0.1 from the blue optical depth values of Fig. 15 to estimate the Rayleigh-equivalent optical depth of the aerosols in blue light. Even after this correction, this Rayleigh-equivalent optical thickness of the aerosols remains larger in blue light than red light at latitudes between about 50”s and 65”s while the opposite is true at higher latitudes. This could be due to a
JOVIAN PHOTOMETRY AND POLARIMETRY gradual increase in the size of the aerosols with increasing latitude. The aerosols could be sufficiently small to be highly polarizing in both colors at latitudes less than 65°S or 70°S. The cross section in blue light of these aerosols would be somewhat greater than in red light, and the equivalent thickness in Fig. 15 would be greater in blue than in red. At higher latitudes, however, the particles could be slightly larger, and the single-scattering polarizing properties of the particles would begin to decrease in blue light before they decreased in red light due to the larger size parameter in the blue relative to the red. The optical depth of the aerosols reaches a Rayleigh-equivalent value of about 0.1 by a latitude of 50°S. This corresponds to a value of 0.5 for the optical depth for forward-scattering particles with an asymmetry parameter of 0.75, and along the slant path seen from the Earth, the scattering optical depth in the blue would be about 0.7. Any appreciable component for the imaginary index could serve to significantly darken the planet in the ultraviolet at latitudes greater than 50° as is observed. The aerosols are seen to produce bright polar hoods in strong methane absorption bands at latitudes greater than about 70° (West, 1979a; West and Tomasko, 1980). Part of the reason for the brightness in the polar hoods is the rise in the level of the aerosols to pressures of a few tens of millibars compared to pressure levels of roughly 100 mb at low latitudes. However, it is also necessary for the aerosols to have a significant optical depth to reflect the observed intensity in these bands. The red Rayleighequivalent optical depths are given at about 0.3 and 0.5 at latitudes of 60°S and 70°S, respectively, in Fig. 15. As seen from the Earth, the slant-scattering optical depths (presumably almost entirely due to aerosols rather than gas) at these latitudes correspond to 0.6 and 1.4, enough to brighten the planet appreciably in strong absorption bands. Further, if the asymmetry parameter is still as large as 0.75 for the haze aero-
59
sols at these latitudes, these optical depth estimates could be four times larger, easily giving the observed brightening. Because the onset of the polar hoods in the methane band data depends on both the pressure level of the haze and its thickness, a detailed estimate for the latitude of this transition from the simple model shown in Fig. 15 is not possible. Nevertheless, the observed polar hood structure seems qualitatively consistent with the simple model of the polarimetry at high latitudes given in Fig. 15. Finally, Jupiter's magnetic pole is found at a latitude of about 80°, about the latitude at which the equivalent optical thickness of the aerosols reaches a maximum. It has been suggested in the past that the aerosols which make the planet dark in the ultraviolet might be associated with energetic particle impact, and such an association could be related to the correlation between the magnetic pole and the location of maximum aerosol polarization seen in the Pioneer data. V. POLARIZATION MODELS WHICH I N C L U D E A HAZE LAYER
A. Analysis o f the STrZ For a number of reasons, it makes sense to begin a more detailed analysis of Jupiter's cloud and haze layers with a consideration of the South Tropical Zone. This zone is a broad, well-defined feature that has been observed for many years (Peek, 1958). It appears relatively unchanged between the times of the Pioneer 10 and 11 encounters and is well resolved on five separate polarization maps spanning phase angles from 43 ° to 117°. Aside from the nearby Red Spot, the zone is essentially free of smallscale features at the resolution of the Pioneer IPP. The Voyager high-resolution images (Smith et al., 1979) do show some small-scale structure in the zone, but the contrast of these features is quite low and the zone is the most nearly horizontally homogeneous region on the planet. Paper I presented a horizontally homogeneous cloud model derived from Pioneer 10
60
SMITH AND TOMASKO
high-resolution (0.5 x 0.5 mrad) photome- ization rises steeply toward the limb and try. While this analysis yielded constraints terminator, we know that the haze particles on the shape of the single-scattering phase must be highly polarizing. We parameterize function, little information was obtained on their polarizing properties by a constant the vertical distribution of the clouds be- times the single-scattering polarization procause the data refer to continuum spectral duced by Rayleigh scattering. regions. One exception was the requireThe polarizing properties of the base ment that a bright, forward-scattering aero- cloud in the model must also be considered. sol haze exists relatively high in the atmo- We expect that there will be some compensphere. The optical thickness of the haze sation between the polarization of the base was estimated to be on the order of a few cloud and the gas above in the sense that it tenths at pressure levels of about 100 mb or may not be possible to uniquely determine less. Other studies, such as observations in either quantity from the polarization obserthe ultraviolet by Voyager (West et al., vations alone. If the cloud is assumed to 1981), confirm the existence of this haze at have its top at a pressure level of some 500about the pressure levels estimated in Pa- 600 mb, the cloud particles are required to produce strong negative polarization to per I. As outlined in the Introduction, several compensate (Stoll, 1980). Recent measurecloud layers are predicted beneath the level ments of the single-scattering polarizing of the haze. An ammonia ice crystal cloud properties of ammonia ice crystals grown in is expected to form with its base near a a laboratory cloud chamber show quite pressure level of about 600 mb. Estimates modest polarizations of less than -10% for the optical thickness of this cloud range (Holmes, 1981; Stahl and Tomasko, 1984). from 2 (West, 1979b) to more than 10 (Sato We prefer to begin by assuming that the and Hansen, 1979). Other cloud layers exist ammonia cloud is unpolarizing, and solve at still deeper levels, but because the polar- for the pressure level of the cloud top. If ization at large phase angles results essen- this level seems unreasonable in light of the tially from single scattering, the thickness many other studies of Jupiter's cloud, we of the ammonia cloud is sufficiently large to can introduce small amounts of polarization prevent the deeper levels from influencing up to the amount measured in the existing laboratory measurements. We would prefer the observed polarization. In this section we consider models for the to avoid introducing clouds which have poPioneer polarimetry which are slightly larizing properties many times those meamore complex than the very simple model sured in the laboratory. The most severe discussed in the last section. We consider a test of the assumption of an unpolarizing model with four layers: clean Rayleigh- base cloud will be in the red models where scattering gas down to a pressure of Ph; a the optical depth of the gas is nearly negligiphysically thin haze layer of optical thick- b l e - i f the base cloud makes a significant ness ~'h, single-scattering albedo 05h, and a contribution to the total polarization, then phase function taken from paper I; another there may be insufficient leverage for adlayer of Rayleigh-scattering gas down to the justments in the thin layer of gas and haze cloud top at a pressure of Pci; and a semi- above to match the observations. The infinite cloud with a phase function as given models consisting of gas over a Lambert in Paper I. In addition to the two pressure surface described in the last section suggest levels and the optical thickness of the haze, that the base cloud polarizations are reathe single-scattering polarizing properties sonably small and perhaps slightly negaof the haze and the cloud both need to be tive. The upper haze layer is thought to be specified as functions of scattering angle. composed of hydrocarbons which result Because we know that the observed polar-
JOVIAN PHOTOMETRY AND POLARIMETRY from photochemical reactions involving methane. The exact composition of these aerosols and their polarizing properties are presently unknown, although if they are similar to the aerosols on Titan (see Tomasko and Smith, 1982) they may be quite strongly polarizing. For Jupiter, there will be a trade-off between the polarizing properties of the haze and the optical thickness of the haze layer. The model polarizations could be increased either by increasing the single-scattering polarization produced by the haze particles or by increasing the optical thickness of the haze layer. Based on experience with Mie scattering and scattering by prolate spheroids, the particle cross sections and therefore the optical thickness of the haze layer will be one to four times larger in the blue than the red passband and the polarization can be expected to be larger in red than blue light. With this introduction, we can begin to fit polarization models to the blue observations using three independent variables: the pressure level of the thin haze, the pressure level of the cloud top, and some, as yet, undetermined combination of optical depth and polarization in the haze. At the onset the base cloud is assumed to be completely depolarizing. To define these variables we will make use of three categories of observation: the central polarization of the 43 ° phase observation (map 01) which may be expected to be sensitive to the total gas abundance above the cloud; the central polarization of the 117° phase observation (map AI) which is likely to be most sensitive to the haze properties; and, finally, the center-to-limb variation of all the observations which will depend on the pressure level of the haze. Let us illustrate these three steps in greater detail starting with the pressure level of the cloud. The basic model is the best fit for the zone in the blue from Table III in Paper I which includes no polarization in either the haze or the cloud. The models will use the optical depths of the gas as free parameters, but it is a simple procedure to convert to pressure once the
61
composition of the gas layer is specified. With a basic composition of 90% H2 and 10% He and an effective acceleration of gravity of 2400 cm/sec z we adopt a Rayleigh-scattering optical depth of 0.025 in the blue (0.44 ~m) and 0.0054 in red (0.64 ~m) per 100 mb of gas. The layer doubling and adding technique is used to evaluate the intensity and polarization of light scattered at the locations given in Table IV (cf. Tomasko and Doose, 1984). Figure 16 compares the best model of Paper I with the polarization data for the STrZ in blue light. The base model, Pd = 680 mb, gives too much polarization. Following the procedure outlined above, the total pressure of gas above the cloud is reduced until the central polarization at 43 ° phase is matched. Judging from the figure this will 301
I
,
,
,', ,
OI
MAP:
, ~ . . rl : ° 01
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201
:: ;"~'~
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.'';
~1 = 0.995
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~
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,
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zoo
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,
, : :
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~oo . . .400 . . . . . 44060o
ROLL------
ROLL-~,,-
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6~o
IROLL-~,"
720
FIG. 16. Points: observations of the linear polarization of the STrZ of Jupiter in blue light at the phase angles of the indicated maps. The bright limb is on the left and the terminator is toward the right in each panel. The curves are model calculations for the structure s h o w n which includes a nonpolarizing base cloud having a double H e n y e y - G r e e n s t e i n phase function taken from Paper I above which is a physically thin layer of haze particles embedded in a region of conservative Rayleigh-scattering gas. The haze particles have a single H e n y e y - G r e e n s t e i n phase function with g = 0.75. In this figure the haze particles are taken to be nonpolarizing and the pressure level of the base cloud is varied. Values of the other model parameters are given in Table V.
62
SMITH AND TOMASKO J
MAP:
01
A3 rl=o.oI TH=0.125
r~=o.o7 Poq~=o:% - - - - 0.50
POL=O
ic
0.75 - - - - -
STrZ
g 260
I00 N
3c
i
vv f
l~
A2
.:
% 2c "
26o
ROLL'----~
J
y/
ic
300 . . . . . ioo
ROLL---~ l
i
02
i
A1 ./
S
2"2"___-2;--
c
360
46o 500'~ 400 ' 440" 600 ' ROLL---~ ROLL-----
r~o
6~0
720
ROLL--,,-
FIG. 17. The same as Fig. 16 but with the pressure levels of the haze and base cloud fixed and the polarizing properties of the haze particles taken as various fractions (shown) times the polarization produced in single Rayleigh scattering.
occur for total gas optical depth (7"1 + 7"2) of about 0.08, or P = 320 mb. Notice that the larger phase angle observations are very sensitive to this value and all require additional positive polarization from the haze. Fixing the cloud pressure at 320 mb, the haze is made to be positively polarizing as seen in Fig. 17. Since we do not know the variation of single-scattering polarization with scattering angle, the Rayleigh shape has been used throughout this section times a constant Polh which must be in the range - 1 -< Polh --< + 1. There are not enough constraints in the observations to solve for the exact shape of the polarization function. The polarization of the haze has little effect on the 43 ° phase scan justifying the choice of independent parameters. Four different haze layers are shown in the figure each with an optical depth of 0.125 but with varying degrees of positive polarization. The optimum choice at the large phase angles seems to be a little greater than 0.5 times Rayleigh. A choice of Polh = 0.6 fits the central polarizations of the five data sets remark-
ably well considering that only two parameters have been varied. Our final independent parameter, the pressure level of the haze, can now be adjusted without disturbing the fits at the disk centers. Figure 18 shows how the center-to-limb profiles change as the haze layer descends toward the main cloud. We estimate that an optical depth of 0.03 above the haze gives the best fit to all the data sets and corresponds to Ph = 120 mb, in reasonable agreement with the uv data. An important test of this model is whether it can simultaneously fit the red polarization data. There are three maps in the red and only one degree of freedom left in the model to fit the data, the ability of the haze to polarize red light. Since an increase in either the haze polarization or optical depth of the haze can cause a larger polarization in the reflected light, either one or both can be varied to fit the red data. The large haze polarization in the blue leads us to believe, based on experience with Mie calculations, that it is likely to be even larger in the red so we set Polh = 0.9 and use the optical depth as the only adjustable parameter. Figure 19a reveals that the fit is
i
30
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I
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20
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,;: .~.
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IdO
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ROLL---"
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. ~
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ROLL---~
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FIG. 18. The same as Fig. 17 but with the polarizing properties of the haze particles fixed and the pressure level of the haze varied as shown.
JOVIAN PHOTOMETRY AND POLARIMETRY 30
I
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i
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/~
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~,=o,9",
IC
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- - ",1=0.0067 P = 120 m ~ P O L H = O . 9 0 X RAYLEIGH TH~ 0.O312 . . . . . . T2=O.Oll 0.0625 P" 320 mb ~ O, 125 ~ - - - -
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,~o
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- 7"1=0.0067 P= 120 mb ~ l I l ~ "~uov.=0.0625 "FOLH= 0.90 X RAYLEIGH
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FIG. 19. (a) Similar to Fig. 18 but in red light. The models have the pressure levels of the haze and cloud fixed at the levels determined from the blue polarimetry (the long-dash line in Fig. 18), but with various optical thicknesses of the haze in red light. The haze is taken to polarize 90% as much as for Rayleigh scattering in each single scattering. (b) Same as (a) but for a base cloud which polarizes as -0.05 times that for Rayleigh scattering in each single scattering.
very good for a haze optical depth of 0.0625. There is agreement to within a percent of polarization everywhere; however, map A2 shows that the center-to-limb variation is not quite as large as observed. Because the total optical depth (gas plus haze) above the base cloud is only 0.08, the resultant polarization is very sensitive to small polarizations in this cloud layer. A slight negative polarization here, Pold = -0.05, can correct the center-to-limb variation (see Fig. 19b). In the reflecting-layer model of the previous section we came to the same conclusion based on an analysis of map A2 alone.
B. Analysis of the SEBn Now that we have a detailed model which satisfies all the Pioneer data for a zone, it is natural to ask what aspects of the model need to be changed for the model to fit the available belt data. It is clear that the single-scattering albedo of the base cloud needs to be decreased to match the ob-
served reflectivity (I/F) of the belt. The simple models of Section IV lead us to suspect that the pressure level of the cloud will remain similar to that of the zone, but what about the vertical location and characteristics of the haze? Following the same procedure used in the reflecting-layer model, the first step is to change only the scattering geometries to those of the SEBn. Figure 20 shows that the resulting polarizations are a few percent low at all phase angles. The next step is to simply decrease the single-scattering albedo of the cloud particles until the observed intensity is reached. Models with several different albedos are shown in the figure in order to illustrate the sensitivity to this parameter. The intensities are best matched for o3d = 0.98 which is already an acceptable fit to the data. The SEBn data are nearer the limb than those for the STrZ and suffer more from foreshortening and contamination by neighboring features. Also, the higher resolution photometry maps taken at nearly the
64
SMITH AND TOMASKO 30
[
i /.'1 MAP:
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FIG. 20. Similar to Fig. 16 but for the latitude of the SEBn. The models u s e the same single-scattering properties as for the STrZ except for the different values of the single-scattering albedo of the base cloud as shown.
same time give evidence for features within the latitude band of the belt while the zone is very uniform. For these reasons, the uncertainties in the SEBn data are on the order of 1-2% in the polarization, a few times larger than the corresponding uncertainties in the zone data. The STrZ model corrected for the proper belt albedo gives a particularly close fit to the map 01 data at 43 ° phase. This is the phase angle least sensitive to the thin haze. Figure 21 illustrates the sensitivity of the belt model to large changes in the haze optical thickness, particularly in map A1 at the largest phase angle. The best fit appears to be for Zh about 0.06 somewhat less than in the STrZ. Note that the exact center-tolimb profile is not matched for map A2. We believe that this is due to a local feature such as a slightly different cloud albedo or a local variation of the haze layer at this Iongitude in the SEBn. Overall, the zone model apparently will be quite acceptable in the belt with only the required change in cloud albedo (that is, a compositional change) and, perhaps, a thinning of the
haze layer. As a final check on the model, the fit to the red SEBn data is shown in Fig. 22. There is actually very little difference between the red polarization in the belts and zone, and what there is can be accounted for by the slight changes in red albedo between the two regions. The enhanced 5-/zm emission of belts relative to zones has been interpreted as arising from a cloud deck at a pressure level of 2 bars or more (Terrile and Westphal, 1977). This would suggest that the base cloud in our belt model may be optically fairly thin in the visible as well, with possibly a large fraction of the solar radiation penetrating to the lower cloud seen in the infrared. To constrain the properties of a two-cloud model with haze, we ran a series o f models with different values for the optical thickness of the upper cloud to see how thick this cloud needs to be to continue to mask the gas layer below it. The blue data from the 98 ° phase map were used because of their sensitivity to the optical thickness of the gas. The exact vertical structure and model results are shown in Fig. 23. Note that for optical depths of the upper cloud less than 1 in the blue the polarization rap30
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FIG. 21. Same as Fig. 20 but for various values of the optical thickness of the haze with the single-scattering albedo of the base cloud fixed at 0.98.
JOVIAN PHOTOMETRY
30
#
I
I "fl
I
MAP: A3
65
AND POLARIMETRY
I
I
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- I"I =0 0067 P= 120 mb ~=l=lElq =0.0625 HI~LH= 0.90 X RAYLEIGH P= 3;~0 m b ~ ~m~T2:0"OII P0L = -0.05
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FIG. 22. Same as Fig. 20 but in red light.
idly increases toward 30% while for optical depths greater than 3 an asymptote is reached such that the lower structure makes no contribution to the polarization. In the intermediate region between I and 3 optical depths there is a trade-off between cloud thickness and the polarizing properties of the clouds (the upper and lower clouds were assigned identical properties). Two curves are shown in the figure. The upper curve for depolarizing, or neutral,
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30
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--.~--TR:O0:
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clouds (as we have assumed throughout this paper so far) implies that the optical thickness of the upper cloud must be at least 3 if the clouds are neutral, while the lower curve shows that the upper cloud could have an optical thickness as low as 1.5 if the particles in the clouds produced -20% polarization in a single scattering through an angle of 90 °. This is felt to be a rather extreme adjustment to the cloud polarization. Finally, the parameters of the best-fitting polarization models are given in Table V. The phase functions of the base cloud and
R=0.0~
TABLE V
POLcl ; Oo~-020 x Roy.~-~-_~.).).~-)-~, POLcI: 0 ~\ ~/-POLcl = -0.20
"XX~
PARAMETERS OF BEST-FITTING POLARIZATION MODELS
~-
X Royleiqh
Blue
Red observed
j
"~ ~ ~ - ~ . . . . . . . . . . . . . . . . .
polorizoli0n
0 O0
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210
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FIG. 23. Computed polarization in blue light for the SEBn near the center of the disk in map A2 at a phase angle of 98° as a function of the optical thickness of the ammonia cloud in the belt. The structure is shown in the figure, and has a lower cloud at a pressure of 2 bars. The solid curve is for clouds that are nonpolarizing, with the dashed curve for clouds that produce - 2 0 % polarization in a single scattering at 90 ° scattering angle and have the same dependence on scattering angle as for Rayleigh scattering. Comparison with the observed polarization o f about 10% indicates that the ammonia cloud in the belt must have an optical thickness of 1.5 or more to mask the underlying gas for realistic single-scattering pobarizing properties.
