Galilean satellite eclipse studies I. Observations and satellite characteristics

ICARUS 44, 102-115 (1980)

Galilean Satellite Eclipse Studies I. Observations and Satellite Characteristics

THOMAS F. G R E E N E , * + ' DALE W. SMITH, *'z'3 ANO RICHARD W. SHORTHILL:~ "1 *Department of Astronomy, University of Washington, Seattle, Washington 98105, #Boeing Aerospace Company, Seattle, Washington 98124, and SGeospace Sciences Laboratory. University of Utah Research Institute. Salt Lake City, Utah 84108 Received August 10, 1979; revised August 22, 1980 Spectrophotometric light c u r v e s of 12 Galilean satellite eclipses are reported. T h e observations were made in 20 to 30 c h a n n e l s over the wavelength range 3240 to 10,500 A, using the 200-in. telescope. The initial data processing is described. T h e s e data m e a s u r e the Jovian aerosol content in the lower stratosphere and u p p e r m o s t troposphere and the m e t h a n e a b u n d a n c e in the lower stratosphere. The data are consistent with a lack o f limb darkening on the Galilean satellites. The orbit of Callisto is s h o w n to be inclined 0.08 -+ 0.02 ° to the equatorial plane of Jupiter.

INTRODUCTION

The atmosphere of Jupiter above the visible cloud tops has been the subject of many investigations in the past decade with the goal of determining its chemical composition, thermal profile, and vertical structure (Gehrels, 1976). Many of these investigations have been on sunlight reflected at some level in the Jovian atmosphere and studied either by absorption line spectroscopy or continuum albedo measurements at a variety of illumination geometries. The presence of particulate matter in the atmosphere above the visible cloud tops has become well established (e.g., Tomasko et al., 1978) and the abundance of minor gases such as methane has been sought. An opportunity for independent study of the upper atmospheric aerosol and methane ' Guest Investigator, Hale Observatories. z Visiting A s t r o n o m e r , K i n Peak National Observatory, which is operated by the Association of Universities for R e s e a r c h in A s t r o n o m y , Inc., under contract with the National Science Foundation. 3 Present address: Department o f Physics and Ast r o n o m y , W e s t e r n Washington University, Bellingham, W a s h . 98225

is provided by eclipses of the Galilean satellites. Because of the long tangential light passage through the Jovian atmosphere during ingress and egress, eclipse light curves are very sensitive to the extinction mechanisms in the stratosphere and upper troposphere. A study of Jupiter using the satellite eclipse technique was begun in 1970 by two of us (TFG and RWS) and later joined by DWS. Twelve eclipses probing the upper atmosphere at a wide variety of Jovian latitudes were successfully observed in the period of 1971 through 1974 (Greene et al., 1971; Greene and Shorthill, 1972). The results of this study are reported herein and in the two companion papers. This paper (hereafter Paper I) reports the observations and data-processing methods and describes relevant satellite characteristics. The next paper (Smith, 1980; hereafter Paper II) reports the results dealing with the stratospheric and tropopausal aerosol. The final paper (Smith and Greene, 1980; hereafter Paper III) reports the results dealing with the stratospheric methane. The aerosol results from one eclipse probing the South Temperate Zone have been reported 102

0019-1035/80/100102-14502.00/0 Copyright (~) 1980by Academic Press, Inc. All fights of reproduction in any form reserved.

JOVIAN ECLIPSE OBSERVATIONS previously (Smith et a/., 1977; hereafter Paper A). Eclipse theory and analytic methods and several details of the observational method and preliminary data processing are contained in Paper A. Additional computational details are reported elsewhere (Smith, 1978).

T A B L E II SPECTROMETER BAN DPASSES Channel

2* 3 40

O B S E R V A T I O N S A N D DATA P R E P A R A T I O N

A. Observations and Locations Probed

Twelve eclipses were observed in the period 1971 to 1974 with the 200-in. Hale telescope and Oke muitichannel spectrometer (Oke, 1969). Table I lists the event name, date and time, eclipsed satellite, and eclipse type (ingress or egress) for these events. The spectrometer is a dual-aperture instrument which simultaneously samples both the object and an adjacent sky region in each of 30 wavelength bandpasses between h = 3240 and 10,500 ,~. The wavelength bandpasses are listed in Table II. The 1971 eclipses were observed in 20 of these bandpasses as indicated. The observational parameters of each eclipse are listed in Table III. These include the number of integrations, integration

TABLE 1 ECLIPSES OBSERVED Event

Date

71-2a 10 Mar. 1971 71-3a 6 Apr. 1971 71-3b 6 Apr. 1971 72-2 8 May 1972 72-3 13 May 1972 72-4 I I Aug. 1972 72-5 28 Aug. 1972 73-1 12 Jul. 1973 73-2a 4 Oct. 1973 74-2 29 Jun. 1 9 7 4 74-5a 27 Nov. 1974 74-5b 27 Nov. 1974

Time (UT) a 13h39m 10~22m 12n02m I Ihl3 m 9~21m 7h34= 3h38m 7h56 m 2h34m 9a43 m lh51m 4h53*~

Satellite

Eclipse type

Ganymede Europa Io Europa Ganymede Callisto Callisto Callisto Callisto Callisto Callisto Callisto

Ingress Ingress Ingress Ingress Ingress Ingress Egress Ingress Ingress Egress Ingress Egress

a Nominal Ephemeris eclipse time.

103

5 6b 7~ 8 9~ 10~ II 12~ 13c 14b 15 16

h (center, A)

Ah (A)

Channel

h

AX

3240 3400 3560 3720 3837 4077 4200 4360 4520 4680 4840 5000 5160 5320 5530

160 160 160 160 160 160 160 160 160 160 160 160 160 160 60

17 18a 19~ 20 21 22 23 24 25 26 ~ 27 28 29~ 30 31

5660 5820 6325 6420 6850 7265 7495 7978 8260 8700 9115 9260 9780 10140 10500

120 360 70 40 100 270 110 115 200 360 70 40 360 360 360

Channel not used in eclipses 71-3a and 71-3b. b Channel not used in any 1971 eclipses. c Channel not used in eclipse 71-2a.

time, sampling frequency, spectrometer aperture diameter, air mass, separation of the satellite from Jupiter, and solar phase angle. The zenographic longitude and latitude and cloud feature probed by each event are listed in Table IV. The Jupiter-satellite configuration determines the Jovian surface region probed by an eclipse. The latitudes range from 72°S to 55°N. The region probed is typically confined to less than 10° in longitude because the planet rotates - 5 ° during the aerosol-measuring portion of a typical eclipse and the angular path length in the atmosphere of the deepest applicable rays is - 5 ° . The extent in latitude is determined principally by the radius of the satellite and is - 3 °. Blue photographs of Jupiter taken approximately one-quarter rotation before each ingress and one-quarter rotation after each egress are shown in Figs. 1 and 2. The crosses indicate the cloud feature probed by each event. It may be noted that the interior (in the planar sense) of the Great Spot is probed by eclipse 72-2 and the edge

104

GREENE, SMITH, AND SHORTHILL T A B L E III OBSERVING DATA

Event

N u m b e r of observations

Integration time (sec)

Sampling frequency (Hz)

Aperture diameters (arcsec)

Air° mass

Distance a.~ (arcsec)

Solaff phase angle (°)

71-2a 71-3a 71-3b 72-2 72-3 72-4 72-5 73- I 73-2a 74-2 74-5a 74-5b

109 113 84 740 1355 1203 1743 277 1542 403 241 433

10.007 10.007 10.007 2.016 2.016 2.016 2.016 10.024 2.016 10.024 10.024 10.024

0.05 0.05 0.05 0.39 0.37 0.37 0.39 0.08 0.37 0.08 0.08 0.08

14.05 5.04 3.58 14.05 6.94 9.92 14.05 9.92 14.05 14.05 9.92 9.92

2.04 1.73 1.74 1.80 2.04 3.21 1.83 I. 76 1.73 I. 83 1.46 1.52

63.8 47.3 37.6 49.6 60.8 81.9 I I 1.2 60.7 84.3 86.3 94.6 122.2

10.3 8.2 8.2 8.4 7.8 - 8.6 10.3 3.8 - 10.6 I I. 3 I 1.4 - I 1.4

At 50~ intensity time. b Separation of satellite from center of Jupiter in equational radii. " Positive at western quadrature, negative for eastern quadrature.

of the GRS with the STrZ is probed by eclipse 71-3b.

B. Data Preparation Telescope aperture change. The teles c o p e ' s primary mirror dust c o v e r was partially closed to an aperture of approxi-

mately 90 in. during the bright portion of an eclipse to avoid possible damage to the photomultiplier tubes. It was opened to the full 200-in. aperture for the faint portions. Eclipses 72-2 and 72-4 were observed exclusively with the full 200-in. aperture with no evident saturation and in eclipse 73-2a the telescope aperture was fully opened

"FABLE IV CI.OUD FEATt:RES PROBED Event

71-2a 71 - 3a 71-3b 72-2 72-3 72-4 72-5 73-1 73-2a 74-2 74-5a 74-5b

Zenographic" longitude (°)

Zenographic latitude (°)

Feature

312 307 7 354 318 90 159 17 162 (i) 204 94 24

-56 30 18 22 -37 -72 - 67 16 5 *29 -55 +55

SPR STZ GRS/STrZ GRS STZ SPR SPR STrZ SEB NTB NPR NPR

" System II except as noted.