STrZ
SEBn
STrZ
SEBn
Tga~ o3os
0.0067 1.00
0.0067 1.00
0.03 1.00
0.03 1.00
~'h O3h Polh gh
0.0625 0.95 0.90 0.75
0.0625 0.95 0.90 0.75
0.125 0.995 0.60 0.75
0.06 0.995 0.60 0.75
r~s OSga~
0.011 1.00
0.011 1.00
0.05 1.00
0.05 1.00
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0.80 0.938 -0.70 0.997 -0.05
0.80 0.938 -0.70 0.9925 -0.05
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0.80 0.969 -0.80 0.980 0.0
Tel
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66
SMITH AND TOMASKO
the haze used in the STrZ are taken from Paper I. Because of the greater evidence for horizontal inhomogeneities in the SEBn than in the STrZ, we have given relatively less attention to deriving details of the cloud structure in the belt compared to the zone. For example, we have used the same double Henyey-Greenstein phase function for the belt clouds as for the zone, instead of using the slightly different parameters for this region given in Paper I. While the belt models of Table V will fit detailed photometry data covering a wide range of phase angles somewhat less well as a result, the conclusions we obtained from the polarimetry would be unchanged if we had used the phase functions actually used in the belt photometry models. The pressure level of the haze has been set using only the polarimetry data, but the photometry data in Paper I require slightly different values for this parameter. These differences are discussed further in the next section; but, in general, the conclusions of Paper I are unchanged by the addition of the polarimetry. They are instead augmented by some constraints on the polarizing properties of the cloud and haze as well as new sensitivity to the abundances of gas above the cloud and haze. VI. DISCUSSION AND SUMMARY
One important objective of this work has been to present the polarization maps of Jupiter obtained by the Pioneer 10 and 11 missions. Detailed measurements of the polarization of the STrZ, the SEBn, and a north-south cut have been presented in the figures and in tables. In addition, we have compared the data for these regions to models and reach several specific conclusions regarding the vertical structure and optical properties of the clouds and aerosols present in these regions. Our conclusions can be grouped and summarized as follows. 1. Pressure Levels o f the Cloud Tops The polarization observations cover a
range of phase angles near 90° where the polarization produced by the gas is very much stronger than that produced by the cloud particles (nearly 100% compared to less than about 10% in a single scattering). Thus, an important feature of the polarimetry data set with high spatial resolution at large phase angles is its ability to discriminate between the effects of scattering by clouds and by gas. This is true at least to levels where the total optical depth reaches a value between ½and 1 where the polarization observed in the multiply scattered light saturates. Because we see no spots with polarization larger than 10-12% in blue light at latitudes less than 40°, we conclude that a cloud of optical depth greater than 1.5 must exist over both belts and zones at a level corresponding to a Rayleigh optical depth of 0.08 (a H2 abundance of 12 km-am equivalent to a pressure of 320 mb). The most recent papers which consider the ammonia cloud to be of finite vertical extent have a cloud extending from a base at about the 630-mb level to a top near 380 mb (Marten et al,, 1981), or possibly even higher (Orton et al., 1982; Sato and Hansen, 1979), in good agreement with this result, if our pressure level is taken as the cloud top. Several earlier papers have used methane band observations to determine the pressure level of the ammonia cloud; however, this level depends on the methane-to-hydrogen mixing ratio for which these authors adopted various values. Adopting a value of 2 x 10 -3, obtained from the Voyager IRIS experiment by Gautier et al. (1982) and accurate to about 10%, gives pressures of about 300 mb from the results of West (1979b) and Bergstralh (1973) and about 200 mb from Wallace and Smith (1977). Buriez and de Bergh (1980) used models of the shapes of the methane bands near I. 1/zm to derive a total pressure as well as a methane abundance (as did Wallace and Smith), and they give a pressure for the upper cloud (again a diffusing sheet) of 260 _ 80 mb in a
JOVIAN PHOTOMETRY AND POLARIMETRY two-cloud model. With the exception of the values determined by Wallace and Smith, these results are reasonably consistent with one another and also with our results. 2. Difference in Levels of Cloud Tops in Belts and Zones In both red and blue light near 90° phase, the polarization of sunlight scattered from belts and zones is very nearly equal with the small differences due primarily to the different reflectivities of the belt and zone clouds. This strongly implies that the cloud tops in both belt and zone regions are reached at essentially the same pressure level. No spots of high polarization analogous to the 5-/xm hot spots are seen in the polarization maps at a spatial resolution greater than that available in 5-/zm maps made from the Earth. The 5-/zm opacity above the region near 2 bars which produces the high 5-~m flux is undeniably less in the belts and hot spots than in the zones; however, significant cloud opacity in the visible (optical depth greater than 1.5) exists in all three features at the level of the upper ammonia cloud. A recent study of the IRIS spectra in the regions of 5 and 45 /.~m by Brzard et al. (1983) is of interest in this regard. These authors point out that the diffuse transmission of the ammonia cloud even in " c l o u d y " regions is as high as 0.70.8 near 5 ~m, and a further increase in this value for "clearer" regions cannot be responsible for enhanced 5-/zm emission. Instead, they require the presence of another cloud at a pressure level near 2 bars to modulate the 5-/zm emission. Because the 5-/zm emission is modulated by clouds at pressures of 2 bars or more, the comparison of 5-/zm maps of Jupiter with visible images of the planet is of limited use in assigning pressure levels for the tops of clouds of various colors seen in visible images, as has been attempted by Owen and Terrile (1981). It is incorrect to associate " b l u e " areas of the planet with Rayleigh scattering. Brzard et ai. cite an example in which a "tawny brown" cloud which
67
has been assigned a pressure level near 2.3 bars by Owen and Terrile produced less emission at 45 /zm than a nearby region which contained no brown cloud, implying that the brown cloud must have substantial opacity at pressure levels where the 45-~m radiation is emitted (less than 1.2 bars). Brzard et al. conclude that the visible appearance of the planet is determined by the colors of the clouds near the ammonia cloud level while the 5-/zm emission depends primarily on the opacity of a deeper cloud layer near 2 bars. 3. Single-Scattering Properties of Cloud Particles Instead of assuming that the top of the ammonia cloud occurred near a pressure level of 600 mb and attempting to find the single-scattering polarizing properties of the ammonia cloud particles as was done by Stoll (1980), we began by assuming that the polarization produced by the cloud particles was relatively small as measured for ammonia crystals and used the data to constrain the pressure level of the top of the cloud. We found that the cloud particles had to be only slightly negatively polarizing (about - 5 % near 90° scattering angle) and that the pressure derived for the clouds was consistent with a variety of other studies of Jupiter. More measurements of the polarizing properties of candidate cloud particles are underway, and should be quite useful for comparison with polarimetry models at a wide range of phase angles. Detailed comparisons of this sort are outside the scope of the present study, except to note that the polarizations of Jupiter's cloud particles need not be nearly so large as in some of the models discussed by Stoll. This work also briefly explored the effects of bumps in the single-scattering phase functions at scattering angles that might correspond to rainbow features from spherical particles. In general, models which contained such features fit the data somewhat worse than the smooth analytic phase functions of Paper I. Models in which
68
SMITH AND TOMASKO
the phase functions in the range of scattering angles from 80 ° to 140° were even flatter than the functions of Paper I fit about as well or marginally better. While the work of B r z a r d et al. (1983) shows that the opacity of the ammonia cloud is not responsible for the 5-~m hot spots, these authors do find evidence for a general correlation between the opacity of the ammonia cloud and the opacity of the deeper cloud which does modulate the 5/zm emission. Thus, while the visible polarimetry [and also other studies in reflected sunlight--see Sato and Hansen (1979) and West and Tomasko (1980)] shows cloud optical depths of at least 1.5 over Jupiter's belts at the level of the ammonia cloud, the diffuse transmission of these clouds near 5 /xm is apparently reasonably high, of the order of 0.7 or more. The known high transmission of the ammonia cloud near 5 ttm has sometimes been taken as implying that this cloud is absent over belts generally, and thus provides negligible optical depth in the visible belts. Furthermore, the lack of infrared spectral features of solid ammonia has been interpreted as evidence for a rather large size (a radius of 30/zm or more) for the particles in the ammonia cloud by Marten et al. (1981) using an analysis based on Mie scattering. The presence of such large particles in the ammonia cloud implies that its optical thickness cannot change very much between the visible and 5/~m. H o w e v e r , such large ammonia particles will be strongly forward scattering at 5/~m, and will have reasonably high single-scattering albedos at this wavelength as well (Orton et al., 1982). Thus the diffuse transmission of the ammonia cloud could be as large as required near 5/xm (about 0.7) and the ammonia cloud could still be moderately thick in the belts. Figure 24 shows the flux transmitted through a cloud of particles having a H e n y e y - G r e e n s t e i n phase function with an asymmetry parameter of 0.8 and various single-scattering albedos as a function of the optical thickness of the cloud. The intensity field incident on the
1.0
i
i
k I
~ 2
i
i
i
i
i
018~ 0.{ "~ 0.'~ 0.2 0.0~
L 0 ' 7 0 3 4 5 OpticoI Depth
h
~ 6
7
FIG. 24. The fractional flux transmission of forwardscattering clouds as a function of their optical depth for various single-scattering albedos. The single-scattering phase function of the cloud particles is taken to be a Henyey-Greenstein function with g = 0.8, and the radiation field incident on the bottom of the cloud is assumed to be isotropic. The transmission is 0.7 or greater for clouds of optical thickness between about 1 and 2.5 for single-scattering albedos greater than 0.9. Thus, belt regions could have ammonia clouds with optical depths as great as 1 or 2 at 5 ttm without violating the observations of the high 5-/zm flux in these regions.
bottom of the cloud is taken as isotropic. The figure indicates that the cloud can have an optical thickness of 1.5 or greater if the single-scattering albedo is 0.95 or larger. The cloud could be even thicker if the ratio of intensities in the upward direction instead of diffuse flux were considered. In any case, this thickness is comparable to the optical depth of the cloud required in the visible from the belt polarimetry, and a model having quite large particles could have fairly high transmission at 5/~m while being quite important at visible wavelengths in studies of reflected sunlight. In this case, the ammonia cloud in the belts would have an optical thickness in the visible as well as at 5/xm of only 2-3, similar to the value preferred by West in his analysis of methane bands. This relatively low value for the ammonia cloud thickness would imply that the lower cloud in the two-cloud models of Sato and Hansen (1979) is nearer to a pressure level of 2-3 bars than their nominal range of 3-5 bars. On the other hand, it has been pointed
JOVIAN PHOTOMETRY AND POLARIMETRY out that small nonspherical particles can have much smaller absorption than spherical particles of similar size (Orton et al., 1982), and it is not completely clear that the ammonia particles must have large size parameters at 5 /xm. If they are relatively small, they will behave as nearly isotropic scatterers at 5/xm, and then they must have an optical thickness of 0.5 or less to give a diffuse transmission as large as 0.7 at this wavelength. This implies a ratio of scattering cross sections greater than 3 between 0.64 and 5 /~m. The particles must have large size parameters in the red to produce the strong forward scattering observed from Jupiter at large phase angles. Adopting a scattering efficiency of 2 in the red implies that the scattering efficiency must be less than z (and the size parameter less than about 2) at 5/zm. This corresponds to a particle radius less than about 1.6 /zm. The Pioneer photometry (Paper I) does require that the particle radius be larger than about 0.3/zm to provide forward scattering. The Pioneer polarimetry cannot rule out particles in the size range from 0.3 to 1.6 /xm radius. In fact, particles of this size would be required if an analysis similar to that of Sato and Hansen (1979)--but for spatially resolved belts--were to strongly require a cloud of optical thickness greater than 2-3 in the visible. Thus, if the constraints on the size of the ammonia particles derived from the lack of features expected for solid ammonia in the infrared continue to imply particle sizes as large as 30/xm when nonspherical shapes are considered, the particles should be fairly forward scattering and have an optical depth of roughly 2 at 5/zm as well as in the visible. On the other hand, if the infrared features of solid ammonia are not present due to an effect which depends on the nonspherical particle shape, then the particles at pressures less than 600 mb would have "radii" from 0.3 to about 1.6 /xm and these belt clouds could have an optical thickness even greater than 3 in the visible and less than - 0 . 5 at 5/zm.
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69
,, SE6.OBSERVEO
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FIG. 25. L i m b darkening in the S E B n in blue light at 12° p h a s e from Pioneer 10 p h o t o m e t r y c o m p a r e d with the best polarization model s h o w n in Fig. 20 except that the u p p e r (ammonia) cloud is taken to have an optical depth of 3. T h e triangles are the observations, and the c u r v e s are models in which the absorbers are limited to the upper cloud, equally distributed between the u p p e r cloud and a lower cloud at 2 bars, or concentrated in the lower cloud with the u p p e r cloud having the s a m e albedo as in the bright STrZ.
In any case, the "ammonia" cloud isdefinitely present in Jupiter's belts, although perhaps at a somewhat reduced optical thickness than in the zones. If the belt cloud is assumed to be as thin as three optical depths, it is possible to use the limb darkening from the high-resolution photometry data at low phase angles in blue light to discriminate among the possible vertical locations for the belt absorber. Is the absorber responsible for the lower albedo of the belts found in either the upper cloud or the lower cloud alone? Figure 25 shows the limb darkening computed under each of these two extreme assumptions, as well as in the case where the single-scattering albedo is equal in the two clouds. The plot suggests that the required amount of absorption can barely be produced by making the lower cloud completely black when the upper cloud is made as bright as in the zones. Although this case more nearly reproduces the shape of the limb darkening than the case in which all the absorption is concentrated in the upper cloud and the lower cloud is conservative, the case in which the single-scattering albedos of the
70
SMITH AND TOMASKO
two clouds are equal in the best match to tenths--before a pressure level of about the observed limb darkening. Thus, the ab- 120 mb is reached--is consistent with all of sorber must be distributed over a significant these other observations. optical depth, and neither a bright layer over a thick dark layer nor the opposite ex- 5. Single-Scattering Properties of the Haze treme fits the data especially well. The measurements by Voyager at vari4. Pressure Level of the Haze ous phase angles in the ultraviolet could not The pressure level of the haze was stud- determine the scattering phase function of ied only in our more detailed models of the the haze due to the large optical depth for STrZ and the SEBn. We found the pressure Rayleigh scattering by the gas above. In Palevel of the haze to affect the center-to-limb per I we found that the haze must be relavariations in the polarization, with best tively forward scattering at both red and agreement for a haze at a pressure level of blue wavelengths. In this work we find that about 120 mb in both the belt and the zone. the haze must be highly polarizing above This value is in good agreement with the both belts and zones to produce the large analysis of ultraviolet photometry from increase in polarization from the center of Voyager by West et al. (1981) who require the disk toward the limb and terminator obthe absorption produced by the haze in the served at phase angles near 90°. Stoll (1980) ultraviolet to occur at pressure levels of found a similar result in his analysis of the about 100 mb or more. The preliminary SEBn data and tried to find a size of spherianalysis of photometry obtained by the IUE cal particles which would simultaneously satellite (with an absolute calibration inde- produce the required high single-scattering pendent of the one used by Voyager) by polarization and the strong forward scatterTomasko and Martinek (1978) placed the ing. He concluded that it was barely possihaze beneath 150 to 200 mb of gas, but more ble to find spherical particles that might be complete analysis of these data allow the able to satisfy both constraints if the phohaze to occur anywhere between about 80 tometry at the largest Pioneer 10 phase anand 200 mb (Martinek, private communica- gles were taken to be as dark as the error tion). In Paper I the brightness at large bars allow. Since the time of Stoll's analyphase indicated that the optical depth for sis, the Pioneer and Voyager observations Rayleigh scattering in blue light above the of Titan have become available. On Titan haze in the SEBn was 0.01 (corresponding the requirement that the aerosols be both to 40 mb), but this limit was uncertain by highly polarizing and forward scattering is about a factor of 2. It is not clear that hav- even more severe than on Jupiter. While ing a physically thin large layer deeper than irregularly shaped particles of the proper the 80-mb level would be formally permit- size, shape, and composition to match the ted by the Pioneer photometry data. How- Titan data remain to be found, particles ever, the haze is actually distributed over produced by similar photochemical prosome range of heights, with the photometry cesses could be responsible for the haze on at 150° phase most sensitive to the upper- Jupiter as well as on Titan. most part of the haze. In this regard we point out the eclipse observations of Smith 6. The Boundary between the Haze and the Upper Cloud Region (1980) and Smith et al. (1977) who found Paper I noted the difference in the singlesmall optical depths of haze of the order of a few hundredths extending upward to scattering phase functions of the haze and pressure levels of some tens of millibars upper cloud region, but could not easily diseven at low latitudes. The polarimetry tinguish between models in which the haze result of a haze optical depth of a few extended down to the top of the ammonia
JOVIAN PHOTOMETRY AND POLARIMETRY
71
cloud and models in which the haze was confined to a physically thin layer. Sato and Hansen (1979) also suggested that the haze might extend down to the top of the ammonia cloud in their models of reflected sunlight, but admitted the difficulty of precisely determining details of the distribution of the aerosols near the " s k i n " of the atmosphere. In this work we treated the haze as a thin diffusing sheet at a discrete pressure level above the ammonia cloud, and determined constraints on the "effective" pressure where the haze acts to form the CTLV observed in the polarimetry. We did not explicitly test models in which the haze was allowed to extend down to the base cloud, although models of this sort could possibly be made to work also. Indeed, the ultraviolet data require appreciable absorption at levels significantly deeper than 100 mb unless the av optical thickness of the haze is larger than several and thus probably larger than permitted by observations at visible wavelengths. It is not clear whether the absorption at the ammonia cloud level in the ultraviolet is due to the presence of separate haze-type aerosols mixed in with brighter ammonia cloud particles, or whether the ammonia cloud particles are themselves darkened at the shorter wavelengths. From the point of view of modeling the observed data, fewer parameters are required to specify a pressure level for a haze layer than to specify the haze/gas mixing ratio at each level above the ammonia cloud, and this is the approach we have followed. In any case, because the haze aerosols seem to have less of a back-scattering peak than the cloud particles (Paper I) and because they must produce strong singlescattering polarization near 90 ° scattering angle while the ammonia clouds are neutral or slightly negative, the populations of particles at the 100 mb and the 300 mb levels are clearly different.
Gehrels et al. (1969) anticipated the Pioneer measurements of high positive polarization near 90° phase in the polar regions. However, the new measurements would require the atmosphere to be clear to a depth of 9 bars to provide the observed polarization by molecular Rayleigh scattering alone as suggested by Gehrels et al. to explain their measurements. The observations of Jupiter in the ultraviolet and in strong methane bands since that time preclude this possibility. Instead, we find that highly polarizing aerosols (such as found over the belts and zones at low latitudes) rapidly increase in thickness north of 40°N and south of 48°S to optical depths in red light as large as ½ or more. There is an indication that the effective size of these aerosols also increases with increasing latitude. Detailed analysis of the polarimetry of the polar regions will be more difficult than similar analyses of the belts and zones at lower latitudes because each pole was well observed at fewer phase angles and over a smaller range of scattering geometries from center to limb. For this reason, we reserve more detailed models of the polarization of the polar regions for later work which will include the auxiliary constraints available from photometry in the ultraviolet and in the methane absorption bands.
7. Variations in H a z e Properties with Latitude
AXEL, L. (1972). Inhomogeneous models of the atmosphere of Jupiter. Astrophys. J. 173, 451-467. BAKER, A. L., L. R. BAKER, E. BESHORE, C. BLENMAN, N. D. CASTILLO, Y. P. CHEN, L. R. DOOSE, J.