Central meridian a of photograph

(°) 215 343 343 4 325 284 148 7 165 (1} 195 99 31

!

I0 MAR '71

J=

SPR

6 APR '71 STZ (71-3o, b) J! 6 APR'71 GRS/STrZ (WIDE LINE ON RED SPOT) jn

(71-2o)

Jg

8 MAY'72 GRS (72-2) (ON RED SPOT)

J~17

II AUG '72

SPR

(7:> -4)

JE

13 MAY'72 (72-3)

STZ

Jr~"

28 AUG '72 (72-,5)

SPR

FIG. 1. Photographs o f Jupiter near eclipse times for 1971 and 1972 eclipses. The crosses indicate the locations probed by each eclipse. Times and cloud features are listed in Table I V . (Photos courtesy o f W. Baum, L o w e l l Observatory.) 105

jIv

12 JUL '73 (73-1)

STrZ

jIV

Jl]Z

JIV

27 NOV '74 (74-5o)

29 JUN '74 (74 -2')

NPR

4 OCT '73 (73-20)

SEB

27 NOV '74 (74 -Sb)

NPR

NTB

j'lv

FiG. 2. Photographs of Jupiter near eclipse times tbr 1973 and 1974. (Photos courtesy of W. Baum,

Lowell Observatory, and R. Beebe, New Mexico State University Observatory [74-2].) 106

JOVIAN ECLIPSE OBSERVATIONS prior to commencement of satellite darkening. The data obtained with the reduced and full telescope aperture were normalized channel by channel by fitting a curve segment through 30 sec of data just prior to and just after the telescope aperture change. The normalizing factors for nine eclipses are plotted in Fig. 3. They usually show little wavelength dependence and average -14. Scattered light removal. The proximity of the satellites to Jupiter led to significant contamination of the data by scattered light in the fainter portions of the light curves. In each eclipse, several minutes of object aperture data tracking the satellite position were obtained while the satellite was invisible against the sky background. Leastsquares curves were fit to these data in each channel and extrapolated to times of satellite visibility. In eclipses in which the satel-

~_.

16F °°

lite disappeared rapidly the extrapolation interval was sufficiently brief to suppress effects of possible errors. The accuracy of the extrapolation was verified in the four eclipses in which the satellite displayed a lingering visibility in the red but not in the blue channels. Differences between the data and the extrapolated curve just after the satellite disappeared in the blue channels were compared with the rms dispersions in the curve-fitting regions. These residuals are plotted in Fig. 4. No systematic variation of the sign or magnitude of the residuals with wavelength is evident. The rms residuals in the blue (h < 6000 A) are -0.2 (ecl. 71-3a), - 0 . 8 (ecl. 71-3b), - 0 . 4 (ecl. 72-2), and -0.5 (eel. 72-3) of the dispersion in the respective skyfitting regions. These demonstrate that in the redder channels also the sky is adequately modeled and free of large extrapolation errors.

~r) •

o

•

°

.

°o

.

•

107

19 E"'"

"°''.'°'' "°

0@

.o

J

@

[,~

11

10

"

24 X

x

• , . , °°,°•° °

X X x

X

t~

x X

1B

X

•

° .° ° •°

tO

°.

12 wx

".

X

B • .

,

",

~l

.

.71-36

t

OQ

t

t

•

Qe

•

Q

18 • dI[I

x

• "*

1B "

8 0.3

Q~

4

0 24

~)

p@gQ@ ~eOQeOQ@ e tQO

i 0.5

, '

'£x~x

~ 0.7

".

l0

• "°

,(w

x

xx

IB

wx

~"

i 0.9

WgVELEN(}TH (MICRONS)

. . •

I I .I

I" • I0 0.3

.°..°.,..

".."

t 0.5

.

"

.

J

J

0.7

0.9

i I .I

WAVELENOTH (MICRONS]

FIG. 3. Normalizing factors between data collected with 90- and 200-in. telescope apertures. In eclipse 72-3, the standard star HDI40283 is also plotted.

108

GREENE, SMITH, AND SHORTHILL source in determining the sky brightness near the source.

71-38

Light Curves The character of the eclipse light curves obtained following normalization for the telescope aperture change and removal of the scattered light contamination is shown in Figs. 6 and 7. Four effects contribute to the uncertainty of satellite brightness relative to out-of-eclipse brightness: the uncertainty arising from normalizing the 90- and 200-in. data, the uncertainty in the mean out-of-eclipse count rate, the uncertainty in each data point due to sky transparency variations and counting statistics, and the uncertainty due to sky removal. The total uncertainty is the rms sum of these terms. Further discussion of these effects is found in Paper A.

71-38

0

-I

72-2

72-3

0

I _! t 3OOO

4000WRVELENGIN

'"

5000

6000

I~[RO~SI 2 r

}h(~. 4. Test point residuals between actual sky brightness and extrapolated sky brightness mode. Ordinate is ratio of residual to rms dispersion in data. Blue channels are shown for the four eclipses with refractive tails in the redder channels.

~A)

EXTINCTIONONLY

~B)

SCRTTERINORND E X T I N C T I O N

~C~

S C R T T E R I N O ONLY

o!--. ,4

-2 L

U)

The best results were obtained by assuming that the logarithm o f the sky brightness decreases quadratically (in some cases, linearly) with apparent distance from the center of Jupiter and increases linearly with terrestrial air mass, by temporarily eliminating noisy data points (those deviating from trial fits by more than 3~r or belonging to consecutive data strings of five or more members whose residuals are of the same sign), and by smoothing in wavelength the coefficient expressing the distance dependence. Treatment of Jupiter as a disk rather than a point source was of negligible effect. The residuals obtained using an alternative air mass dependence are shown in Fig. 5 and demonstrate that the column length for scattering dominates the extinction of the

s 2F E

{

c

]

/

~ z

_?

ul

Z

L

-2 L 3000

I .......

~.. 4000

. ~ .

I,~VELENGTH

z SO00

I 6000

{ RN06TROt18 ;

Ft(,. 5. Effect of air mass dependence on test point residuals of eclipse 72-3. (a) Residuals assuming sky brightness is proportional to brightness of Jupiter. (b) Residuals assuming sky brightness is proportional to brightness of Jupiter and linearly proportional to air mass. (c) Residuals assuming sky brightness is linearly proportional to air mass (nominal case).

JOVIAN ECLIPSE OBSERVATIONS

0

-.

4-

....... .

1

I

.

......... .

BAND PRSS CHANNEL NO

I

.

I

..............

6290-6360 19

.*.

l*.

.

I

’

.

I

‘.....

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

I

I

SATELLITE DATE OBSVD TINE ORIGIN

.

R

109

. . . ,. :lL_A

I’l ‘I-

..#.

JII 4-6-71 1022 UT

’

*..

’

.

.

10320-10680 31

A

4

. .

...

. .

8

.

.

16

12

%

6

8.. . I -16

-12

1 -8

I

I

I

-4

0

4

TIME

l*

.

.

BAND PASS CHANNEL NO

l

I . 8

,

‘I. 12

4 .

. , .. .

16

tMIN1

FIG. 6. Light curves in channels 19 and 31 of eclipse 71-3a after sky removal. The error bars show the lo uncertainty in the data including effects of counting statistics, sky subtraction, and normalization. In portions without error bars, the uncertainty is given by the dispersion in the data. The tic marks represent one, two, and three times the dispersion of the postdisappearance data.

The light curves in Fig. 6 show a rapid drop in brightness as the satellite enters the umbra and then a lingering visibility as the satellite is illuminated by light refracted into the umbra by the Jovian atmosphere. This extended portion of the light curve is described as a “refractive tail” and is diagnostic of the aerosol abundance near the tropopause or the upper troposphere and of the methane abundance near the tropopause or lower stratosphere. The refractive tail is not visible when the vertical aerosol optical depth above the tropopause exceeds -0.01. Refractive tails are also suppressed by Rayleigh scattering at A < 5500 A. Several eclipses do not exhibit refractive tails at even the reddest wavelengths. The light curves in Fig. 7 are representative of this class of eclipse. The shapes of the light curves in all

channels are controlled by the satellite kinematics and reflectivity and by Jovian atmospheric refraction, Rayleigh scattering, and aerosol extinction. In addition, some of the channels lie at wavelengths containing molecular absorption bands. The light curves in these absorption channels are darker than those in the neighboring continuum channels that are free of band absorption. This phenomenon is illustrated in Fig. 8 for the eclipses exhibiting refractive tails, the light curve portion where the effect is most prominent. The uniform shapes of the bright portions of the light curves here and in similar plots for other eclipses demonstrate the reliability of the 90/200-in. normalization. The continuum channels are used in Paper II to determine the aerosol profile in the Jovian surface region probed by each

110

GREENE, SMITH, AND SHORTHILL

° ° ' * ° * ° ° * ° , , , D o °

4

.