The
ground-based
observations
of
ACKNOWLEDGMENTS We are indebted to many colleagues for important help in acquiring, reducing, displaying, and analyzing the Pioneer photometry and polarimetry discussed here. T. Gehrels has provided support and encouragement throughout this work. D. L. Coffeen contributed important guidance in the early phases involving the design of observing sequences. L. R. Doose and N. D. Castillo provided the detailed computing support without which this program would not have been possible. We are especially grateful also to the Pioneer Project Office of the NASA-Ames Research Center and the Planetary Atmosphere Section of NASA's office of Space Sciences for their financial support of this work. REFERENCES
72
SMITH AND TOMASKO
P. ELSTON, J. W. FOUNTAIN, T. GEHRELS, J. H. KENDALL, C. E. KENKNIGHT, R. A. NORDEN, W. SWINDELL, AND i . G. TOMASKO (1975). The imaging photopolarimeter experiment on Pioneer 11. Science 188, 468-472. BERGSTRALH, J. T. (1973). Methane absorption in the Jovian atmosphere. II. Absorption line formation. Icarus 29, 390-418. BI~ZARD, B., J. P. BALUTEAU, AND A. MARTEN (1983). Study of the deep cloud structure in the Equatorial region of Jupiter from Voyager infrared and visible data. Icarus 54, 434-455. BURIEZ, J. C., AND C. DE BERGH (1980). Methane line profiles near 1.1 /zm as a probe of the Jupiter cloud structure and C/H ratio. Astron. Astrophys. 83, 149-162. CALDWELL, J., A. T. TOKANUGA, AND G. S. ORTON (1983). Further observations of the 8 /zm polar brightenings of Jupiter. Icarus 53, 133-140. COFFEEN, D. L. (1974). Optical polarization measurements of the Jupiter atmosphere at 103° phase angle. J. Geophys. Res. 79, 3645-3652. DOLLFUS, A. (1957). Etude des planetes par la polarisation de leur lumiere. Ann. Astrophys. Suppl. 4. [English transl. NASA-TT F-188 (1964).] DousE, L. R. (1976). Light Scattering Properties o f Jupiter's R e d Spot. Ph.D. dissertation, Department of Astronomy, University of Arizona, Tucson. FIMMEL, R. O., J. A. VAN ALLEN, AND E. BURGESS (1980). Pioneer: First to Jupiter, Saturn, and Beyond, NASA SP-466. U.S. Govt. Printing Office, Washington, D.C. GAUTIER, D., B. BI~ZARD, A. MARTEN, J. P. BALUTEAU, N. SCOTT, A. CHEDIN, V. KUNDE, AND R. HANEL (1982). The C/H ratio in Jupiter from the Voyager experiment. Astrophys. J. 257, 901-912. GEHRELS, T., O. L. COEFEEN, M. G. TOMASKO, L. R. DOUSE, W. SWINDELL,N. D. CASTILLO,J. KENDALL, A. E. CLEMENTS, J. HAMEEN-ANTILLA, C. KENKNIGHT, C. BLENMAN, R. BAKER, G. BEST, AND L. BAKER (1974). The imaging photopolarimeter experiment on Pioneer 10. Science 183, 318-320. GEHRELS, T., B. M. HERMAN, AND T. OWEN (1969). Wavelength dependence of polarization. XIV. Atmosphere of Jupiter. Astron. J. 74, 190-199. HALL, J. S., AND L. A. RILEY (1969). Polarization measures of Jupiter and Saturn. J. Atmos. Sci. 26, 920-923. HAYES, D. S., AND D. W. LATHAM (1975). A rediscussion of the atmospheric extinction and the absolute spectral-energy distribution of Vega. Astrophys. J. 197, 593-601. HOLMES, A. (1981). Light Scattering from Ammonia and Water Crystals. Ph.D. dissertation, Optical Sciences Center, University of Arizona, Tucson. LABS, D., AND H. NECKEL (1970). Transformation of the absolute solar radiation data into the "International practical temperature scale of 1968." Solar Phys. 15, 79-87.
LIOU, K. N., R. BALDWIN, AND T. KASER (1976). Preliminary experiments on the scattering of polarized laser light by ice crystals. J. Atmos. Sci. 35, 553-557. LYOT, B. (1929). Recherches sur la polarisation de la lumiere des planetes et de quelque substances terrestres. Ann. Ob. Paris (Meudon) VIII. [English transl. NASA TT F-187 (1964).] MARTEN, A., D. ROUAN, J. P. BALUTEAU, D. GAUTIER, B. J. CONRATH, R. A. HANEL, V. G. KUNDE, R. SAMUELSON, A. CHEDIN, AND N. SCOTT (1981). Study of the ammonia ice cloud layer in the Equatorial region of Jupiter from the infrared interferometric experiment on Voyager. Icarus 46, 233-248. MOROZHENKO, A. V., AND E. G. YANOVlTSKII (1973). The optical properties of Venus and the Jovian planets. I. The atmosphere of Jupiter according to polarimetric observations. Icarus 18, 583-592. ORTON, G. S. (1975). Spatially resolved absolute spectral reflectivity of Jupiter: 3390-8400 ,g,. Icarus 26, 159-174. ORTON, G. S., J. F. APPLEBY, ANDJ. W. MARTONCHIK (1982). The effect of ammonia ice on the outgoing thermal radiance from the atmosphere of Jupiter. Icarus 52, 94-116. OWEN, T., AND R. J. TERRILE (1981). Colors on Jupiter. J. Geophys. Res. 86, 8797-8814. PEEK, B. M. (1958). The Planet Jupiter. Faber & Faber, London. SATO, M., AND J. E. HANSEN (1979). Jupiter's atmospheric composition and cloud structure deduced from absorption bands in reflected sunlight. J. A tmos. Sci. 36, 1133-1167. SMITH, B. A., L. A. SODERBLOM, T. V. JOHNSON, A. P. INGERSOLL,S. A. COLLINS,E. M. SHOEMAKER, G. E. HUNT, H. MASURSKY, M. H. CARR, M. E. DAVIES, A. F. COOK II, J. BOYCE, G. E. DANIELSON, T. OWEN, C. SAGAN, R. F. BEEBE, J. VEVERKA, R. E. STRUM, J. F. MCCAULEY, D. MORR1SON, G. A. BRIGGS, AND V. E. SUOMI (1979). The Jupiter system through the eyes of Voyager 1. Science 204, 951-972. SMITH, D. W. (1980). Galilean satellite eclipse studies. II. Jovian stratospheric and tropospheric aerosol content. Icarus 44, 116-133. SMITH, D. W., T. F. GREENE, AND R. W. SHORTHILL (1977). The upper Jovian atmosphere aerosol content determined from a satellite eclipse observation. Icarus 30, 697-729. STAHL, H. P., AND M, G. TOMASKO (1984). Measurements of the single-scattering properties of ammonia ice crystals. In preparation. STOLL, C. P. (1980). Polarimetry o f Jupiter at Large Phase Angles. Ph.D. dissertation, Department of Planetary Sciences, University of Arizona, Tucson. TERRILE, R. J., AND J. A. WESTPHAL (1977). The vertical cloud structure of Jupiter from 5/.*m measurements. Icarus 30, 274-281.
JOVIAN PHOTOMETRY TOMASKO, M. G. (1977). Photometry of Jupiter from Pioneer l 1. Bull. Amer. Astron. Soc. 9, 533. TOMASKO, M. G., AND L. R. DOOSE (1984). Polarimetry and photometry of Saturn from Pioneer 11 : Observations and constraints on the distribution and properties of cloud and aerosol particles. Icarus 58, 1-34. TOMASKO, M. G., AND S. MARTINEK (1978). Centerto-limb variations in the ultraviolet spectrum of Jupiter. Bull. Amer. Astron. Soc. 10, 562. TOMASKO, M. G., AND P. H. SMITH (1982). Photometry and polarimetry of Titan: Pioneer ! l observations and their implications for aerosol properties. Icarus 51, 65-95. TOMASKO, M. G., R. A. WEST, AND N. D. CASTILLO (1978). Photometry and polarimetry of Jupiter at large phase angles. 1. Analysis of imaging data of a prominent belt and a zone from Pioneer 10. Icarus 33, 558-592. VAN ALLEN, J. A. (1976). High-energy particles in the Jovian magnetosphere. In Jupiter (T. Gehrels, Ed.). Univ. of Arizona Press, Tucson. WALLACE, L., J. J. CALDWELL, AND B. D. SAVAGE (1972). Ultraviolet photometry from the Orbiting Astronomical Observatory. III. Observations of Venus, Mars, Jupiter, and Saturn longward of 2000 A. Astrophys. J. 172, 755-769.
AND POLARIMETRY
73
WALLACE, L., AND D. M. HUNTEN (1978). The Jovian spectrum in the region 0.4-1.1 p.m: The C/H ratio. Rev. Geophys. Space Phys. 16, 289-319. WALLACE, L., AND G. R. SMITH (1977). The interpretation of Jovian methane absorption. Astrophys. J. 212, 252-261. WEIDENSCHILEING~ S. J.~ AND J. S. LEWIS (1973). Atmospheric and cloud structure of the Jovian planets. Icarus 20, 465-476. WEST, R. A. (1979a). Spatially resolved methane band photometry of Jupiter. I. Absolute reflectivity and center-to-limb variations in the 6190-, 7250-, and 8900-A bands. Icarus 38, 12-33. WEST, R. A. (1979b). Spatially resolved methane band photometry of Jupiter. II. Analysis of the South Equatorial Belt and South Tropical Zone reflectivity. Icarus 38, 34-53. WEST, R. A., C. A. HORD, K. E. SIMMONS, D. L. COFFEEN, M. SATO, AND A. L. LANE (1981). Near ultraviolet scattering properties of Jupiter. J. Geophys. Res. 86, 8783-8792. WEST, R. A., AND M. G. TOMASKO (1980). Spatially resolved methane band photometry of Jupiter. III. Cloud vertical structures for several axisymmetric bands and the Great Red Spot. Icarus 41, 278292.
Photometry and Polarimetry of Jupiter at Large Phase Angles II. Polarimetry of the South Tropical Zone, South Equatorial Belt, and the Polar
Regions from the Pioneer 10 and 11 Missions PETER H. SMITH AND MARTIN G. TOMASKO Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721 Received June 15, 1983; revised December 2, 1983 The imaging photopolarimeter (IPP) experiment on the Pioneer 50 and 11 missions to Jupiter measured the intensity and linear polarization of red and blue sunlight reflected from the planet over a range of phase angles inaccessible from the Earth. We give an overview of the polarization data obtained in the two Jupiter encounters at phase angles from 43° to 117° and briefly describe the photometry data from the Pioneer 15 encounter at phase angles between 34° and 80° which partially fill a gap in the phase coverage from Pioneer 10 (M. G. Tomasko, R. A. West, and N. D. Castillo, 5978, Icarus 33, 558-592). The polarimetry and photometry of the South Tropical Zone (STrZ), the north component of the South Equatorial Belt (SEBn), and a north-south cut extending to the south pole are given in detailed tables. Comparison of the data to multiple-scattering models yields several details of the distribution and single-scattering properties of the clouds and aerosols on Jupiter. The observed polarization in blue light at latitudes less than about 40 ° shows only small variations between belts and zones. Simple models indicate that the tops of the belt and zone clouds are reached at nearly the same pressure level of about 320 mb and that the polarization differences are a result of the lower cloud albedo in the belt. The optical thickness of the belt as well as the zone clouds at this level must be at least 1.5 to prevent the polarization produced by underlying gas from being seen in the data. The polarization rises abruptly toward the limb and terminator in red light, indicating a haze of positively polarizing particles with an optical thickness of a few tenths at a pressure level of about 120 rob. The polarization in both colors increases abruptly from latitudes north of 40°N and south of 48°S to values as high as 60% at high latitudes. This effect is not due to a longer slant path but must be due to a large increase in the optical thickness of the polarizing haze at high latitudes. There is some indication that the size of the haze aerosols grows with increasing latitude as well. The photometry data indicate little change in the brightness of planetary features in the year between the two Pioneer encounters. Photometric models that fit the Pioneer 50 data fit the Pioneer 15 data remarkably well with essentially the same phase functions. Using a two-cloud model, we find that our models best fit the limb darkening at 12° phase when the belt absorbers are evenly distributed in both the clouds. There is no evidence for rainbow-like bumps on the singlescattering phase functions in the range of scattering angles from 120° to 140° as might result from scattering by spherical particles.
amount of information is required also to describe the vertical distribution and the single-scattering properties of the particles. Several types of data have been used in studies aimed at determining the distribution and scattering properties of Jupiter's clouds. Observations in the ultraviolet between 2000 and 3000 ,~ from Voyager (West et al., 1981), the International Ultraviolet Explorer (Tomasko and Martinek, 1978), the OAO satellite (Wallace et al., 1972), as
I. INTRODUCTION
The optical properties and vertical distribution of aerosol and cloud particles are important in controlling many of the physical processes occurring in Jupiter's atmosphere, and so are of considerable interest. Even a glance at an image of the planet conveys the fact that a great deal of information is required to specify the horizontal distribution of the aerosols. A considerable 35
0059-5035/84 $3.00 Copyright© 1984by AcademicPress, Inc. All rightsof reproductionin any formreserved.
36
SMITH AND TOMASKO
well as various rocket flights have indicated the presence of high-level aerosols with an optical thickness of several tenths and a low albedo shortward of 3000 A. This haze is seen at pressure levels of roughly 100 mb at low latitudes rising to pressures of a few tens of millibars or less at latitudes greater than - 4 0 °. Studies in absorption bands of methane, ammonia, and the quadrupole lines of hydrogen [see Wallace and Hunten (1978) for a review] in the visible and near infrared are sensitive to deeper levels. In combination with the predictions of thermodynamic equilibrium models (see Weidenschilling and Lewis, 1973) such data often are interpreted in terms of two cloud layers. An upper cloud (presumably of ammonia crystals) is thought to have its base near 600 mb. A deeper cloud occurs with its top at a pressure of about 2 bars (Axel, 1972), or more (Sato and Hansen, 1979). Finally, observations near 5 ~m where gaseous opacity is a minimum reveal small regions with brightness temperatures of 260°K indicating the presence of significant gaps at some locations in the cloud layers (Terrile and Westphal, 1977; Marten et al., 1981). Despite the large number of high-quality observations of Jupiter, the constituent responsible for the colors of the clouds remains to be identified. In principle, measurements of the polarization of reflected sunlight as a function of phase angle a can yield constraints on the single-scattering polarizing properties of the cloud particles at the corresponding single-scattering angles (180-a) and ultimately can constrain the refractive index and composition of the particles. Interpretation of existing groundbased measurements of polarization (Lyot, 1929; Dollfus, 1957; Hall and Riley, 1969; Gehrels et al., 1969; Morozhenko and Yanovitskii, 1973) have been hampered by the small range of phase angles accessible to ground-based studies and also by the fact that the cloud particles are expected to be nonspherical. In this case laboratory measurements are required to convert con-
straints on the single-scattering phase matrix to constraints on the size, shape, and refractive index of the cloud particles. Near the limb at small phase angles, the polarization results primarily from secondorder scattering, and will be radial for a phase matrix that produces positive polarization (maximum electric vector perpendicular to the scattering plane) at intermediate scattering angles (near 90°), and tangential to the limb for a phase matrix that is negative at intermediate angles. The observations of Gehrels et al. (1969) showed very different behavior near the poles compared with the east and west limbs at low latitudes, indicating much more positively polarizing material in the polar regions. The Pioneer 10 and 11 missions to Jupiter provided the first opportunity to measure the brightness and polarization of Jupiter at phase angles larger than the maximum of about 12° obtainable from the Earth. The measurements of the brightness of a dark belt (the SEBn at 5°S-7°S) and a bright zone (the STrZ at 18°S-21°S) made by Pioneer 10 at phase angles from 12° to 150° (with a gap between 34° and 109°) were reported by Tomasko et al. (1978) (hereafter referred to as Paper I). Here we present the photometry of these regions obtained by Pioneer 11 at phase angles from 34° to 80°, partially filling the gap in coverage from Pioneer 10. Both Pioneer 10 and 11 made measurements of the degree and position angle of polarization of sunlight reflected from Jupiter (Gehrels et al., 1974; Coffeen, 1974; Baker et al., 1975). The polarimetry of the Great Red Spot has been presented by Doose (1976). The SEBn was discussed by Stoll (1980) who derived constraints on the single-scattering polarization of the cloud particles assuming the ammonia cloud top occurs near 600 mb. Here we proceed using a different approach and compare a belt and a zone as well as discuss the polarimetry of the polar regions. In Section II of this paper we present the
JOVIAN PHOTOMETRY AND POLARIMETRY
photometry data from Pioneer 11 and the polarimetry from both missions. In Section III we compare the photometric models derived from the Pioneer 10 data to the data obtained on Pioneer 11. In Section IV we compare the polarimetry of the belt, zone, and the polar regions to simple models. Section V describes more detailed models of the belt and zone polarimetry. We discuss our results in the context of other work and summarize our conclusions in a final section. I1. DATA
A. Photometry
The imaging data from Pioneer 10 have been presented and the reductions have been described in Paper I. The instrument on Pioneer 11 was almost identical, but the trajectory was considerably different. In contrast to the very nearly equatorial trajectories of Pioneer 10 and both Voyager spacecraft, the trajectory of Pioneer 11 was at a high inclination permitting especially good views of both the south and north polar regions of Jupiter. The highest resolution images from both Pioneer encounters are shown in Fimmel et al. (1980). A typical Pioneer 11 blue and red image pair is shown in Fig. 1. While the spatial resolution is less than for images made at the same range by the subsequent Voyager mission, the Pioneer data have the advantage of having been obtained by sweeping the same channeltron detector over the entire image--a procedure that permits more accurate relative photometry than usually obtained with vidicon systems. Within about 1 hr of the closest approach to Jupiter, the imaging photopolarimeter (IPP) instrument on each Pioneer mission received a dose of energetic particle radiation sufficient to darken the glass windows over the channeltron detectors. On both missions, the size of this effect was monitored by frequent observations of an internal lamp throughout the encounter (see Paper I). Because of the different trajectory of
37
the Pioneer 11 encounter, the dose received was substantially less than that received by Pioneer 10 (Van Allen, 1976). The postpericenter Pioneer 11 photometry data have been corrected to the prepericenter system by multiplication by 1.03 and 1.05 in red and blue, respectively. Ground-based absolute photometry of Jupiter (Orton, 1975) near the time of the Pioneer 10 Jupiter encounter was used to provide an absolute calibration of the IPP on Pioneer 10. No comparable groundbased observations were made near the time of the Pioneer 11 encounter with Jupiter. However, an absolute calibration of the Pioneer 11 IPP is available from comparison of the Pioneer 11 observations of Saturn with ground-based observations of Saturn near the time of the Saturn encounter (Tomasko and Doose, 1984). In order to use the Pioneer 11 calibration at Saturn at the time of the Pioneer I 1 Jupiter encounter, the change in instrument sensitivity between the two encounters must be determined. Observations of Sirius made periodically during the interplanetary cruise can be used to monitor the changing sensitivity of the instrument to high accuracy. Figure 2 shows the average data number recorded for Sirius at gain 19 after correction for the effects of the changing spacecraft spin period and Sirius cone angle. The Pioneer 10 Sirius observations are shown on a scale displaced by one year for comparison. Both instruments experienced significant decreases in sensitivity between launch and Jupiter encounter, with a lesser rate of decline after Jupiter encounter. The abrupt decrease in sensitivity within an hour of closest approach indicated by the on-board lamp is also apparent in the figure. The values of F0, where ~'F0 is the solar flux in the Pioneer 11 passbands at Saturn's distance from the Sun, are given as 49.8 -+ 5.2 and 85.7 --- 6.8 in blue and red, respectively, in imaging mode data numbers at gain step 18 by Tomasko and Doose (1984). The corresponding values just before the Jupiter encounter at gain 13 are 47.5 - 5.3
38
SMITH AND TOMASKO
FIG. 1. (a) Pioneer 11 image C6 of Jupiter in blue light at a phase angle of 60 ° obtained from a range of 940,000 km at 18 hr 43 min UT on Dec. 2, 1974. This image was obtained in the higher resolution photometry mode. (b) Same as (a) but in red light.
JOVIAN PHOTOMETRY AND POLARIMETRY
FIG.l--Continued.
39
40
SMITH AND TOMASKO TIME (PIONEER I 0 ) ~ 1972 50
1973
1974
I
I
1975 I
1976 I
1978 I
1~,
4a
""30
PIONEER10 . . . . . PIONEER il - -
"4. "~
G 200 AIN --o .....
~
LUE
I6'~
15C> VEGA-x SIRIUS- ALL
lj
where R(h) is the relative spectral response for the respective instrument, and Rpeak is the peak responsivity. Then the ratio of the values ofF0 on the two instruments is given by F0(Pl0 F0(PI0)
19o
~
20
_
1977 I
0,-HE, S
l(h)dh
Rpeak(PI l) fF®(h)RP 1
Rpeak(PI0) fFG(X)RP~o(X)dX
The ratio of the counts on the star can be used to give the ratios of the peak responsivities from C*(P~I) = Rpeak(Pll) fF*(X)RPll(h)dh. C*(PI0) Rpeak(P10)fF*OORelo(h)dh
I
1973
I
1974
I
1975
I
1976
1977
I
I
1978
1979
TIME (PIONEER I I ) - ' - - " -
FIG. 2. The sensitivities of the Pioneer 10 and 11 IPP instruments as functions of time determined by observations of the star Sirius in the polarimetry mode (with the depolarizer in place). The plotted points are the star counts normalized to compensate for changes in the cone angle of the star and in the spin period of the spacecraft: the normalized counts are defined as the sum of the counts in all the sectors of one roll multiplied by the sine of the cone angle and divided by the spin period in seconds. The amplifier gain setting for each observation is given in the legend. All points have been converted to gain step 19 by using gain ratios determined from postlaunch observations. The time scales for the two missions have been displaced by one year as indicated. For Pioneer 11 some of the points were determined from observations of Vega adjusted for a difference of 1.49 and 1.53 magnitudes between Vega and Sirius in our blue and red channels, respectively.
and 66.8 -+ 5.8 when changes in distance, gain, Jovian radiation factors, and Sirius data numbers are taken into account. A second, completely independent, method of calibrating the Pioneer 11 IPP is available. It is possible to use the observations of Sirius on each mission as an intermediate standard to tie the calibration of the Pioneer 11 instrument to that on Pioneer 10. The value ofF0 for each instrument can be defined by F0 = RpeakfFo(h)R(h)d)t
Finally, the ratios of the star counts should be taken at the same gain step (13) where the ratio of the values of Rpeak and F0 are required. Taking the shape of the solar spectrum from Labs and Neckel (1970) gives the ratio of the Pioneer 11 divided by Pioneer I0 integrals of spectral response and solar flux as 1.417 in the blue and 1.283 in the red. With the shape of the relative spectrum of Sirius taken from Hayes and Latham (1975), we have the ratio of the Pioneer I0 to Pioneer 11 integrals of the Sirius flux times the IPP relative response as 0.718 in blue and 0.797 in the red. Combining these values gives F0(blue) = 42.4 -+ 3.6 and F0(red) = 61.6 -+ 4.0. This includes an adjustment for changes in the distance between Jupiter and the Sun. In view of the size of the uncertainty associated with each of these independent calibrations of the Pioneer I I IPP, the two approaches lead to consistent results. Forming a weighted average of these values gives F0(blue) = 44.3 _+ 3 and F0(red) = 63.5 -+ 3 for Pioneer I I at Jupiter in the imaging mode at gain 13.
41
JOVIAN PHOTOMETRY AND POLARIMETRY TABLE I PIONEER II IMAGES AND PHOTOMETRIC REDUCTION FACTORS
Image No.
Mid-time"
Phase (°)
Pixel size (km)
Lat. b
Gain
GR c
GB c
C26 C18 C6 C4 C2-CI
335:17:16 336:00:41 336:18:51 336:22:58 337:02:15
48 50 60 67 80
1127 943 433 293 168
- 12.4 - 13.8 -22.1 -27.6 -37.6
DI6 D22
338:10:20 338:21:32
37 34
915 1193
38.4 36.7
13 14 13 14 13 14 15 14 13
1.00 1.46 1.00 1.46 1.00 1.46 2.073 i.46 ! .00
1.00 1.41 1.00 1.41 1.00 1.41 1.974 1.41 1.00
a Earth receipt time of middle of image (UT) in day of year:hr:min. b Latitude o f s u b s p a c e c r a f t point. c Intensities from Pioneer 1 i imaging data were put on the same relative intensity scale by dividing the data n u m b e r s by GR in red (or GB in blue). In addition, data obtained after pericenter (images D l 6 and D22) were multiplied by 1.03 in red and 1.05 in blue to adjust for the radiation-induced darkening which occurred within 1 hr o f pericenter.
The scattering geometries of each pixel in Pioneer l l images at seven phase angles from 34° to 80° have been computed from the trajectory and housekeeping data for the flyby. The phase angles of these images, their spatial resolution, and the instrument gain settings and gain ratios appropriate for each are given in Table I, while the brightness (in data numbers normalized to prepericenter gain 13 counts) are given in Table II for the STrZ and the SEBn. Figure 3 shows a north-south scan of reflectivity (actually IIF~owhere/~0 is the cosine of the solar zenith angle) from image A28 of the Pioneer l0 encounter and image C6 from Pioneer 1I. The figure shows that the latitude limits and relative brightness of Jupiter's main belts and zones remained relatively unchanged in the one-year interval between the two encounters. A more rigorous comparison of the brightness of the planet at the times of the two encounters follows in Section III where scattering models are presented, but is not possible from a visual inspection of Fig. 3 alone because the phase angles of the two images are appreciably different. The brightness of
the Pioneer 11 images (in data numbers normalized to prepericenter gain 13 counts) are given in Table II for the STrZ and the SEBn. 1,0
'
'
,
~
I
~
I -60
,
I
I
'
~.
I
I 0
L
~
.I 50
0.8
l
0~6
~_o =~
0.4
0.2 -90
,
I -30
,
~
,
, 60
LATITUDE
FIG. 3. T h e refiectivity of a L a m b e r t surface, I/ (p.oF0), as a function of latitude along the central meridian o f image C6 at a p h a s e angle of 60 ° (see Figs. la,b) from the Pioneer I l e n c o u n t e r and from image A28 at 23 ° phase (see Paper I) from Pioneer 10. The boundaries of the principal belts and zones are seen to be similar at the times o f the two encounters. The difference in the phase angles of the two images precludes quantitative c o m p a r i s o n of the reflectivities of the planet at the times of the two encounters without detailed scattering models, but the reflectivities of the bright zones s e e m quite similar.
42
Phase
(°)
SMITH A N D TOMASKO T A B L E IIA
T A B L E liB
PIONEER 11 PHOTOMETRY STrZ
PIONEER 11 PHOTOMETRY SEBn
Roll
/z
go
A~
/red
/blue
Phase (°)
Roll
/x
~o
A~
Led
lblu¢
34
65 81 101 121 141 161 181 200
0.2064 0.3878 0.5661 0.6841 0.7028 0.6339 0.4696 0.2490
0.3961 0.6162 0.8295 0.9604 0.9833 0.8932 0.6954 0.4132
144.45 141.95 137.43 137.80 154.13 134.14 139.69 143.68
15.0 24.5 34.0 39.9 41.0 37.0 28.5 17.1
13.5 16.1 18.8 20.7 20.9 19.9 17.4 13.1
37
11 29 51 71 91 109 135 155
0.1621 0.3665 0.5550 0.6589 0.6744 0.6165 0.4036 0.1617
0.3310 0.5825 0.8204 0.9532 0.9853 0.9213 0.6717 0.3657
142.72 139.80 134.33 133.92 163.57 135.38 140.69 143.09
13.6 23.7 32.4 38.0 4L0.3 39.6 30.0 14.1
12.7 15.4 17.7 19.5 20.5 20.4 17.7 12.6
48
485 505 525 545 560 570
0.8468 0.9768 0.9854 0.8701 0.6551 0.3092
0.2030 0.5244 0.7688 0.9383 0.9878 0.8972
164.59 147.96 22.94 12.81 88.31 150.02
7.5 21.9 33.5 40.3 40.5 32.7
4.5 11.5 16.4 19.5 19.9 18.5
50
44 49 57 80 108 139
0.2916 0.5082 0.6855 0.9262 0.9909 0.8543
0.8996 0.9714 0.9870 0.8771 0.6144 0.2023
148.28 127.97 61.86 3.95 108.94 161.34
30.9 37.1 39.9 36.2 24.3 6.3
18.5 19.9 20.0 17.1 12.2 4.2
60
1026 1060 1090 1120 1150 1180 1210 1240 1250
0.8395 0.9200 0.9553 0.9573 0.9232 0.8506 0.7223 0.4704 0.2288
0.1153 0.3143 0.4715 0.6218 0.7510 0.8597 0.9466 0.9867 0.9385
146.11 3.5 2.5 130.44 12.2 7.0 104.83 19.5 10.4 65.77 26.2 13.0 36.27 32.0 15.0 17.59 40.0 17.5 4.31 39.6 19.5 82.29 "38.0 20.2 132.57 30.6 - 1%3
68
360 400 500 600 675
0.8532 0.8750 0.9095 0.9173 0.9085
0.7724 0.7268 0.6065 0.4767 0.3743
34.41 41.36 60.36 82.26 97.67
35.3 32.8 27.3 20.7 15.2
17.1 16.1 13.7 10.6 8.3
80
287 325 375 426 460 500
0.7494 0.7818 0.8063 0.8125 0.8097 0.8151
0.6862 0.6013 0.4878 0.3779 0.2983 0.2086
45.34 54.11 65.71 76.64 84.15 91.67
32.0 27.6 21.8 15.7 12.2 8.1
15.7 14.0 11.8 9.0 7.2 4.6
34
91 111 130 151 171 191 211
0.1504 0.3207 0.4601 0.5086 0.4835 0.3577 0.1658
0.4805 0.7015 0.8598 0.9201 0.8802 0.7269 0.4849
148.22 149.55 155.80 178.15 156.17 148.55 147.74
17.9 28.5 36.8 40.1 38.3 31.0 19.1
18.0 23.4 29.5 30.0 28.9 24.7 17.0
37
49 71 89 109 131 149 167
0.1764 0.3486 0.4409 0.4719 0.4158 0.2809 0.1001
0.5214 0.7509 0.8716 0.9183 0.8532 0.7006 0.4757
145.99 t47.65 154.98 179.27 154.71 149.17 147.78
21.9 33.1 38.9 41.2 38.2 30.6 20.8
20.0 25.1 28.4 30.0 27.9 24.1 18.9
480 500 520 540 555 563
0.8257 0.9651 0.9771 0.8581 0.6239 0.3059
0.1447 0.4702 0.7150 0.8999 0.9160 0.8193
174.70 137.95 74.59 64.87 103.64 135.46
5.1 20.5 33.0 40.9 40.5 32.7
4.5 15.1 23.5 29.3 29.7 24.9
52 54 62 72 91 114 146
0.2762 0.4148 0.6486 0.8008 0.9492 0.9883 0.8332
0.8085 0.8688 0.9191 0.9001 0.7835 0.5623 0.1318
134.27 125.11 95.12 68.99 56.20 135.28 176.79
31.8 36.6 40.9 40.9 35.6 24.6 4.0
23.4 26.7 29.5 29.5 25.7 18.0 3.5
1020 1070 1110 1150 1180 1200 1219 1229
0.9016 0.9913 0.9930 0.9232 0.6154 0.8970 0.5000 0.2508
0.1382 0.4156 0.6008 0.7687 0.8618 0.9058 0.9145 0.8600
169.30 162.28 13.36 24.83 38.46 56.39 89.28 117.93
4.7 17.5 27.5 36.5 41.2 42.5 40.8 33.3
4.3 12.8 19.6 25.9 29.0 30.2 29.0 25.0
360 375 400 500 600 680
0.8571 0.8714 0.8929 0.9540 0.9840 0.9892
0.7944 0.7795 0.7539 0.6429 0.5212 0.4173
17.40 15.12 11.35 5.47 33.37 79.10
38.6 38.1 36.5 30.7 24.5 18.3
27.8 27.3 26.2 21.9 17.7 13.5
287 295 325 375 426 475 525 575
0.8048 0.8181 0.8598 0.9066 0.9304 0.9398 0.9344 0.9165
0.7201 0.7031 0.6384 0.5282 0.4209 0.3086 0.1923 0.0750
5.74 7.98 16.59 31.93 49.54 69.96 90.35 106.94
33.6 35.3 32.3 25.9 19.8 13.2 7.6 2.2
20.8 23.0 22.3 17.8 13.7 9.7 5.8 2.3
48
50
60
67
80
JOVIAN PHOTOMETRY
43
AND POLARIMETRY
T A B L E III PIONEER 10 AND 11 POLARIMETRY OF JUPITER Map
Start time a
End time a
Phase (°)
Pixel size b (km)
Gain
Dist. C
Pioneer 10 01 02 03 04
337:23:33 338:02:28 338:03:23 338:07:12
338:01:07 338:02:53 338:03:56 338:07:57
43 103 141 157
1970 1080 1070 2830
--- 350 --- 28 -+ 55 --- 180
0 0 0 0
4.57 2.949 2.929 6.12
-+ .63 +- .05 +- .10 -.33
Pioneer 11 A3 A2 A1 A0 B1 B2 B3
337:01:03 337:03:10 337:04:24 337:05:17 337:06:43 337:07:03 337:07:51
337:01:42 337:04:17 337:05:07 337:05:22 337:06:52 337:07:40 337:08:52
80 98 120 150 140 104 82
2710 1140 500 340 1020 1440 2100
-+ 220 --- 330 -+ 130 -+ 6 --+ 30 _+ 220 -+ 330
2 2,3,4,5 2,3 1 2 2,3 2,3
5.91 3.06 1.91 1.61 2.85 3.60 4.80
---+ -+ -+ -+ -+
.40 .60 .23 .01 .05 .40 .60
Note. The values ofF0 for the polarimetry-mode data are 1400 in red and 1360 in blue for Pioneer 11 and 440 in blue for Pioneer 10. These values should be used with Table IV to obtain I/F from instrument counts. a All times are UT Earth receipt times of data in day of year:hr:min (Pioneer 10: 1973, Pioneer 11: 1974). b Pixel size = (Dist. - 1)(70,850 km) (7.8 × 10 -3 radians). c Distance to center of Jupiter in units of Jupiter's radius (adopted as 70,850 km).
B. Polarimetry A summary of the operation of the IPP in the polarization mode is given by Coffeen (1974). Details of the reduction procedure for Pioneer I 1 polarimetry are given by Tomasko and Smith (1982) and Tomasko and Doose (1984). The data maps were obtained by accumulating one scan line of information on each rotation of the spacecraft. The motion of the spacecraft relative to the planet over a period on the order of an hour was sufficient to sweep the scan lines from the limb of the planet to the terminator. Table III summarizes the phase angles at which polarization maps are available from the Pioneer 10 and 11 Jupiter encounters. Due to a problem that developed with the Pioneer 10 instrument, red polarization data are not available for that encounter. The imaging-mode data use another detector, and so the intensity data were not affected by this problem. Because of the motion of the spacecraft and the planet during the map, it is not possible to display the data on the planet as it appeared from the spacecraft at any one instant of time and preserve both the local
illumination conditions and the apparent locations of the pixels. Figure 4 shows one of the polarization maps displayed in a way that nevertheless gives a good feeling for the coverage on the planet. The globe outline shows the appearance of the planet from the spacecraft at a time halfway through the map. All the pixels are displayed at the latitudes at which the data were obtained. Each pixel is rotated in longitude and displayed at the same fractional longitude from the central meridian to the limb at which it was observed. Line segments are used to indicate the direction of maximum electric vector with vertical lines representing light polarized perpendicular to the scattering plane. The magnitude of the polarization is indicated by the length of the plotted line segment. In order to prevent overcrowding, only a fraction of the av~ailable blue and red data is displayed in Figs. 4a and b. In both colors the polarization is oriented essentially perpendicular to the scattering plan e everywhere in the map. This is the case generally in the Pioneer observations of Jupiter except over the Great Red Spot in red light (Doose, 1976). In both
44
SMITH AND TOMASKO
Ii
I
b
i ill J r l t i i
t jI
,~
, '
i , '
, '
ill
r
20%
T
~(
FIG. 4. Polarization map A2 obtained from Pioneer 1! at a phase angle of 98° between 3 hr 10 min and 4 hr 17 min UT on Dec. 2, 1974. The globe outline shows the appearance of the planet halfway through the map. Vertical lines represent polarization perpendicular to the local scattering plane, with the length of the line segment proportional to the degree of polarization. To avoid overcrowding, only every fourth roll of polarization data and every other sector along a roll are displayed. The data are displayed at the latitude where they were observed, but are rotated in longitude to the same fractional longitude from the central meridian to the limb in the display as that at which they were observed. The data extend all the way to the terminator. (a) In blue light. (b) In red light. colors, the polarization increases dramatically toward the terminator and toward the pole south of about 50°S. The polarization also increases toward the bright limb in both colors. At phase angles near 90 ° , the polarization is m u c h larger in blue light than in the red at low latitudes, although, at high latitudes, the opposite is true. Displays such as Fig. 4 are quite useful but are not well suited for the examination of relatively small-scale features. F o r this purpose, all the original data pixels can be displayed in a rectangular grid exactly as they were obtained. The m a p shown in Fig. 4 is displayed in this w a y in Figs. 5 and 6. Contours of constant degree of polarization are given in Fig. 5. The dramatic increase in polarization in both colors for latitudes south of 50°S is apparent. The degree of polarization in red light is r e m a r k a b l y unif o r m at low latitudes where belt and zone structure appears in ordinary images. A modest a m o u n t of contrast is seen across belts and zones in the polarization in blue light superimposed on the strong gradient of polarization caused b y the increasing
slant path through the a t m o s p h e r e a w a y f r o m the subspacecraft point. In Fig. 6, the polarizations h a v e been divided by (1//z + 1/p-0) to roughly c o m p e n s a t e for the effects of different slant paths through the atmosphere in different parts of the map. The brightness in this figure is proportional to the adjusted polarization in the map. The contrast across the belts and zones in blue light is easier to see than in Fig. 5, and the increase in polarization toward the pole remains, indicating that this is not a slant path effect in the map. Relatively little fine scale structure is apparent at different longitudes, although close examination of the entire Pioneer data set does reveal polarizations different f r o m the surrounding regions for the G r e a t Red Spot, a few large ovals, and some other locations. O v e r the equatorial and t e m p e r a t e regions the areas of higher polarization are associated with the low albedo features. This is not the case with the poles where no corresponding decrease in albedo is associated with the large increase in polarization measured. Figure 7 shows the polarization of the northern hem-
45
JOVIAN PHOTOMETRY AND POLARIMETRY a SO
70
t 60
6 z g
50
40
30
20
300
350
400
450
500
550
ROLL-
I
L
P
I
I
I
I
80-
70-
I
60-
B 6 %
50-
40-
30-
20-
300
350
450
400
500
550
ROLL-
FIG. 5. Contours of the degree of polarization in map A2 with the data not projected onto the planet but simply laid down into a rectangular grid. (a) In blue light. (b) In red light. There are data dropouts before rolls 500 and 550.
isphere of Jupiter as seen from Pioneer 11 in a projection similar to that of Fig. 3. The polarization is seen to increase dramatically toward the north pole similar to the situation in the south. Reduced intensities, degree of polarization, and angle of polarization relative to the normal to the scattering plane are given in Table IV for the STrZ and the SEBn at each map covering these latitudes, and for a north-south cut in map A2 at a phase angle of 98”. Near the center of the disk, the polarization in blue light is generally largest near 90” phase, decreasing toward both
larger and smaller phase angles. In red light, the polarization is fairly small and independent of phase near the central meridian with an abrupt rise toward the limb and terminator in maps near 90” phase. III. PHOTOMETRY
MODELS
In view of the similarity in the appearance of Jupiter at the times of the Pioneer 10 and 11 encounters seen in Fig. 3, it is interesting to compare the reflectivity of the planet at the two encounter periods in a more quantitative manner. This is especially important as a prelude to the polar-
46
SMITH AND TOMASKO
FIG. 6. Polarization map A2 displayed as an image in which the brightness is proportional to the degree of polarization divided by the quantity (1//.t + 1/p.o) to roughly correct for the different slant paths through the gas seen in different parts of the map. (a) In blue light. (b) In red light.