SATELLITE Jl I~qTE OBBVD 4-6-71 TIME ORIOIN 1202 UT

BAND PASS 6290-6360 A CHANNEL NO t9

(X; Is c.b

z

B

z ILl

,~ cr

0

° ° ' ' ' ' o ° ' * - ° ° , ° °

° I

b-* ._1

-~

4

BAND PASS CHANNEL NO

10320-10680 A 31.

•

.0

•

~

=

°

t

•

•

2

I •

*I

4

=I

e

°I

°

6

°I ~

8

°

I"

1O

III.

(/3

D 8

1.2 -8

i

I

-6

i

I

-4

i

l

-2

i

I

0

i

I

2

*

*

l*

"

I •

4

i

*I*

6

•

"I

*

*l"

8

10

T I I'IE (MIN) Fnc,. 7. Light curves in channels 21 and 31 o f eclipse 71-2a after sky removal.

eclipse. The absorption channels are used in Paper III to determine the methane abundance in these locations. SATELLITE LIMB DARKENING AND KINEMATICS

The illumination of the satellite disk is nonuniform during eclipse ingress or egress and the brightness distribution across the surface varies as the event progresses. As a consequence, the shape of the light curve depends on the satellite's albedo distribution and photometric function, collectively referred to as "limb darkening." Because the aerosol and methane reductions in this study were undertaken prior to the availability of the Voyager imaging results, it was necessary to determine the limb darkening from portions of the light curves unaffected by aerosol or methane darkening. The results obtained here generally agree with the Voyager images (B. Smith e t a / . , 1979) and are briefly described in this section. In the case of Cailisto, it was also

possible to determine the inclination and nodes of the orbit. The orbits of Io, Europa, and G a n y m e d e were assumed to lie in the plane of the Jovian equator. The following satellite radii were used: Io, 1829 km (Hubbard and Van Flandern, 1972): Europa, 1550 km (Hollingsworth-Smith, 1978); G a n y m e d e , 2635 km (Carlson et al., 1973); Callisto, 2500 km (Dollfus, 1970). Using the Voyager radii would have little effect on the results below. Eclipse light curve data between 0.5 and nominally 1.5 magnitudes of darkening were used in determining the limb darkening. Brighter data do not vary significantly with time and darker data may be influenced by the then-undetermined aerosol extinction. (The limb darkening must be computed before the aerosol extinction can be determined.) These data were also used to determine a time constant S which relates the satellite's position in its orbit to the observed time scale. Numerically, S is the constant difference between the time scales of a theoretical light curve with time

JOVIAN ECLIPSE

FIG. 8. Satellite depicted.

darkening

in eclipse

OBSERVATIONS

72-3 vs time and wavelength.

zero when the satellite crosses the projected Jovian terminator and of the observed light curve with time zero at Ephemeris eclipse time. It was necessary to determine S from the data because the satellite’s orbital longitude was not sufficiently well known a priori. The satellite reflectivity was postulated to be circularly symmetric about the subearth point and was parametrized in terms of a single constant k acting as a modifier to the Lambert photometric function. Thus dZ m co@-’ i cask e ds, where dZ is the

A subset

of the total data is

brightness of a surface element of area ds and i and e are the angles of incidence and reflection, respectively. The exponent k quantifies the degree of limb darkening: k= 1 corresponds to a fully Lambert disk and k = 0.5 corresponds to a flat disk with no center-to-limb variation. The satellite was not uniformly illuminated at the times used to determine the limb darkening. The derived k is diagnostic of the more highly illuminated half-disk. Nonpolar ingresses and egresses thus measure trailing and leading half-disks, respec-

I 12

GREENE, SMITH. AND SHORTHILL

tively, while north and south polar eclipses measure the north and south half-disks, respectively. Optimum values of k were determined individually for several channels in each eclipse. In each channel, trial eclipse light curves were calculated for different values o f k spaced by 0.05. For each trial value of k, the value of S was optimized so as to minimize the rms dispersion in the data relative to the trial theoretical light curve. Finally, a parabolic fit was made through the resulting minimum dispersion values to estimate the value o f k best minimizing the dispersion and to determine the associated time constant S. Erroneously large or small values of k will cause the theoretical curve to darken too rapidly or too slowly, respectively, and hence alter the mean time difference between the theoretical and observed curves. For the optimum k, the two curves darken at the same rate and produce single, welldefined time difference. Hence both parameters can be reliably determined from the observations. It is estimated that the internal uncertainty in k in the individual channels does not exceed _ 0.15. Limb-darkening results. The values of k derived from each eclipse are shown in Fig. 9 at the surface locations they describe.

!g

F U R O ~ f -\

G,QNYMEDE

C A L L S ITO ~ )

FIG. 9. Limb-darkening maps of Io, Europa, Ganymede, and Callisto. The hemisphere facing Jupiter is the one shown for each satellite. Each coefficient is placed near the center o f the portion o f the hemisphere it describes. North is at top, east is at right.

Each value listed is the average of results in six to eight channels covering the range of the spectrometer. No clear wavelength dependence is evident in any of the cases. The uncertainty in the average is - 0 . 0 5 . The primary conclusion is that, with the possible exception of Europa, the trailing hemispheres exhibit little or no limb darkening. The lack of limb darkening is not expected from the other known photometric properties of the surfaces. Io, Europa, and G a n y m e d e all have high geometric visual aibedos (0.62, 0.68, 0.44, resp.) and small opposition effects ( - 0 . 0 3 , 0.03, 0.15 mag., resp.) (Morrison et al., 1974). The high albedos might initially lead one to expect a pronounced limb darkening (Veverka et al., 1978). The lack of a substantial opposition effect leads to the same expectation. The absence of limb darkening at small phase angles may be indicative of porous surfaces. The full moon also shows no limb darkening, but the moon has a low albedo and exhibits a strong opposition effect. The full phase behavior of the moon is explained by single scattering from a dark, porous surface: at full phase no shadowing is presented to the observer and there is strong backscattering (Hapke and Van Horn, 1963). In the case of bright surfaces, the singly scattered component is dominated by a multiply scattered component at large phase angles. If the surface is relatively smooth, the multiply scattered component is also dominant at small phase angles and leads to Lambert limb darkening. But if the surface is porous the singly scattered component will dominate at small phase angles and lead to little limb darkening (Hapke, 1977). Laboratory measurement of near-opposition limb darkening of bright powders by Veverka e t a / . (1978) show that k depends on surface roughness. Using BaSO4 powder they find k - 1.0 for a compact surface, but k - 0.8 for a level, uncompacted surface. While this exceeds the values of k found here, it is possible that a greater surface

JOVIAN ECLIPSE OBSERVATIONS roughness could further reduce the laboratory value o f k. In the case of Callisto, the lower albedo readily suggests that the presence of a dark, porous c o m p o n e n t may be responsible for the lack of limb darkening. The regions of greater limb darkening may be less porous. The average slope of a reflecting surface can be estimated from its small limb darkening by comparing the polar angle (0 ° at disk center, 90° at limb) at which a given fractional brightness occurs for some k < i with the angle at which it would have occurred for k = i (Hapke, 1977). For k 0.55, the differences suggest a typical slope of --45 ° . Results fi~r the orbit o f Callisto. The availability of six reliable eclipses of Callisto, including four in the Jovian polar regions, enables a determination of Callisto's orbital inclination and the longitude of the descending node. The jovicentric latitude ~b o f Callisto at the time of polar region events can be constrained because a small variation of ~b from zero strongly affects the impact parameter (the minimum distance of the satellite from the center of the umbral cross section between ingress and egress) and hence changes the angle between the satellite path and the umbra at the point of entry. In a polar region eclipse this change would strongly alter the rate at which the satellite radially enters or leaves

113

the umbral region. The effect on the rate of radial entry is much smaller at low latitudes. Hence the derived limb darkening in polar region eclipses is strongly dependent on the value of tb employed. If k is constrained to lie between 0.5 and I, then the corresponding dfs will bracket the true cb at eclipse time. When two adjacent eclipses are available at nearly the same orbital longitude, the overlap o f their acceptable values permits a further refinement since 4~ must be virtually the same for both. Two pairs o f polar region eclipses, one in each region, are among the eclipse data sets. Eclipses 72-4 and 72-5 were south polar eclipses occurring on successive orbits and hence at nearly the same orbital longitude. The range of ~ values corresponding to the permitted range of k is shown in Fig. l0 for these eclipses. The range is independent of wavelength. It is evident that the more southerly event (724) constrains cb more tightly and is within the d~ range of event 72-5. An intermediate value, 4~, = 0.033 °N -+ 0.01 °, is adopted for both. Eclipses 74-5a and 74-5b were the ingress and egress of the same shadow passage and hence were at nearly the same orbital longitude. The allowed range of t# values determined for these two events is also shown in Fig. 10. Although neither of these eclipses individually constrains d~ as tightly as the I (74- 50) I k = l ( 7 4 - 5b)

I

0.15 °

72 -5 " ' : ~ d ~

~

72-4

0.I0

I °

~=

0.05 °

N

I

I

0.0 °

0.05

{k=l I O03°N

~

°

1{72-5) (72-4}

FIG. 10. Out-of-plane determination for Callisto. The left portion of the figure shows the path of Callisto relative to the Jovian umbra in each of its six eclipses. The right portion shows the range of possible jovicentric latitudes ~bfor each polar eclipse. The overlap of the ranges within each polar pair bounds the value of ~bat the time of eclipse. The adopted values are shown for each polar pair. It can be noted that smaller values of ~brequire a larger limb darkening. The midlatitude eclipses are used to bound the radius.