JOVIAN PHOTOMETRY AND POLARIMETRY
FIG.
6---Continued.
47
48
SMITH AND TOMASKO
ization models discussed in the following sections where the polarimetry from the two encounters is combined into a single data set to constrain scattering models, implicitly assuming that the scattering properties of the planet changed relatively little between the encounters. For the best Pioneer 10 models of the STrZ given in Table III of Paper I, the values of F0 that gave the
best fits to the photometry data were 1.043 and 1.002 times the nominal values in red and blue, respectively. When exactly the same model structures are compared to the Pioneer 11 photometry data of the STrZ, the values of F0 that minimize the residuals are 1.065 and 1.034 times the weighted average values of F0 from the two ways of calibrating the Pioneer 11 instrument at Ju-
TABLE IVA POLARIMETRY OF JUPITER STrZ
Phase
Map
Roll
/z
/z0
(°)
A~ (°)
lbJ~e (counts)
Pblue (%)
0bJue (°)
/red (counts)
/)red (%)
0red (o)
43
01
3 56 94 147 208 242 269 288 299
0.8104 0.9218 0.9684 0.9843 0.9436 0.8904 0.8297 0.7765 0.7370
0.9284 0.8707 0.8052 0.6770 0.4859 0.3568 0.2409 0.1517 0.0935
85.3 69.1 71.7 122.1 163.3 169.6 171.9 173.4 172.9
292.0 273.5 247.8 204.5 139.5 98.5 63.5 39.0 23.7
1.4 1.3 1.4 1.5 2.2 3.3 4.6 6.8 9.2
172.0 174.0 171.0 177.0 179.0 177.0 178.0 181.0 182.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
80
A3
123 127 143 151
0.3394 0.4571 0.5545 0.5988
0.9159 0.9159 0.8896 0.8749
-66.8 -44.5 -30.0 -22.3
797.0 850.0 845.0 845.5
9.3 6.9 5.9 5.5
179.0 177.0 175.0 174.0
793.0 857.0 870.0 868.0
3.3 1.8 1.3 1.1
166.0 158.0 148.0 148.0
98
A2
262 272 282 294 314 338 362 386 406 430 446 458 466
0.2784 0.3539 0.4129 0.5174 0.6153 0.6885 0.7441 0.7664 0:7945 0.8077 0.8106 0.8201 0.8186
0.9018 0.8719 0.8448 0.7775 0.6830 0.5790 0.4814 0.3843 0.3079 0.2164 0.1563 0.1127 0.0830
-20.2 -12.1 -5.4 6.9 17.9 28.1 35.3 46.4 51.9 60.5 66.3 69.8 72.6
821.0 829.0 827.0 796.0 718.0 616.5 504.0 391.5 301.5 200.0 135.5 95.0 68.5
10.1 8.4 7.5 6.6 6.2 6.4 6.8 8.5 10.0 13.8 18.1 22.0 25.4
178.0 177.0 175.0 174.0 173.0 173.0 173.0 174.0 175.0 175.0 177.0 I77.0 177.7
845.0 857.3 856.7 828.5 748.0 650.5 527.0 413.5 312.0 201.5 133.5 90.0 64.0
4.1 2.8 2.1 1.4 1.2 1.3 1.5 2.3 3.5 5.8 8.7 11.4 14.4
172.0 168.0 166.0 162.0 156.0 157.0 164.0 167.0 169.0 171.0 173.0 174.0 174.5
103
02
390 404
0.4891 0.6055
0.6610 0.5508
32.1 31.8
241.6 199.2
6.0 5.8
179.0 178.0
0.0 0.0
0.0 0.0
0.0 0.0
120
A1
600 610 620 630 640 650 660 694
0.2591 0.3531 0.4082 0.4527 0.4915 0.4897 0.5197 0.5357
0.6604 0.5428 0.4473 0.3356 0.2313 0.1860 0.1116 0.0639
24.0 30.7 36.0 42.2 47.0 50.0 52.8 54.7
782.0 703.5 599.5 453.5 315.0 248.5 144.5 86.0
10.0 8.1 8.3 9.9 12.4 15.5 20.6 25.7
173.0 171.0 171.0 172.0 172.0 174.0 175.0 176.4
831.0 753.0 643.0 484.5 333.0 262.0 149.0 86.0
4.8 3.3 3.3 4.3 6.5 9.0 13.0 17.0
171.0 166.0 164.0 165.0 167.0 169.0 171.0 173.6
JOVIAN PHOTOMETRY AND POLARIMETRY
piter, indicating that the zone got brighter by about 2% in red light and 3% in blue. These changes are, however, fairly small compared to the uncertainties in connecting
49
the calibration of the two Pioneer instruments. If the Pioneer 10 calibration transferred through the star observations to Pioneer 11 is used instead of the average of the
TABLE IVB POLARIMETRY OF JUPITER SEBn
Phase
Map
Roll
p,
/.to
(°)
Ibi.~
A~p (°)
(counts)
Pbl.e (%)
0brae (o)
/red (counts)
Pred (%)
0~a (o)
7.8 -24.9 -91.8 - 144.3 -157.2 - 164.3 - 166.6
187.0 164.5 148.5 114.7 85.0 39.5 20.0
2.0 2.0 2.2 2.4 3.5 6.9 10.6
177.0 173.0 176.0 175.0 180.0 178.0 179.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
43
O1
18 79 132 189 230 280 299
0.8902 0.9718 0.9883 0.9579 0.9027 0.7928 0.7348
0.9602 0.8625 0.7365 0.5635 0.4106 0.1987 0.1045
80
A3
70 82 94 111 139 171 207
0.2218 0.3264 0.4287 0.5078 0.5989 0.6734 0.7272
0.9880 0.9855 0.9624 0.9312 0.8767 0.8116 0.7328
-68.8 - 14.6 - 1.6 14.8 23.2 30.1 39.9
545.0 588.0 596.0 577.0 552.0 534.0 489.0
15.8 11.1 9.2 8.1 7.4 7.3 7.4
180.0 179.0 177.0 175.0 174.0 175.0 174.0
672.0 792.0 824.0 830.0 805.0 758.0 694.5
6.0 3.0 1.9 1.3 1.0 1.1 1.1
172.0 169.0 166.0 158.0 148.0 151.0 153.0
98
A2
266 290 330 370 410 450
0.2806 0.4235 0.5362 0.5930 0.6190 0.6117
0.8950 0.7728 0.5982 0.4362 0.2809 0.1300
27.1 38.4 49.8 59.5 68.5 77.1
580.0 551.0 468.0 350.0 227.0 101.0
12.6 9.9 9.6 11.6 15.5 27.0
177.0 174.0 172.0 172.0 175.0 177.0
745.5 716.0 608.0 449.0 274.0 112.0
3.5 2.3 2.3 3.3 5.7 12.8
172.0 166.0 165.0 163.0 189.0 173.0
103
02
394 408 433 451 465
0.6174 0.7142 0.8381 0.9010 0.9373
0.6204 0.5141 0.3348 0.2113 0.1179
2.9 2.4 2.8 4.6 7.8
170.4 138.8 85.2 47.6 22.5
6.0 6.3 8.4 12.6 22.1
181.0 181.0 181.0 181.0 182.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
120
A1
628 648 670 686 702
0.1658 0.1817 0.2524 0.2564 0.2379
0.5515 0.4213 0.2790 0.1871 0.1049
46.8 52.9 55.7 58.6 61.3
544.0 492.0 391.0 289.0 187.0
15.9 18.0 19. I 23.0 31.2
174.0 174.0 175.0 176.0 178.0
8.9 10.3 11.3 15.0 22.1
171.0 170.0 171.0 171.0 174.0
0.0 0.0 0.0 0.0 0.0 611.0 549.0 434.0 310.0 189.0
TABLE IVC POLARIMETRY OF JUPITER SOUTH POLAR REGION (PHASE 98°, MAP A2) Lat. (°)
/~
-85.0 -80.0 -70.0 -60.0 -50.0 -45.0
0.5571 0.5536 0.5578 0.5756 0.5945 0.5913
~
0.0427 0.1289 0.2724 0.4114 0.5320 0.5890
Atp (°)
/blue
Pblue
ObJ~e
/red
/°red
Orcd
(counts)
(%)
(°)
(counts)
(%)
(°)
-77.8 -74.4 -67.7 -58.8 -47.1 -40.5
41.0 112.0 250.0 335.0 428.0 498.0
50.6 47.6 41.7 32.7 19.6 11.5
178.0 179.0 181.0 182.0 181.0 179.0
41.4 111.0 257.0 378.0 526.0 596.0
54.7 53.1 42.7 23.3 6.3 1.3
177.0 179.0 181.0 182.0 178.0 162.0
50
SMITH AND TOMASKO
i FIG. 7. Contours of polarization in map B3 obtained at a phase angle of 82 °. The projection scheme is similar to that used for Fig. 4. The longitude of the terminator at the mid-time of the map is also drawn. (a) In blue light. (b) In red light.
two independent calibration methods, one would conclude that the zone got darker (by 3% in the red and 4% in the blue) instead of brighter in the year between the two encounters. A similar comparison for the SEBn (based on the average of the two methods of evaluating F0 for Pioneer 11) indicates that this belt got brighter by some 8% in red light and 11% in blue between the two encounters. Even these differences are less than the differences between the two techniques for calibrating the Pioneer 11 instrument, so it is difficult to rule out the possibility that the belt remained roughly the same brightness between the two encounters and the zone actually got somewhat darker. In any case, the reflectivity of the STrZ seems to have changed relatively little between the two encounters, with the best estimate being an increase of about 2% in red light and 3% in blue. The SEBn got brighter relative to the STrZ by some 6% in the red and 8% in the blue in the year between the encounters. The general quality of the fits of models using the phase functions derived from the Pioneer 10 data to the Pioneer 11 imaging data is shown in Fig. 8. Also shown are models in which the single-scattering phase functions of the clouds are changed to have
a local bump similar to that produced by a rainbow for spherical particles (see Fig. 9) at scattering angles from 120° to 140°. Phase functions with bumps in this range of scattering angles make the fits to the observed data somewhat worse than the standard Henyey-Greenstein functions of Paper I. On the other hand, more gradual changes in the phase functions in the range of scattering angles from 80° to 140° (see Fig. 10) are more difficult to distinguish because of the relatively low values of any of these singlescattering phase functions in this range and the large contribution of multiple scattering compared to single scattering in the intensities observed at this range of phase angles. In general, phase functions with deeper minima than the double H enyey-G reenstein functions given in Paper I fit slightly worse, and ones that are even flatter in this range fit about as well or marginally better. All of the smooth phase functions give models that are a few percent too dark at 67° phase compared to the observations. However, because the models fit well at 60° and 80° phase, the required feature on the phase function would have to be very narrow and very high to account for the observed effect. It seems more likely that the discrepancy is the result of uncertainties in the scattering geometries assigned to the
JOVIAN PHOTOMETRY AND POLARIMETRY pixels in this image which contained only a very limited portion of the limb. The photometry models have an additional use regarding the polarization data. The data in the polarization mode use an aperture nominally 256 times larger in area and a different effective integration time per pixel than the imaging-mode data, and data in the two modes generally are not available at exactly the same phase. The data in the polarimetry mode can be calibrated in terms of intensity level by comparisons with models which fit the imagingmode data. Comparison with the STrz models of Table III of Paper I yields values for F0 in the polarimetry mode on Pioneer I 1 at gain step 2 of F0(red) = 1400 and F0(blue) = 1360. The uncertainties in these values are about 6.5% in the blue and 5.0% in the red primarily due to the uncertainties in the reference ground-based photometry. Examination of the Pioneer I0 polarization-mode data in blue light indicates that these data obtained at gain step 0 must be multiplied by 3.09 to put them on the same scale as the Pioneer 11 polarization-mode observations. An additional uncertainty is present in the intensity scales of Pioneer 10 polarization maps 02, 03, and 04 because these data were obtained while the Pioneer 10 instrument sensitivity was decreasing with time due to exposure to the large energetic particle flux, and calibration lamp data were not obtained at sufficient time resolution to follow the decrease at these times (see Paper I). IV. OVERVIEWOF POLARIMETRY COMPARED TO A REFLECTING-LAYER MODEL
A. Comparison o f the STrZ and SEBn A simple model with few free parameters has great virtue as a general introduction to a complex subject. For this reason, we begin the analysis of the Jupiter polarimetry
51
with the analysis of a single high-quality polarization map at a phase angle of 98° using a simple reflecting-layer (RL) model. The model consists of a polarizing Rayleighscattering layer--not necessarily pure gas--above a depolarizing Lambert surface. The free parameters are the optical thickness and single-scattering albedo of the Rayleigh layer and the reflectivity of the " c l o u d " surface. While it is known from the outset that the model does not match the photometry at all phase angles, it does fairly well at a single phase angle. Other phase angles would need different effective cloud reflectivities to reproduce the effect of the actual cloud phase function. In addition, while such a model is known to fail in reproducing ground-based observations of the center-to-limb variations (CTLV) in the intensity in molecular absorption bands, the intensity of light emerging from the atmosphere at small phase depends on scattering properties at moderately large scattering optical depths (z - 10). The observed polarization at large phase, on the other hand, is formed essentially in single scattering and depends on the polarizing properties of the atmosphere above the level with optical depth -½. Unfortunately, because the gas layer above Jupiter's clouds is known to contain a thin haze, the gas optical depth in the RL model overestimates the actual pressure level at the cloud tops. Section V explores the question of the actual cloud heights with a model that explicitly includes the haze. Since the Rayleigh-scattering optical depth of the gas is much larger in blue light than red, the blue data are expected to be more sensitive to the location of the cloud top and will be discussed first. Figure 6a shows a small but definite increase in the polarization of belts compared to zones in blue light. This effect could be caused by two mechanisms. The higher belt polarization is due at least partially to the fact that the belts have a darker underlying cloud and so a smaller dilution of the polarized light scattered from the Rayleigh region by unpolarized light scattered from the de-
60
I
I
I
I//I
I
PHASE=36°
I
I//
I
I
PHASE=58*
I
PHASE=48* -
40
20 LATITUDES
T
1 I00
>l--
Z LtJ l-Z
l
I
60
~, 0.95 0.95
a ILl
-18"
I 140
TO
-'21 °
I 180
I// I 220 60
7"1
I
HAZE:
//
I I00 ROLL I
I
GAS :
"rM ~H 0,25 0 . 7 5 0 . 2 5 O,75
(~R 0.997 0.879
I 140
I z, 180 560
I
//
520
I
480
I
I
CLC~JOS:
TR 0.04 0.08
OJ¢ 0.997 0.997
gT fl 92 0 . 8 0 0.9~8 - 0 . 7 0 RZ 3
F, 62.7 62.5
- -
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I100
PHASE= 67 ° "4 ./
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100"6 500 ROLL
I
600
PHASE=80°'~ /.,1
500
I
!_
400
500
"
FIG. 8. (a) Pioneer l I photometry of the South Tropical Zone at 7 phase angles in red light as marked. The bright limb is toward the left and the terminator is on the right side in each panel. The model shown by the solid line uses a double Henyey-Greenstein phase function with the indicated parameters (taken from Paper I). The cloud particle phase function for the model shown by the dashed lines uses a similar phase function except for a local bump between scattering angles of 120° and 140° shown in Fig. 10 as "RZ3." (b) Same as (a) but in blue light and showing only the double HenyeyGreenstein phase function taken from Paper I with the indicated parameters. (c) Same as (b) but for the SEBn in red light. (d) Same as (b) but for the SEBn in blue light. 52
JOVIAN PHOTOMETRY AND POLARIMETRY 60
I
I
I
I
I
PHASE=36 °
I
I
I
53 I
PHASE=38 °
.
I
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40
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;
i
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20
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HAZE: "rH gH 60 -•. 0.7'5 0.95 0.25
I
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I
II
fl g2 0.938-0.65
540
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I
I
F= 73.!-
--'I
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20
40
80
120
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,;,I
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PH/SE=67°I 500
ROLL FIG. 8---Continued.
600
// 1 300
I 400
54
SMITH AND TOMASKO ,<---PHASE ANGLE a
140 I00 TIT . .
T >l-_z
2.C
60 .
.
20 IT't
+I
WATER DROPLETS
ICE PLATES
STrZ RED
g, =0.80 f =0.938
60 90 120 150 30
610 910 1210 1510 "310 610 910 120 150 180
SCATTERING ANGLE ( ° ) ~
F16.9. (left) Solid curve: the double Henyey-Greenstein phase function from Paper I for the STrZ in red light on a linear scale. Dashed line: the bump introduced for the model shown by the dashed line in Fig. 8a. The Pioneer 10 data used to derive the solid curve were obtained at the phase angles marked by arrows at the top of the figure and by vertical lines on the curve. The locations of the Pioneer 11 data are marked at the bottom of the figure. Phase functions for ice plates and water droplets as measured in one polarization state by Liou et al. (1976) are also shown. Note the similarity between the HenyeyGreenstein function and the curve for "ice plates." *---PHASE ANGLE a 180
polarizing base cloud. Additionally, the polarization in the belt may be changed by a different effective thickness of the polarizing region above the belt clouds. We will apply the reflecting-layer model to estimate the change in cloud heights necessary to explain the observed polarization differences between the zone and belt. Starting with the STrZ and the singlescattering albedo of the overlying medium (primarily Rayleigh-scattering gas) set to 1.00, it is possible to find values of cloud reflectivity and optical thickness of the overlying Rayleigh-scattering medium (0.762 and 0.11, respectively) that match the brightness and positive polarization observed at the center of the disk. It happens that the observed increase in polarization toward the limb and teminator is closely fit also, as shown by the short-dash curve in Fig. ll. This gives some confidence in the simple model since no adjustments were made to force this agreement. The addition of a modest amount of absorption in the gas above the cloud (e.g., reducing the singlescattering albedo from 1.00 to 0.90) makes
Ill
140
I00
60
20
TlI . . . .
TIlT
2.0
g,: 0.80 T
1.0
o_ 0.0
RZ3
-I.0
RZ2~\ O- = J.28
-2.0
30
6'0
/
/ \
90
/
120
150
180
SCATTERING ANGLE ( ° ) - ~
FIG. 10. Phase functions (on a log scale) used in models of the Pioneer i 1 photometry of the STrZ in red light (at the scattering angles marked by arrows along the bottom of the figure) together with the standard deviations of the fits. The phase functions containing the modifications labeled RZ1 and RZ2 fit about as well as the standard Henyey-Greenstein function alone, while the modification which includes a bump similar to a rainbow for spherical particles (labeled RZ3) fits somewhat worse. The RZ3 fit to the data is shown in Fig. 8a.
JOVIAN PHOTOMETRY AND POLARIMETRY 60
/ /
/
/
,/ /
40
\
/
i./. SEBn
..~ -
-STrZ
~-ec (u
-a._.,Ik ....
.
.
.
.
. . . .
• ....
"'-"
3;o . . . .
. . . .
4;o . . . .
Spacecraft Roll N u m b e r ~
FIG. l 1. Observed degree of linear polarization in map A2 at a phase angle of 98° in blue light. The triangles are the observed points for the latitude of the STrZ and the circles are for the SEBn. The bright limb is on the left side and the terminator is toward the right. The short-dash curve is for a model consisting of an optical depth of 0.11 of conservative Rayleigh scatterers above a Lambert surface of reflectivity 0.762 computed at the scattering geometries of the STrZ. The solid curve shows the effect of changing only the scattering geometries in the model to those appropriate for the SEBn data points. The dot-dash curve shows the effect of also changing the reflectivity of the Lambert surface to reproduce the observed brightness of the SEBn. The polarization that would be observed from such a model if the Lambert surface were placed at a pressure level of 2 bars in the belt is shown by the long-dash curve.