114

GREENE, SMITH, AND S H O R T H I L L

-0.5

ECLIPgE 78-1. U

3.0 ~ 0.5

1.0

LATITUDE 0.040~ . . . . .

~

"

_~ 1.5

/,"

-- 2 . 0 5 t~

~ 2.s 3.0 3.5

-60

FI(; II

-50

-40

-30

-20 -10 TIME [MINI

C

tO

20

30

The light curve in U o f the 12 F e b 1978

eclipse of Callisto and three theoretical curves resulting from small orbital latitudes of Callisto relative to the equatorial plane of Jupiter. The data are expressed relative to out-of-eclipse brightness. The time origin is 5"53mUT.

p r e v i o u s pair, the o v e r l a p o f their d~ range is small and the c o m m o n d~ is well determined. A value o f &2 = 0.073°S ~- 0 .01° is a d o p t e d . An additional north polar region eclipse was o b s e r v e d to a u g m e n t the t w o p r e v i o u s pairs. Figure I I s h o w s the light c u r v e in U o f the 12 Feb. 1978 eclipse r e a p p e a r a n c e o f Callisto (eclipse 78-1) m e a s u r e d with the # 2 - 0 . 9 - m t e l e s c o p e and t h r e e - c h a n n e l phot o m e t e r at Kitt Peak. T h e data were corrected for scattered-light c o n t a m i n a t i o n by using several spot m e a s u r e m e n t s o f sky brightness at different radial distances from Jupiter. At mideclipse, the air mass was 1.22 and the satellite was 104 a r c s e c from the c e n t e r o f Jupiter. The u n c e r t a i n t y in the satellite d a r k e n i n g is c o m p a r a b l e to the spread o f the data. The nearly polar latitude o f eclipse 78-1 is d e m o n s t r a t e d by the visibility o f the satellite t h r o u g h mideclipse and renders the light c u r v e highly sensitive to small n o n z e r o orbital latitudes. Theoretical light c u r v e s for three values o f d~ are s h o w n in Fig. l l. T h e best fit is o b t a i n e d for ~b 0.045°S. T h e theoretical c u r v e s a s s u m e no limb

darkening (k - 0.5) and no aerosol d a r k e n ing. C u r v e s usingk - 1 do not fit the data as well and would yield ~b - 0.040°S. If 0.25 mag. o f aerosol darkening were present (more than seen in o t h e r eclipses at corres p o n d i n g satellite darkening), d~ - 0.040°S would be obtained. H e n c e , a value o f ~b3 = 0.045°S -+ 0.005 ° is a d o p t e d . A mideclipse time o f 5"16.5 m UT is o b t a i n e d by an empirical fit to the data below 1.8 mag. o f darkening. T h e a d o p t e d values o f ~b at the three times can be used to infer the inclination and n o d e s o f the orbit. Due to the heliocentric motion o f Jupiter, the orbital longitude o f Cailisto during the 1974 eclipses was 70 ° greater than during the 1972 eclipses and in the 1978 eclipse it was 156° greater. The effect o f p r e c e s s i o n during this interval b e t w e e n eclipses was m u c h smaller and is not included. K n o w i n g the orbital latitude at three longitudes o f k n o w n separation allows a unique d e t e r m i n a t i o n o f both the orbital inclination and the longitude o f the d e s c e n d i n g n o d e referred to the equatorial plane o f Jupiter. T h e inclination is 0.08 ° +_ 0.02 ° and the d e s c e n d i n g node was within 20 ° o f superior g e o c e n t r i c c o n j u n c t i o n in m i d - M a r c h 1973. T h e fit o f this orbit to the data is s h o w n in Fig. 12.

0.12 0.09 l

oo/\

2~ 9.33- /

~2-,.s

o.oo L/.............

.............

1

-0.09i -0.12 4S

90

13S

]80

225

i 270

315

J 360

RELATIVE ORB:IRL LONC,ITUOE IOEO;

FIG. 12. The best fit orbit of Callisto to the three measured points of orbital longitude and latitude. The 180° point in longitude is the point of superior conjunction in mid-March 1973.

JOVIAN ECLIPSE OBSERVATIONS ACKNOWLEDGMENTS Appreciation is expressed to the Hale Observatories for use of the 200-in. telescope. This project was helped by discussions and assistance of Dr. Z. Kopal and Dr. J. B. Oke. Dr. William Baum and the Planetary Patrol Program made available the many photographs and coordinate grids which permitted identification of the surface regions probed by each eclipse. The early observing phase of this work was supported by NASA Contracts NASw-2205 and NASw2390 to the Boeing Company. Later observing phases and the analysis have been supported by NASA Grant NGR 48-002-142 to the University of Washington. Partial computing support was provided by the University of Washington Computer Center.

REFERENCES CARLSON, R. W., BHATTACHARYGA, J. C., SMITH, B. A., JOHNSON, T. V., HIDAYAT, B., SMITH, S. A., TAYLOR, G. E., O'LEARY, B. T., AND BRINKMANN, R. T. (1973). An atmosphere on Ganymede from its occulation of SAO 186800 on 7 June 1972. Science 182, 53-55. DOEI_FUS, A. (1970). Diametres des planetes et satellites. In Surfaces and Interiors" o f Planets and Satellites (A. Dollfus, Ed.), pp. 46-139. Academic Press, New York. GEHRELS, T. (Ed.) (1976). Jupiter. Univ. of Arizona Press, Tucson. GREENE, T. F., AND SHORTHILL, R. W. (1972). Jovian satellite eclipse study. II. 1972 eclipse data. The Boeing Company, Seattle, Document DI8015151-1, 1972 October, and Document DI80-151512, 1972 November. GREENE, T. F., SHORTHILL, R. W., AND DESPAIN, L. G. (1971). Jovian satellite eclipse study. 1. 1971 eclipses. The Boeing Company, Seattle, Document DI80-14193-1, 1971 October. HAPKE, B. (1977). Private communication. HAPKE, B., AND VAN HORN, H. (1963). Photometric

1 15

studies of complex surfaces with applications to the moon. J. Geophys. Res. 68, 4545-5470. HOLLINGSWORTH-SMITH, P. (1978). Diameters of the Galilean satellites from Pioneer data. h'arus 35, 167-176. HUBBARD, W. B., AND VAN FLANOERN, T. C. (1972). The occulation of Beta Scorpii by Jupiter. III. Astrometry. Astron. J. 77, 65-74. MORRISON, D., MORRISON, N. D., AND LAZAREWlCZ, A. R. (1974). Four-color photometry of the Galilean satellites. Icarus 23, 399-416. OKE, J. B. (1969). A multichannel photoelectric spectrometer. Pub. Astron. Soc. Pacific" 81, 11-22. SMITH, B. A., SODERBLOM, L. A.', JOHNSON, T. V., INGERSOLl., A. P., COLLINS, S. A., SHOEMAKER, E. M., HUNT, G. E., MASURSKY, H., CARR, M. H., DAVIES, M. E., COOK, A. F., II, BOYCE, J., DANIELSON, G. E., OWEN, T., SAGAN, C., BEEBE, R. F., VEVERKA, J., STROM, R. G., MCCAULEY, J. F., MORRISON, D., BRIGGS, G. A., AND SUOMI, V. E. (1979). The Jupiter system through the eyes of the Voyager I. Science 204, 951-971. SMITH, D. W. (1978). The Aerosol Content in the Jovian Lower Stratosphere and Upper Troposphere Determ#zed by Satellite Eclipse Observations. Ph.D. thesis, University of Washington. SMITH, D. W. (1980). Galilean satellite eclipse studies. 11. Jovian stratospheric and tropospheric aerosol content. Icarus 44, 116-133. SMITH, D. W., AND GREENE, T. F. (1980). Galilean satellite eclipse studies. III. Jovian methane adundance. Icarus 44, 134- 141. SMITH, D. W., GREENE, T. F., AND SHORFHILL, R. W. (1977). The upper Jovian atmosphere aerosol content determined from a satellite eclipse observation. Icarus 30, 697-729. TOMASKO, M. G., WEST, R. A., AND CASTILLO, N. D. (1978). Photometry and polarimetry of Jupiter at large phase angles. I. Analysis of imaging data of a prominent belt and a zone from Pioneer 10. Icarus 33, 558-592. VEVERKA, J., GOGUEN, J., YANG, S., AND ELLIOT, J. L. (1978). Near-opposition limb darkening of solids of planetary interest. Icarus 33, 368-379.