55
particles compensates for the different amounts of gas above the clouds. This seems unlikely. At this point it is interesting to consider the polarization which the model would predict if the ammonia cloud were absent over the belt so that the cloud top occurred at a pressure level as great as 2 bars. This possibility has been suggested by Owen and Terrile (1981) among others based on the high brightness temperature of the belts as seen as 5 /zm in the infrared. The upper curve in Fig. 11 shows that nearly 30% positive polarization results from 2 bars of gas for blue light (corresponding to a Rayleigh optical depth of -½). Under this assumption, any of the so-called "hot spots" seen in the infrared should also show up as strong polarization features in the equatorial regions. None have been observed. This implies that the upper (ammonia) cloud layer exists at nearly the same pres-
PRESSURE (rnb)
0
,
15
200 ,
,
400 600 REFLIECTIVITY'0.51,~/70.55'
_
a negligible difference for such a thin gas layer. The next step is to repeat the procedure for the SEBn. The solid curve in Fig. I1 shows the result of changing only the scattering geometries and leaving the gas layer thickness and the albedo of the underlying cloud the same as for the STrZ. The dotdash curve shows the effect of lowering the cloud reflectivity to 0.55 to fit the measured belt intensities. No changes are necessary to the cloud heights in order to obtain a good fit. The relationship between the optical thickness of the overlying Rayleigh layer and the polarization of the belt and zone at the center of the disk is shown in Fig. 12. The clouds in the two regions could be at appreciably different levels only if the intrinsic polarization produced by the cloud
SEBn
_/.~).x,~ _
_
800
/0,;,,
--/~jo.az
,////__ ~,~:f_,~.
-
2 ~ 5 ./
0
r
i 0.05
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i o.lo BLUE
OPTICAL
i 0.15
0.20
DEPTH
FIG. 12. The polarization at the center of the disk in the STrZ and the SEBn in blue light as a function of the optical thickness of a conservative Rayleigh-scattering medium above a Lambert surface of various reflectivities as labeled (98° phase). If the Rayleigh-scattering medium is assumed to be pure gas, the total pressure at the Lambert surface is indicated along the top of the figure. The observed polarizations at the center of the disk in these two regions are indicated by the horizontal lines. Notice that the different polarizations observed for the two regions occur for nearly the same amount of gas above the STrZ and SEBn clouds when the different reflectivity of the clouds in these regions is taken into account.
SMITH AND TOMASKO
56
SPACECRAFT ROLL
FIG. 13. Similar to Fig. 11 but in red light. The models indicated by the solid curves are for the indicated optical depths of conservative Rayleigh scatterers above Lambert clouds with the labeled reflectivities. Note the need for a progressively greater optical depth of the positively polarizing medium to reproduce the observations as the limb and terminator are approached.
sure level throughout the equatorial and temperate regions, but that it nevertheless can have a high diffuse transmission at 5 pm. This conciusion will be discussed further in Section VI. By applying the same technique to the analysis of the red observations, it is possible to compare the ratio of optical thicknesses computed at the two wavelengths to that for a pure Rayleigh-scattering gas. The comparison will be significantly different from the pure gas case if haze aerosols are important. Actually, we would predict that haze aerosols should be relatively important in red light since they are thought to have optical depths (scaled for isotropic scattering) of several hundredths (see Paper I), comparable to the Rayleigh-scattering optical depth of the gas above the clouds in red light. Starting again with the STrZ and setting the cloud reflectivity to 0.71 to match the intensity, the optical depth of polarizing material necessary to match the polarization at the center of the
scan is 0.02. However, as is seen in Fig 13, the center-to-limb variation is incorrect. Because of the extremely small optical .depths of the polarizing layer, the scattering model is now very sensitive to slight polarizing effects of the base cloud layer. It may well be that there is a small negative polarization produced in the base cloud which would require a thicker Rayleigh layer and, consequently, produce a larger increase in polarization from the center of the planet toward the limbs. An indication of the thickness of the Rayleigh layer above the cloud top comes from the optical depth necessary to fit the polarization at the limb. This is seen to be on the order of 0.04. The SEBn is similar: the polarization is slightly higher and the reflectivity is a little less (0.64) such that the same optical thickness is required. There is some evidence that the cloud polarization needs to be slightly negative in the belt also to match the center-tolimb variations. Again an optical depth of 0.04 is needed to match the large limb polarizations. The red data suggest that two types of polarizers are necessary: (a) an optical depth of about 0.04 of Rayleigh-scattering material above the base cloud to produce the large increase in polarization at the limb and terminator; (b) a slightly negatively polarizing base cloud to reduce the polarization at the disk center to the observed value and to shape the center-to-limb variation properly. From the thickness of the top layer in red and blue a rough estimate of the optical thicknesses of haze and gas in this region can be made. The ratio of gas optical depths is known from Rayleigh theory; therefore,
= (2)4 = cC?J4
= 4.48
where b and r signify blue and red. The haze particles are known to be strongly forward scattering (Paper I). If we assume that
JOVIAN PHOTOMETRY AND POLARIMETRY 50 ~0
40
40
50
60
70
80
90
/x (b.)
.mr~"/i'/k A ,
30
~'~'xJ a.A
I 20
+~:
x/
-'~"
x-'¢
a-z'jr'~ /x,x' c~ I0 NORTH REDLX
,.,.,-"
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/÷-+-+ p
xs
BLUE~/
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-
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+/ S
p~t~"°" BLUE o.o~
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.~0 to
SOUTH
-30
(0.1
+/+'÷ i4~+-+-+/
-40
l
-50
i
-60
-70
-dO
0 -90
LATITUDE
FIG. 14. T h e a v e r a g e p o l a r i z a t i o n in a 20 ° w i d e interval in l o n g i t u d e a s a f u n c t i o n o f l a t i t u d e in m a p A2 at a p h a s e a n g l e o f 98 ° in r e d a n d blue light as m a r k e d . (b) S a m e as (a) b u t for t h e n o r t h e r n h e m i s p h e r e in m a p B3 at a p h a s e a n g l e o f 82 °.
the haze particles are large enough to have about the same cross section in red and blue light, "/'haze = "J'haze r = T b aze,
then '/'haze =
1.3r[otal-
0.3"rbotal •
Substituting the total optical depths found above we find the haze to be equivalent in terms of polarization to an optical depth of 0.02 of Rayleigh-scattering gas. The actual optical depth of the haze can be estimated by dividing by 1 - g, where g is the asymmetry parameter found to be about 0.75 in Paper I. Therefore, the haze optical depth is estimated to be about 0.08 or a little greater if the haze particles produce singlescattering polarizations that are somewhat less than occur in Rayleigh scattering. The optical depth of the gas above the cloud in the blue is 0.11 - 0.02 = 0.09 which corresponds to a pressure at the cloud tops of 360 mb. Because of the number of assumptions made to obtain this value, we expect a more meaningful pressure to come from the more detailed models in the next section.
57
Even so, based on a simple reflectinglayer model applied to both a belt and zone in the red and blue we can draw several preliminary conclusions. The belt and zone cloud tops are at nearly the same pressure on the order of 360 mb. They both have an optical depth of about 0.1 of strongly polarizing haze mixed into the clear gas. And finally, on the basis of the center-to-limb variations the particles in the base cloud are seen to produce slightly negative polarization in red light and are fairly neutral in the blue. The increased polarization of a few percent observed in the belt relative to the zone in the blue can be entirely accounted for by the increased absorption in the base cloud which reduces its depolarizing influence. In no circumstances can the belt cloud top be as deep as 2 bars.
B. The Polar Regions The remarkably high polarizations observed in the polar regions can also be compared with the reflecting-layer model. Table IVC and Fig. 14a show the averaged polarizations and scattering geometries in 2 × 20° latitude-longitude bins for a north-south scan from latitude 40°S to the south pole in map A2 at a phase angle of 98 °. If the planet behaves as a Lambert surface, the range of reflectivities in this scan is fairly narrow, varying only from 0.6 to 0.7 in either color. In these preliminary models we assume that the reflectivity of the base cloud can be approximated as a Lambert surface of reflectivity 0.63 in the blue and 0.67 in the red (the average values in each color) independent of latitude. The larger polarizations in the polar regions will require thicker polarizing layers above the base cloud than the equatorial regions, and therefore the singlescattering albedo of any gas-aerosol mixture above the Lambert surface will be more important. In order that the intensities continue to fit the observations independent of the choice of optical depth of the polarizing layer, the single-scattering albedo of this region is chosen to give the observed brightness in the semi-infinite
SMITH AND TOMASKO
58
1 O,g E x
B D
008
5
006
_
./
O.l-
2
\x,
J ‘%
:
. 0°4. 002.-0
POLAR CAP+
i .
UV DARKENING i &j,..:.:: :.'r
MAGN%
POLE
LAMBERT SURFACE 0 01 -40
-50
-60
-70
-80
-90
LATITUDE
FIG. 15. The optical thickness of a Rayleigh-polarizing layer above a Lambert cloud necessary to fit the data in Fig. 14a as a function of latitude in blue or red light as marked. The latitudes of the onset of polar darkening in the ultraviolet and the bright polar hood in the strong near-infrared methane bands as well as the latitude of Jupiter’s magnetic pole are indicated for reference.
limit. This means that whether the upper layer is thin, so that the Lambert surface dominates, or thick enough to reflect the majority of the light, the calculated intensity is essentially unchanged. We use values in the blue and red of 0.964 and 0.983 for the single-scattering albedos of the upper layer. By calculating a series of models with the optical thickness of the upper layer as the remaining free parameter, it is possible to assign an optical depth to each latitude bin such that the observed polarization at that latitude is reproduced by the model. The plot of optical thickness of the Rayleigh region in each color as a function of latitude for the south polar region is shown in Fig. 15. Because the optical thicknesses shown in Fig. 15 are the equivalent Rayleigh-scattering optical depths of haze plus gas in each color, the interpretation of the figure is somewhat complex, and more detailed analyses are required to extract separate constraints on haze thickness and polariz-
ing properties as a function of latitude in each color. Nevertheless, because the haze aerosols are known to be highly polarizing at low latitudes from the increase in polarization toward the limb and terminator in red light, the large increases in polarization toward the poles shown in Fig. 15 for red light can only result from a greater optical thickness of the haze aerosols at high latitude. The figure shows the required red optical thickness of the haze reaching a value as large as 0.5 by 75”s latitude. A haze this thick produces about as much polarization as can be obtained from highly polarizing particles even if they have an arbitrarily large optical depth. The decrease in polarization toward still higher latitudes could be due to an increase in particle size rather than a true decrease in haze thickness. The Rayleigh-equivalent thickness of the aerosols in blue light must be estimated by subtracting the Rayleigh optical depth of the gas above the clouds from the values given in Fig. 15. Because the planet has been observed to become very dark in the ultraviolet for latitudes nearer to the pole than 48”s (West et al., 1981), it is natural to associate the increased polarization at high latitudes with an increased thickness of polarizing aerosols rather than an increased pressure level for the cloud top. (Note that the Rayleigh-equivalent optical depth of 0.5 in red light would require the atmosphere to be clear to a pressure level greater than 9 bars in the polar regions-a situation precluded by the observations of low albedo in the ultraviolet and high albedo in strong methane bands near the poles.) If the cloud top is assumed to occur at the same level at high latitudes as in the STrZ and SEBn, we can subtract about 0.1 from the blue optical depth values of Fig. 15 to estimate the Rayleigh-equivalent optical depth of the aerosols in blue light. Even after this correction, this Rayleigh-equivalent optical thickness of the aerosols remains larger in blue light than red light at latitudes between about 50”s and 65”s while the opposite is true at higher latitudes. This could be due to a
JOVIAN PHOTOMETRY AND POLARIMETRY gradual increase in the size of the aerosols with increasing latitude. The aerosols could be sufficiently small to be highly polarizing in both colors at latitudes less than 65°S or 70°S. The cross section in blue light of these aerosols would be somewhat greater than in red light, and the equivalent thickness in Fig. 15 would be greater in blue than in red. At higher latitudes, however, the particles could be slightly larger, and the single-scattering polarizing properties of the particles would begin to decrease in blue light before they decreased in red light due to the larger size parameter in the blue relative to the red. The optical depth of the aerosols reaches a Rayleigh-equivalent value of about 0.1 by a latitude of 50°S. This corresponds to a value of 0.5 for the optical depth for forward-scattering particles with an asymmetry parameter of 0.75, and along the slant path seen from the Earth, the scattering optical depth in the blue would be about 0.7. Any appreciable component for the imaginary index could serve to significantly darken the planet in the ultraviolet at latitudes greater than 50° as is observed. The aerosols are seen to produce bright polar hoods in strong methane absorption bands at latitudes greater than about 70° (West, 1979a; West and Tomasko, 1980). Part of the reason for the brightness in the polar hoods is the rise in the level of the aerosols to pressures of a few tens of millibars compared to pressure levels of roughly 100 mb at low latitudes. However, it is also necessary for the aerosols to have a significant optical depth to reflect the observed intensity in these bands. The red Rayleighequivalent optical depths are given at about 0.3 and 0.5 at latitudes of 60°S and 70°S, respectively, in Fig. 15. As seen from the Earth, the slant-scattering optical depths (presumably almost entirely due to aerosols rather than gas) at these latitudes correspond to 0.6 and 1.4, enough to brighten the planet appreciably in strong absorption bands. Further, if the asymmetry parameter is still as large as 0.75 for the haze aero-
59
sols at these latitudes, these optical depth estimates could be four times larger, easily giving the observed brightening. Because the onset of the polar hoods in the methane band data depends on both the pressure level of the haze and its thickness, a detailed estimate for the latitude of this transition from the simple model shown in Fig. 15 is not possible. Nevertheless, the observed polar hood structure seems qualitatively consistent with the simple model of the polarimetry at high latitudes given in Fig. 15. Finally, Jupiter's magnetic pole is found at a latitude of about 80°, about the latitude at which the equivalent optical thickness of the aerosols reaches a maximum. It has been suggested in the past that the aerosols which make the planet dark in the ultraviolet might be associated with energetic particle impact, and such an association could be related to the correlation between the magnetic pole and the location of maximum aerosol polarization seen in the Pioneer data. V. POLARIZATION MODELS WHICH I N C L U D E A HAZE LAYER
A. Analysis o f the STrZ For a number of reasons, it makes sense to begin a more detailed analysis of Jupiter's cloud and haze layers with a consideration of the South Tropical Zone. This zone is a broad, well-defined feature that has been observed for many years (Peek, 1958). It appears relatively unchanged between the times of the Pioneer 10 and 11 encounters and is well resolved on five separate polarization maps spanning phase angles from 43 ° to 117°. Aside from the nearby Red Spot, the zone is essentially free of smallscale features at the resolution of the Pioneer IPP. The Voyager high-resolution images (Smith et al., 1979) do show some small-scale structure in the zone, but the contrast of these features is quite low and the zone is the most nearly horizontally homogeneous region on the planet. Paper I presented a horizontally homogeneous cloud model derived from Pioneer 10
60
SMITH AND TOMASKO
high-resolution (0.5 x 0.5 mrad) photome- ization rises steeply toward the limb and try. While this analysis yielded constraints terminator, we know that the haze particles on the shape of the single-scattering phase must be highly polarizing. We parameterize function, little information was obtained on their polarizing properties by a constant the vertical distribution of the clouds be- times the single-scattering polarization procause the data refer to continuum spectral duced by Rayleigh scattering. regions. One exception was the requireThe polarizing properties of the base ment that a bright, forward-scattering aero- cloud in the model must also be considered. sol haze exists relatively high in the atmo- We expect that there will be some compensphere. The optical thickness of the haze sation between the polarization of the base was estimated to be on the order of a few cloud and the gas above in the sense that it tenths at pressure levels of about 100 mb or may not be possible to uniquely determine less. Other studies, such as observations in either quantity from the polarization obserthe ultraviolet by Voyager (West et al., vations alone. If the cloud is assumed to 1981), confirm the existence of this haze at have its top at a pressure level of some 500about the pressure levels estimated in Pa- 600 mb, the cloud particles are required to produce strong negative polarization to per I. As outlined in the Introduction, several compensate (Stoll, 1980). Recent measurecloud layers are predicted beneath the level ments of the single-scattering polarizing of the haze. An ammonia ice crystal cloud properties of ammonia ice crystals grown in is expected to form with its base near a a laboratory cloud chamber show quite pressure level of about 600 mb. Estimates modest polarizations of less than -10% for the optical thickness of this cloud range (Holmes, 1981; Stahl and Tomasko, 1984). from 2 (West, 1979b) to more than 10 (Sato We prefer to begin by assuming that the and Hansen, 1979). Other cloud layers exist ammonia cloud is unpolarizing, and solve at still deeper levels, but because the polar- for the pressure level of the cloud top. If ization at large phase angles results essen- this level seems unreasonable in light of the tially from single scattering, the thickness many other studies of Jupiter's cloud, we of the ammonia cloud is sufficiently large to can introduce small amounts of polarization prevent the deeper levels from influencing up to the amount measured in the existing laboratory measurements. We would prefer the observed polarization. In this section we consider models for the to avoid introducing clouds which have poPioneer polarimetry which are slightly larizing properties many times those meamore complex than the very simple model sured in the laboratory. The most severe discussed in the last section. We consider a test of the assumption of an unpolarizing model with four layers: clean Rayleigh- base cloud will be in the red models where scattering gas down to a pressure of Ph; a the optical depth of the gas is nearly negligiphysically thin haze layer of optical thick- b l e - i f the base cloud makes a significant ness ~'h, single-scattering albedo 05h, and a contribution to the total polarization, then phase function taken from paper I; another there may be insufficient leverage for adlayer of Rayleigh-scattering gas down to the justments in the thin layer of gas and haze cloud top at a pressure of Pci; and a semi- above to match the observations. The infinite cloud with a phase function as given models consisting of gas over a Lambert in Paper I. In addition to the two pressure surface described in the last section suggest levels and the optical thickness of the haze, that the base cloud polarizations are reathe single-scattering polarizing properties sonably small and perhaps slightly negaof the haze and the cloud both need to be tive. The upper haze layer is thought to be specified as functions of scattering angle. composed of hydrocarbons which result Because we know that the observed polar-
JOVIAN PHOTOMETRY AND POLARIMETRY from photochemical reactions involving methane. The exact composition of these aerosols and their polarizing properties are presently unknown, although if they are similar to the aerosols on Titan (see Tomasko and Smith, 1982) they may be quite strongly polarizing. For Jupiter, there will be a trade-off between the polarizing properties of the haze and the optical thickness of the haze layer. The model polarizations could be increased either by increasing the single-scattering polarization produced by the haze particles or by increasing the optical thickness of the haze layer. Based on experience with Mie scattering and scattering by prolate spheroids, the particle cross sections and therefore the optical thickness of the haze layer will be one to four times larger in the blue than the red passband and the polarization can be expected to be larger in red than blue light. With this introduction, we can begin to fit polarization models to the blue observations using three independent variables: the pressure level of the thin haze, the pressure level of the cloud top, and some, as yet, undetermined combination of optical depth and polarization in the haze. At the onset the base cloud is assumed to be completely depolarizing. To define these variables we will make use of three categories of observation: the central polarization of the 43 ° phase observation (map 01) which may be expected to be sensitive to the total gas abundance above the cloud; the central polarization of the 117° phase observation (map AI) which is likely to be most sensitive to the haze properties; and, finally, the center-to-limb variation of all the observations which will depend on the pressure level of the haze. Let us illustrate these three steps in greater detail starting with the pressure level of the cloud. The basic model is the best fit for the zone in the blue from Table III in Paper I which includes no polarization in either the haze or the cloud. The models will use the optical depths of the gas as free parameters, but it is a simple procedure to convert to pressure once the
61
composition of the gas layer is specified. With a basic composition of 90% H2 and 10% He and an effective acceleration of gravity of 2400 cm/sec z we adopt a Rayleigh-scattering optical depth of 0.025 in the blue (0.44 ~m) and 0.0054 in red (0.64 ~m) per 100 mb of gas. The layer doubling and adding technique is used to evaluate the intensity and polarization of light scattered at the locations given in Table IV (cf. Tomasko and Doose, 1984). Figure 16 compares the best model of Paper I with the polarization data for the STrZ in blue light. The base model, Pd = 680 mb, gives too much polarization. Following the procedure outlined above, the total pressure of gas above the cloud is reduced until the central polarization at 43 ° phase is matched. Judging from the figure this will 301
I
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0
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,
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zoo
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, A2
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360
460
~oo . . .400 . . . . . 44060o
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6~o
6~o
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FIG. 16. Points: observations of the linear polarization of the STrZ of Jupiter in blue light at the phase angles of the indicated maps. The bright limb is on the left and the terminator is toward the right in each panel. The curves are model calculations for the structure s h o w n which includes a nonpolarizing base cloud having a double H e n y e y - G r e e n s t e i n phase function taken from Paper I above which is a physically thin layer of haze particles embedded in a region of conservative Rayleigh-scattering gas. The haze particles have a single H e n y e y - G r e e n s t e i n phase function with g = 0.75. In this figure the haze particles are taken to be nonpolarizing and the pressure level of the base cloud is varied. Values of the other model parameters are given in Table V.
62
SMITH AND TOMASKO J
MAP:
01
A3 rl=o.oI TH=0.125
r~=o.o7 Poq~=o:% - - - - 0.50
POL=O
ic
0.75 - - - - -
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g 260
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i
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ic
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i
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c
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r~o
6~0
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FIG. 17. The same as Fig. 16 but with the pressure levels of the haze and base cloud fixed and the polarizing properties of the haze particles taken as various fractions (shown) times the polarization produced in single Rayleigh scattering.
occur for total gas optical depth (7"1 + 7"2) of about 0.08, or P = 320 mb. Notice that the larger phase angle observations are very sensitive to this value and all require additional positive polarization from the haze. Fixing the cloud pressure at 320 mb, the haze is made to be positively polarizing as seen in Fig. 17. Since we do not know the variation of single-scattering polarization with scattering angle, the Rayleigh shape has been used throughout this section times a constant Polh which must be in the range - 1 -< Polh --< + 1. There are not enough constraints in the observations to solve for the exact shape of the polarization function. The polarization of the haze has little effect on the 43 ° phase scan justifying the choice of independent parameters. Four different haze layers are shown in the figure each with an optical depth of 0.125 but with varying degrees of positive polarization. The optimum choice at the large phase angles seems to be a little greater than 0.5 times Rayleigh. A choice of Polh = 0.6 fits the central polarizations of the five data sets remark-
ably well considering that only two parameters have been varied. Our final independent parameter, the pressure level of the haze, can now be adjusted without disturbing the fits at the disk centers. Figure 18 shows how the center-to-limb profiles change as the haze layer descends toward the main cloud. We estimate that an optical depth of 0.03 above the haze gives the best fit to all the data sets and corresponds to Ph = 120 mb, in reasonable agreement with the uv data. An important test of this model is whether it can simultaneously fit the red polarization data. There are three maps in the red and only one degree of freedom left in the model to fit the data, the ability of the haze to polarize red light. Since an increase in either the haze polarization or optical depth of the haze can cause a larger polarization in the reflected light, either one or both can be varied to fit the red data. The large haze polarization in the blue leads us to believe, based on experience with Mie calculations, that it is likely to be even larger in the red so we set Polh = 0.9 and use the optical depth as the only adjustable parameter. Figure 19a reveals that the fit is
i
30
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FIG. 18. The same as Fig. 17 but with the polarizing properties of the haze particles fixed and the pressure level of the haze varied as shown.
JOVIAN PHOTOMETRY AND POLARIMETRY 30
I
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FIG. 19. (a) Similar to Fig. 18 but in red light. The models have the pressure levels of the haze and cloud fixed at the levels determined from the blue polarimetry (the long-dash line in Fig. 18), but with various optical thicknesses of the haze in red light. The haze is taken to polarize 90% as much as for Rayleigh scattering in each single scattering. (b) Same as (a) but for a base cloud which polarizes as -0.05 times that for Rayleigh scattering in each single scattering.
very good for a haze optical depth of 0.0625. There is agreement to within a percent of polarization everywhere; however, map A2 shows that the center-to-limb variation is not quite as large as observed. Because the total optical depth (gas plus haze) above the base cloud is only 0.08, the resultant polarization is very sensitive to small polarizations in this cloud layer. A slight negative polarization here, Pold = -0.05, can correct the center-to-limb variation (see Fig. 19b). In the reflecting-layer model of the previous section we came to the same conclusion based on an analysis of map A2 alone.
B. Analysis of the SEBn Now that we have a detailed model which satisfies all the Pioneer data for a zone, it is natural to ask what aspects of the model need to be changed for the model to fit the available belt data. It is clear that the single-scattering albedo of the base cloud needs to be decreased to match the ob-
served reflectivity (I/F) of the belt. The simple models of Section IV lead us to suspect that the pressure level of the cloud will remain similar to that of the zone, but what about the vertical location and characteristics of the haze? Following the same procedure used in the reflecting-layer model, the first step is to change only the scattering geometries to those of the SEBn. Figure 20 shows that the resulting polarizations are a few percent low at all phase angles. The next step is to simply decrease the single-scattering albedo of the cloud particles until the observed intensity is reached. Models with several different albedos are shown in the figure in order to illustrate the sensitivity to this parameter. The intensities are best matched for o3d = 0.98 which is already an acceptable fit to the data. The SEBn data are nearer the limb than those for the STrZ and suffer more from foreshortening and contamination by neighboring features. Also, the higher resolution photometry maps taken at nearly the
64
SMITH AND TOMASKO 30
[
i /.'1 MAP:
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FIG. 20. Similar to Fig. 16 but for the latitude of the SEBn. The models u s e the same single-scattering properties as for the STrZ except for the different values of the single-scattering albedo of the base cloud as shown.
same time give evidence for features within the latitude band of the belt while the zone is very uniform. For these reasons, the uncertainties in the SEBn data are on the order of 1-2% in the polarization, a few times larger than the corresponding uncertainties in the zone data. The STrZ model corrected for the proper belt albedo gives a particularly close fit to the map 01 data at 43 ° phase. This is the phase angle least sensitive to the thin haze. Figure 21 illustrates the sensitivity of the belt model to large changes in the haze optical thickness, particularly in map A1 at the largest phase angle. The best fit appears to be for Zh about 0.06 somewhat less than in the STrZ. Note that the exact center-tolimb profile is not matched for map A2. We believe that this is due to a local feature such as a slightly different cloud albedo or a local variation of the haze layer at this Iongitude in the SEBn. Overall, the zone model apparently will be quite acceptable in the belt with only the required change in cloud albedo (that is, a compositional change) and, perhaps, a thinning of the
haze layer. As a final check on the model, the fit to the red SEBn data is shown in Fig. 22. There is actually very little difference between the red polarization in the belts and zone, and what there is can be accounted for by the slight changes in red albedo between the two regions. The enhanced 5-/zm emission of belts relative to zones has been interpreted as arising from a cloud deck at a pressure level of 2 bars or more (Terrile and Westphal, 1977). This would suggest that the base cloud in our belt model may be optically fairly thin in the visible as well, with possibly a large fraction of the solar radiation penetrating to the lower cloud seen in the infrared. To constrain the properties of a two-cloud model with haze, we ran a series o f models with different values for the optical thickness of the upper cloud to see how thick this cloud needs to be to continue to mask the gas layer below it. The blue data from the 98 ° phase map were used because of their sensitivity to the optical thickness of the gas. The exact vertical structure and model results are shown in Fig. 23. Note that for optical depths of the upper cloud less than 1 in the blue the polarization rap30
i;' MAP:
f
i
01
A3
--~
:003
20 POL:O, ~CJ :0.98
_l ,0
j ~
" ....
___
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,~o
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0 3bo
4;0 % 0
ROLL~
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&o"
6~6
6;0
720
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FIG. 21. Same as Fig. 20 but for various values of the optical thickness of the haze with the single-scattering albedo of the base cloud fixed at 0.98.
JOVIAN PHOTOMETRY
30
#
I
I "fl
I
MAP: A3
65
AND POLARIMETRY
I
I
d/
I
I
A2
- I"I =0 0067 P= 120 mb ~=l=lElq =0.0625 HI~LH= 0.90 X RAYLEIGH P= 3;~0 m b ~ ~m~T2:0"OII P0L = -0.05
AI
I'
SEBn kkl ee"
,;o
3;o ,;o 5;o" 6,~o
2;o"
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~o
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FIG. 22. Same as Fig. 20 but in red light.
idly increases toward 30% while for optical depths greater than 3 an asymptote is reached such that the lower structure makes no contribution to the polarization. In the intermediate region between I and 3 optical depths there is a trade-off between cloud thickness and the polarizing properties of the clouds (the upper and lower clouds were assigned identical properties). Two curves are shown in the figure. The upper curve for depolarizing, or neutral,
TH=0 t 2 5
* 0 536
30
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--.~--TR:O0:
POLH = +0.60 X ROyleigh
,,o: 0:59,
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~--r
clouds (as we have assumed throughout this paper so far) implies that the optical thickness of the upper cloud must be at least 3 if the clouds are neutral, while the lower curve shows that the upper cloud could have an optical thickness as low as 1.5 if the particles in the clouds produced -20% polarization in a single scattering through an angle of 90 °. This is felt to be a rather extreme adjustment to the cloud polarization. Finally, the parameters of the best-fitting polarization models are given in Table V. The phase functions of the base cloud and
R=0.0~
TABLE V
POLcl ; Oo~-020 x Roy.~-~-_~.).).~-)-~, POLcI: 0 ~\ ~/-POLcl = -0.20
"XX~
PARAMETERS OF BEST-FITTING POLARIZATION MODELS
~-
X Royleiqh
Blue
Red observed
j
"~ ~ ~ - ~ . . . . . . . . . . . . . . . . .
polorizoli0n
0 O0
I I.O
210
31.0
t 4.0,
5.0
Tcl0u d
FIG. 23. Computed polarization in blue light for the SEBn near the center of the disk in map A2 at a phase angle of 98° as a function of the optical thickness of the ammonia cloud in the belt. The structure is shown in the figure, and has a lower cloud at a pressure of 2 bars. The solid curve is for clouds that are nonpolarizing, with the dashed curve for clouds that produce - 2 0 % polarization in a single scattering at 90 ° scattering angle and have the same dependence on scattering angle as for Rayleigh scattering. Comparison with the observed polarization o f about 10% indicates that the ammonia cloud in the belt must have an optical thickness of 1.5 or more to mask the underlying gas for realistic single-scattering pobarizing properties.
STrZ
SEBn
STrZ
SEBn
Tga~ o3os
0.0067 1.00
0.0067 1.00
0.03 1.00
0.03 1.00
~'h O3h Polh gh
0.0625 0.95 0.90 0.75
0.0625 0.95 0.90 0.75
0.125 0.995 0.60 0.75
0.06 0.995 0.60 0.75
r~s OSga~
0.011 1.00
0.011 1.00
0.05 1.00
0.05 1.00
gld f~l g2cJ o~d Polcl
0.80 0.938 -0.70 0.997 -0.05
0.80 0.938 -0.70 0.9925 -0.05
0.80 0.969 -0.80 0.995 0.0
0.80 0.969 -0.80 0.980 0.0
Tel
~C
3C
3C
~¢
66
SMITH AND TOMASKO
the haze used in the STrZ are taken from Paper I. Because of the greater evidence for horizontal inhomogeneities in the SEBn than in the STrZ, we have given relatively less attention to deriving details of the cloud structure in the belt compared to the zone. For example, we have used the same double Henyey-Greenstein phase function for the belt clouds as for the zone, instead of using the slightly different parameters for this region given in Paper I. While the belt models of Table V will fit detailed photometry data covering a wide range of phase angles somewhat less well as a result, the conclusions we obtained from the polarimetry would be unchanged if we had used the phase functions actually used in the belt photometry models. The pressure level of the haze has been set using only the polarimetry data, but the photometry data in Paper I require slightly different values for this parameter. These differences are discussed further in the next section; but, in general, the conclusions of Paper I are unchanged by the addition of the polarimetry. They are instead augmented by some constraints on the polarizing properties of the cloud and haze as well as new sensitivity to the abundances of gas above the cloud and haze. VI. DISCUSSION AND SUMMARY
One important objective of this work has been to present the polarization maps of Jupiter obtained by the Pioneer 10 and 11 missions. Detailed measurements of the polarization of the STrZ, the SEBn, and a north-south cut have been presented in the figures and in tables. In addition, we have compared the data for these regions to models and reach several specific conclusions regarding the vertical structure and optical properties of the clouds and aerosols present in these regions. Our conclusions can be grouped and summarized as follows. 1. Pressure Levels o f the Cloud Tops The polarization observations cover a
range of phase angles near 90° where the polarization produced by the gas is very much stronger than that produced by the cloud particles (nearly 100% compared to less than about 10% in a single scattering). Thus, an important feature of the polarimetry data set with high spatial resolution at large phase angles is its ability to discriminate between the effects of scattering by clouds and by gas. This is true at least to levels where the total optical depth reaches a value between ½and 1 where the polarization observed in the multiply scattered light saturates. Because we see no spots with polarization larger than 10-12% in blue light at latitudes less than 40°, we conclude that a cloud of optical depth greater than 1.5 must exist over both belts and zones at a level corresponding to a Rayleigh optical depth of 0.08 (a H2 abundance of 12 km-am equivalent to a pressure of 320 mb). The most recent papers which consider the ammonia cloud to be of finite vertical extent have a cloud extending from a base at about the 630-mb level to a top near 380 mb (Marten et al,, 1981), or possibly even higher (Orton et al., 1982; Sato and Hansen, 1979), in good agreement with this result, if our pressure level is taken as the cloud top. Several earlier papers have used methane band observations to determine the pressure level of the ammonia cloud; however, this level depends on the methane-to-hydrogen mixing ratio for which these authors adopted various values. Adopting a value of 2 x 10 -3, obtained from the Voyager IRIS experiment by Gautier et al. (1982) and accurate to about 10%, gives pressures of about 300 mb from the results of West (1979b) and Bergstralh (1973) and about 200 mb from Wallace and Smith (1977). Buriez and de Bergh (1980) used models of the shapes of the methane bands near I. 1/zm to derive a total pressure as well as a methane abundance (as did Wallace and Smith), and they give a pressure for the upper cloud (again a diffusing sheet) of 260 _ 80 mb in a
JOVIAN PHOTOMETRY AND POLARIMETRY two-cloud model. With the exception of the values determined by Wallace and Smith, these results are reasonably consistent with one another and also with our results. 2. Difference in Levels of Cloud Tops in Belts and Zones In both red and blue light near 90° phase, the polarization of sunlight scattered from belts and zones is very nearly equal with the small differences due primarily to the different reflectivities of the belt and zone clouds. This strongly implies that the cloud tops in both belt and zone regions are reached at essentially the same pressure level. No spots of high polarization analogous to the 5-/xm hot spots are seen in the polarization maps at a spatial resolution greater than that available in 5-/zm maps made from the Earth. The 5-/zm opacity above the region near 2 bars which produces the high 5-~m flux is undeniably less in the belts and hot spots than in the zones; however, significant cloud opacity in the visible (optical depth greater than 1.5) exists in all three features at the level of the upper ammonia cloud. A recent study of the IRIS spectra in the regions of 5 and 45 /.~m by Brzard et al. (1983) is of interest in this regard. These authors point out that the diffuse transmission of the ammonia cloud even in " c l o u d y " regions is as high as 0.70.8 near 5 ~m, and a further increase in this value for "clearer" regions cannot be responsible for enhanced 5-/zm emission. Instead, they require the presence of another cloud at a pressure level near 2 bars to modulate the 5-/zm emission. Because the 5-/zm emission is modulated by clouds at pressures of 2 bars or more, the comparison of 5-/zm maps of Jupiter with visible images of the planet is of limited use in assigning pressure levels for the tops of clouds of various colors seen in visible images, as has been attempted by Owen and Terrile (1981). It is incorrect to associate " b l u e " areas of the planet with Rayleigh scattering. Brzard et ai. cite an example in which a "tawny brown" cloud which
67
has been assigned a pressure level near 2.3 bars by Owen and Terrile produced less emission at 45 /zm than a nearby region which contained no brown cloud, implying that the brown cloud must have substantial opacity at pressure levels where the 45-~m radiation is emitted (less than 1.2 bars). Brzard et al. conclude that the visible appearance of the planet is determined by the colors of the clouds near the ammonia cloud level while the 5-/zm emission depends primarily on the opacity of a deeper cloud layer near 2 bars. 3. Single-Scattering Properties of Cloud Particles Instead of assuming that the top of the ammonia cloud occurred near a pressure level of 600 mb and attempting to find the single-scattering polarizing properties of the ammonia cloud particles as was done by Stoll (1980), we began by assuming that the polarization produced by the cloud particles was relatively small as measured for ammonia crystals and used the data to constrain the pressure level of the top of the cloud. We found that the cloud particles had to be only slightly negatively polarizing (about - 5 % near 90° scattering angle) and that the pressure derived for the clouds was consistent with a variety of other studies of Jupiter. More measurements of the polarizing properties of candidate cloud particles are underway, and should be quite useful for comparison with polarimetry models at a wide range of phase angles. Detailed comparisons of this sort are outside the scope of the present study, except to note that the polarizations of Jupiter's cloud particles need not be nearly so large as in some of the models discussed by Stoll. This work also briefly explored the effects of bumps in the single-scattering phase functions at scattering angles that might correspond to rainbow features from spherical particles. In general, models which contained such features fit the data somewhat worse than the smooth analytic phase functions of Paper I. Models in which
68
SMITH AND TOMASKO
the phase functions in the range of scattering angles from 80 ° to 140° were even flatter than the functions of Paper I fit about as well or marginally better. While the work of B r z a r d et al. (1983) shows that the opacity of the ammonia cloud is not responsible for the 5-~m hot spots, these authors do find evidence for a general correlation between the opacity of the ammonia cloud and the opacity of the deeper cloud which does modulate the 5/zm emission. Thus, while the visible polarimetry [and also other studies in reflected sunlight--see Sato and Hansen (1979) and West and Tomasko (1980)] shows cloud optical depths of at least 1.5 over Jupiter's belts at the level of the ammonia cloud, the diffuse transmission of these clouds near 5 /xm is apparently reasonably high, of the order of 0.7 or more. The known high transmission of the ammonia cloud near 5 ttm has sometimes been taken as implying that this cloud is absent over belts generally, and thus provides negligible optical depth in the visible belts. Furthermore, the lack of infrared spectral features of solid ammonia has been interpreted as evidence for a rather large size (a radius of 30/zm or more) for the particles in the ammonia cloud by Marten et al. (1981) using an analysis based on Mie scattering. The presence of such large particles in the ammonia cloud implies that its optical thickness cannot change very much between the visible and 5/~m. H o w e v e r , such large ammonia particles will be strongly forward scattering at 5/~m, and will have reasonably high single-scattering albedos at this wavelength as well (Orton et al., 1982). Thus the diffuse transmission of the ammonia cloud could be as large as required near 5/xm (about 0.7) and the ammonia cloud could still be moderately thick in the belts. Figure 24 shows the flux transmitted through a cloud of particles having a H e n y e y - G r e e n s t e i n phase function with an asymmetry parameter of 0.8 and various single-scattering albedos as a function of the optical thickness of the cloud. The intensity field incident on the
1.0
i
i
k I
~ 2
i
i
i
i
i
018~ 0.{ "~ 0.'~ 0.2 0.0~
L 0 ' 7 0 3 4 5 OpticoI Depth
h
~ 6
7
FIG. 24. The fractional flux transmission of forwardscattering clouds as a function of their optical depth for various single-scattering albedos. The single-scattering phase function of the cloud particles is taken to be a Henyey-Greenstein function with g = 0.8, and the radiation field incident on the bottom of the cloud is assumed to be isotropic. The transmission is 0.7 or greater for clouds of optical thickness between about 1 and 2.5 for single-scattering albedos greater than 0.9. Thus, belt regions could have ammonia clouds with optical depths as great as 1 or 2 at 5 ttm without violating the observations of the high 5-/zm flux in these regions.
bottom of the cloud is taken as isotropic. The figure indicates that the cloud can have an optical thickness of 1.5 or greater if the single-scattering albedo is 0.95 or larger. The cloud could be even thicker if the ratio of intensities in the upward direction instead of diffuse flux were considered. In any case, this thickness is comparable to the optical depth of the cloud required in the visible from the belt polarimetry, and a model having quite large particles could have fairly high transmission at 5/~m while being quite important at visible wavelengths in studies of reflected sunlight. In this case, the ammonia cloud in the belts would have an optical thickness in the visible as well as at 5/xm of only 2-3, similar to the value preferred by West in his analysis of methane bands. This relatively low value for the ammonia cloud thickness would imply that the lower cloud in the two-cloud models of Sato and Hansen (1979) is nearer to a pressure level of 2-3 bars than their nominal range of 3-5 bars. On the other hand, it has been pointed
JOVIAN PHOTOMETRY AND POLARIMETRY out that small nonspherical particles can have much smaller absorption than spherical particles of similar size (Orton et al., 1982), and it is not completely clear that the ammonia particles must have large size parameters at 5 /xm. If they are relatively small, they will behave as nearly isotropic scatterers at 5/xm, and then they must have an optical thickness of 0.5 or less to give a diffuse transmission as large as 0.7 at this wavelength. This implies a ratio of scattering cross sections greater than 3 between 0.64 and 5 /~m. The particles must have large size parameters in the red to produce the strong forward scattering observed from Jupiter at large phase angles. Adopting a scattering efficiency of 2 in the red implies that the scattering efficiency must be less than z (and the size parameter less than about 2) at 5/zm. This corresponds to a particle radius less than about 1.6 /zm. The Pioneer photometry (Paper I) does require that the particle radius be larger than about 0.3/zm to provide forward scattering. The Pioneer polarimetry cannot rule out particles in the size range from 0.3 to 1.6 /xm radius. In fact, particles of this size would be required if an analysis similar to that of Sato and Hansen (1979)--but for spatially resolved belts--were to strongly require a cloud of optical thickness greater than 2-3 in the visible. Thus, if the constraints on the size of the ammonia particles derived from the lack of features expected for solid ammonia in the infrared continue to imply particle sizes as large as 30/xm when nonspherical shapes are considered, the particles should be fairly forward scattering and have an optical depth of roughly 2 at 5/zm as well as in the visible. On the other hand, if the infrared features of solid ammonia are not present due to an effect which depends on the nonspherical particle shape, then the particles at pressures less than 600 mb would have "radii" from 0.3 to about 1.6 /xm and these belt clouds could have an optical thickness even greater than 3 in the visible and less than - 0 . 5 at 5/zm.
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69
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SPACECRAFTROLLNUMBER~
FIG. 25. L i m b darkening in the S E B n in blue light at 12° p h a s e from Pioneer 10 p h o t o m e t r y c o m p a r e d with the best polarization model s h o w n in Fig. 20 except that the u p p e r (ammonia) cloud is taken to have an optical depth of 3. T h e triangles are the observations, and the c u r v e s are models in which the absorbers are limited to the upper cloud, equally distributed between the u p p e r cloud and a lower cloud at 2 bars, or concentrated in the lower cloud with the u p p e r cloud having the s a m e albedo as in the bright STrZ.
In any case, the "ammonia" cloud isdefinitely present in Jupiter's belts, although perhaps at a somewhat reduced optical thickness than in the zones. If the belt cloud is assumed to be as thin as three optical depths, it is possible to use the limb darkening from the high-resolution photometry data at low phase angles in blue light to discriminate among the possible vertical locations for the belt absorber. Is the absorber responsible for the lower albedo of the belts found in either the upper cloud or the lower cloud alone? Figure 25 shows the limb darkening computed under each of these two extreme assumptions, as well as in the case where the single-scattering albedo is equal in the two clouds. The plot suggests that the required amount of absorption can barely be produced by making the lower cloud completely black when the upper cloud is made as bright as in the zones. Although this case more nearly reproduces the shape of the limb darkening than the case in which all the absorption is concentrated in the upper cloud and the lower cloud is conservative, the case in which the single-scattering albedos of the
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two clouds are equal in the best match to tenths--before a pressure level of about the observed limb darkening. Thus, the ab- 120 mb is reached--is consistent with all of sorber must be distributed over a significant these other observations. optical depth, and neither a bright layer over a thick dark layer nor the opposite ex- 5. Single-Scattering Properties of the Haze treme fits the data especially well. The measurements by Voyager at vari4. Pressure Level of the Haze ous phase angles in the ultraviolet could not The pressure level of the haze was stud- determine the scattering phase function of ied only in our more detailed models of the the haze due to the large optical depth for STrZ and the SEBn. We found the pressure Rayleigh scattering by the gas above. In Palevel of the haze to affect the center-to-limb per I we found that the haze must be relavariations in the polarization, with best tively forward scattering at both red and agreement for a haze at a pressure level of blue wavelengths. In this work we find that about 120 mb in both the belt and the zone. the haze must be highly polarizing above This value is in good agreement with the both belts and zones to produce the large analysis of ultraviolet photometry from increase in polarization from the center of Voyager by West et al. (1981) who require the disk toward the limb and terminator obthe absorption produced by the haze in the served at phase angles near 90°. Stoll (1980) ultraviolet to occur at pressure levels of found a similar result in his analysis of the about 100 mb or more. The preliminary SEBn data and tried to find a size of spherianalysis of photometry obtained by the IUE cal particles which would simultaneously satellite (with an absolute calibration inde- produce the required high single-scattering pendent of the one used by Voyager) by polarization and the strong forward scatterTomasko and Martinek (1978) placed the ing. He concluded that it was barely possihaze beneath 150 to 200 mb of gas, but more ble to find spherical particles that might be complete analysis of these data allow the able to satisfy both constraints if the phohaze to occur anywhere between about 80 tometry at the largest Pioneer 10 phase anand 200 mb (Martinek, private communica- gles were taken to be as dark as the error tion). In Paper I the brightness at large bars allow. Since the time of Stoll's analyphase indicated that the optical depth for sis, the Pioneer and Voyager observations Rayleigh scattering in blue light above the of Titan have become available. On Titan haze in the SEBn was 0.01 (corresponding the requirement that the aerosols be both to 40 mb), but this limit was uncertain by highly polarizing and forward scattering is about a factor of 2. It is not clear that hav- even more severe than on Jupiter. While ing a physically thin large layer deeper than irregularly shaped particles of the proper the 80-mb level would be formally permit- size, shape, and composition to match the ted by the Pioneer photometry data. How- Titan data remain to be found, particles ever, the haze is actually distributed over produced by similar photochemical prosome range of heights, with the photometry cesses could be responsible for the haze on at 150° phase most sensitive to the upper- Jupiter as well as on Titan. most part of the haze. In this regard we point out the eclipse observations of Smith 6. The Boundary between the Haze and the Upper Cloud Region (1980) and Smith et al. (1977) who found Paper I noted the difference in the singlesmall optical depths of haze of the order of a few hundredths extending upward to scattering phase functions of the haze and pressure levels of some tens of millibars upper cloud region, but could not easily diseven at low latitudes. The polarimetry tinguish between models in which the haze result of a haze optical depth of a few extended down to the top of the ammonia
JOVIAN PHOTOMETRY AND POLARIMETRY
71
cloud and models in which the haze was confined to a physically thin layer. Sato and Hansen (1979) also suggested that the haze might extend down to the top of the ammonia cloud in their models of reflected sunlight, but admitted the difficulty of precisely determining details of the distribution of the aerosols near the " s k i n " of the atmosphere. In this work we treated the haze as a thin diffusing sheet at a discrete pressure level above the ammonia cloud, and determined constraints on the "effective" pressure where the haze acts to form the CTLV observed in the polarimetry. We did not explicitly test models in which the haze was allowed to extend down to the base cloud, although models of this sort could possibly be made to work also. Indeed, the ultraviolet data require appreciable absorption at levels significantly deeper than 100 mb unless the av optical thickness of the haze is larger than several and thus probably larger than permitted by observations at visible wavelengths. It is not clear whether the absorption at the ammonia cloud level in the ultraviolet is due to the presence of separate haze-type aerosols mixed in with brighter ammonia cloud particles, or whether the ammonia cloud particles are themselves darkened at the shorter wavelengths. From the point of view of modeling the observed data, fewer parameters are required to specify a pressure level for a haze layer than to specify the haze/gas mixing ratio at each level above the ammonia cloud, and this is the approach we have followed. In any case, because the haze aerosols seem to have less of a back-scattering peak than the cloud particles (Paper I) and because they must produce strong singlescattering polarization near 90 ° scattering angle while the ammonia clouds are neutral or slightly negative, the populations of particles at the 100 mb and the 300 mb levels are clearly different.
Gehrels et al. (1969) anticipated the Pioneer measurements of high positive polarization near 90° phase in the polar regions. However, the new measurements would require the atmosphere to be clear to a depth of 9 bars to provide the observed polarization by molecular Rayleigh scattering alone as suggested by Gehrels et al. to explain their measurements. The observations of Jupiter in the ultraviolet and in strong methane bands since that time preclude this possibility. Instead, we find that highly polarizing aerosols (such as found over the belts and zones at low latitudes) rapidly increase in thickness north of 40°N and south of 48°S to optical depths in red light as large as ½ or more. There is an indication that the effective size of these aerosols also increases with increasing latitude. Detailed analysis of the polarimetry of the polar regions will be more difficult than similar analyses of the belts and zones at lower latitudes because each pole was well observed at fewer phase angles and over a smaller range of scattering geometries from center to limb. For this reason, we reserve more detailed models of the polarization of the polar regions for later work which will include the auxiliary constraints available from photometry in the ultraviolet and in the methane absorption bands.
7. Variations in H a z e Properties with Latitude
AXEL, L. (1972). Inhomogeneous models of the atmosphere of Jupiter. Astrophys. J. 173, 451-467. BAKER, A. L., L. R. BAKER, E. BESHORE, C. BLENMAN, N. D. CASTILLO, Y. P. CHEN, L. R. DOOSE, J.
The
ground-based
observations
of
ACKNOWLEDGMENTS We are indebted to many colleagues for important help in acquiring, reducing, displaying, and analyzing the Pioneer photometry and polarimetry discussed here. T. Gehrels has provided support and encouragement throughout this work. D. L. Coffeen contributed important guidance in the early phases involving the design of observing sequences. L. R. Doose and N. D. Castillo provided the detailed computing support without which this program would not have been possible. We are especially grateful also to the Pioneer Project Office of the NASA-Ames Research Center and the Planetary Atmosphere Section of NASA's office of Space Sciences for their financial support of this work. REFERENCES
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P. ELSTON, J. W. FOUNTAIN, T. GEHRELS, J. H. KENDALL, C. E. KENKNIGHT, R. A. NORDEN, W. SWINDELL, AND i . G. TOMASKO (1975). The imaging photopolarimeter experiment on Pioneer 11. Science 188, 468-472. BERGSTRALH, J. T. (1973). Methane absorption in the Jovian atmosphere. II. Absorption line formation. Icarus 29, 390-418. BI~ZARD, B., J. P. BALUTEAU, AND A. MARTEN (1983). Study of the deep cloud structure in the Equatorial region of Jupiter from Voyager infrared and visible data. Icarus 54, 434-455. BURIEZ, J. C., AND C. DE BERGH (1980). Methane line profiles near 1.1 /zm as a probe of the Jupiter cloud structure and C/H ratio. Astron. Astrophys. 83, 149-162. CALDWELL, J., A. T. TOKANUGA, AND G. S. ORTON (1983). Further observations of the 8 /zm polar brightenings of Jupiter. Icarus 53, 133-140. COFFEEN, D. L. (1974). Optical polarization measurements of the Jupiter atmosphere at 103° phase angle. J. Geophys. Res. 79, 3645-3652. DOLLFUS, A. (1957). Etude des planetes par la polarisation de leur lumiere. Ann. Astrophys. Suppl. 4. [English transl. NASA-TT F-188 (1964).] DousE, L. R. (1976). Light Scattering Properties o f Jupiter's R e d Spot. Ph.D. dissertation, Department of Astronomy, University of Arizona, Tucson. FIMMEL, R. O., J. A. VAN ALLEN, AND E. BURGESS (1980). Pioneer: First to Jupiter, Saturn, and Beyond, NASA SP-466. U.S. Govt. Printing Office, Washington, D.C. GAUTIER, D., B. BI~ZARD, A. MARTEN, J. P. BALUTEAU, N. SCOTT, A. CHEDIN, V. KUNDE, AND R. HANEL (1982). The C/H ratio in Jupiter from the Voyager experiment. Astrophys. J. 257, 901-912. GEHRELS, T., O. L. COEFEEN, M. G. TOMASKO, L. R. DOUSE, W. SWINDELL,N. D. CASTILLO,J. KENDALL, A. E. CLEMENTS, J. HAMEEN-ANTILLA, C. KENKNIGHT, C. BLENMAN, R. BAKER, G. BEST, AND L. BAKER (1974). The imaging photopolarimeter experiment on Pioneer 10. Science 183, 318-320. GEHRELS, T., B. M. HERMAN, AND T. OWEN (1969). Wavelength dependence of polarization. XIV. Atmosphere of Jupiter. Astron. J. 74, 190-199. HALL, J. S., AND L. A. RILEY (1969). Polarization measures of Jupiter and Saturn. J. Atmos. Sci. 26, 920-923. HAYES, D. S., AND D. W. LATHAM (1975). A rediscussion of the atmospheric extinction and the absolute spectral-energy distribution of Vega. Astrophys. J. 197, 593-601. HOLMES, A. (1981). Light Scattering from Ammonia and Water Crystals. Ph.D. dissertation, Optical Sciences Center, University of Arizona, Tucson. LABS, D., AND H. NECKEL (1970). Transformation of the absolute solar radiation data into the "International practical temperature scale of 1968." Solar Phys. 15, 79-87.
LIOU, K. N., R. BALDWIN, AND T. KASER (1976). Preliminary experiments on the scattering of polarized laser light by ice crystals. J. Atmos. Sci. 35, 553-557. LYOT, B. (1929). Recherches sur la polarisation de la lumiere des planetes et de quelque substances terrestres. Ann. Ob. Paris (Meudon) VIII. [English transl. NASA TT F-187 (1964).] MARTEN, A., D. ROUAN, J. P. BALUTEAU, D. GAUTIER, B. J. CONRATH, R. A. HANEL, V. G. KUNDE, R. SAMUELSON, A. CHEDIN, AND N. SCOTT (1981). Study of the ammonia ice cloud layer in the Equatorial region of Jupiter from the infrared interferometric experiment on Voyager. Icarus 46, 233-248. MOROZHENKO, A. V., AND E. G. YANOVlTSKII (1973). The optical properties of Venus and the Jovian planets. I. The atmosphere of Jupiter according to polarimetric observations. Icarus 18, 583-592. ORTON, G. S. (1975). Spatially resolved absolute spectral reflectivity of Jupiter: 3390-8400 ,g,. Icarus 26, 159-174. ORTON, G. S., J. F. APPLEBY, ANDJ. W. MARTONCHIK (1982). The effect of ammonia ice on the outgoing thermal radiance from the atmosphere of Jupiter. Icarus 52, 94-116. OWEN, T., AND R. J. TERRILE (1981). Colors on Jupiter. J. Geophys. Res. 86, 8797-8814. PEEK, B. M. (1958). The Planet Jupiter. Faber & Faber, London. SATO, M., AND J. E. HANSEN (1979). Jupiter's atmospheric composition and cloud structure deduced from absorption bands in reflected sunlight. J. A tmos. Sci. 36, 1133-1167. SMITH, B. A., L. A. SODERBLOM, T. V. JOHNSON, A. P. INGERSOLL,S. A. COLLINS,E. M. SHOEMAKER, G. E. HUNT, H. MASURSKY, M. H. CARR, M. E. DAVIES, A. F. COOK II, J. BOYCE, G. E. DANIELSON, T. OWEN, C. SAGAN, R. F. BEEBE, J. VEVERKA, R. E. STRUM, J. F. MCCAULEY, D. MORR1SON, G. A. BRIGGS, AND V. E. SUOMI (1979). The Jupiter system through the eyes of Voyager 1. Science 204, 951-972. SMITH, D. W. (1980). Galilean satellite eclipse studies. II. Jovian stratospheric and tropospheric aerosol content. Icarus 44, 116-133. SMITH, D. W., T. F. GREENE, AND R. W. SHORTHILL (1977). The upper Jovian atmosphere aerosol content determined from a satellite eclipse observation. Icarus 30, 697-729. STAHL, H. P., AND M, G. TOMASKO (1984). Measurements of the single-scattering properties of ammonia ice crystals. In preparation. STOLL, C. P. (1980). Polarimetry o f Jupiter at Large Phase Angles. Ph.D. dissertation, Department of Planetary Sciences, University of Arizona, Tucson. TERRILE, R. J., AND J. A. WESTPHAL (1977). The vertical cloud structure of Jupiter from 5/.*m measurements. Icarus 30, 274-281.
JOVIAN PHOTOMETRY TOMASKO, M. G. (1977). Photometry of Jupiter from Pioneer l 1. Bull. Amer. Astron. Soc. 9, 533. TOMASKO, M. G., AND L. R. DOOSE (1984). Polarimetry and photometry of Saturn from Pioneer 11 : Observations and constraints on the distribution and properties of cloud and aerosol particles. Icarus 58, 1-34. TOMASKO, M. G., AND S. MARTINEK (1978). Centerto-limb variations in the ultraviolet spectrum of Jupiter. Bull. Amer. Astron. Soc. 10, 562. TOMASKO, M. G., AND P. H. SMITH (1982). Photometry and polarimetry of Titan: Pioneer ! l observations and their implications for aerosol properties. Icarus 51, 65-95. TOMASKO, M. G., R. A. WEST, AND N. D. CASTILLO (1978). Photometry and polarimetry of Jupiter at large phase angles. 1. Analysis of imaging data of a prominent belt and a zone from Pioneer 10. Icarus 33, 558-592. VAN ALLEN, J. A. (1976). High-energy particles in the Jovian magnetosphere. In Jupiter (T. Gehrels, Ed.). Univ. of Arizona Press, Tucson. WALLACE, L., J. J. CALDWELL, AND B. D. SAVAGE (1972). Ultraviolet photometry from the Orbiting Astronomical Observatory. III. Observations of Venus, Mars, Jupiter, and Saturn longward of 2000 A. Astrophys. J. 172, 755-769.
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WALLACE, L., AND D. M. HUNTEN (1978). The Jovian spectrum in the region 0.4-1.1 p.m: The C/H ratio. Rev. Geophys. Space Phys. 16, 289-319. WALLACE, L., AND G. R. SMITH (1977). The interpretation of Jovian methane absorption. Astrophys. J. 212, 252-261. WEIDENSCHILEING~ S. J.~ AND J. S. LEWIS (1973). Atmospheric and cloud structure of the Jovian planets. Icarus 20, 465-476. WEST, R. A. (1979a). Spatially resolved methane band photometry of Jupiter. I. Absolute reflectivity and center-to-limb variations in the 6190-, 7250-, and 8900-A bands. Icarus 38, 12-33. WEST, R. A. (1979b). Spatially resolved methane band photometry of Jupiter. II. Analysis of the South Equatorial Belt and South Tropical Zone reflectivity. Icarus 38, 34-53. WEST, R. A., C. A. HORD, K. E. SIMMONS, D. L. COFFEEN, M. SATO, AND A. L. LANE (1981). Near ultraviolet scattering properties of Jupiter. J. Geophys. Res. 86, 8783-8792. WEST, R. A., AND M. G. TOMASKO (1980). Spatially resolved methane band photometry of Jupiter. III. Cloud vertical structures for several axisymmetric bands and the Great Red Spot. Icarus 41, 278292.