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Thermal properties of the Galilean satellites
ICARUS
l&224-236
(1973)
Thermal DAVID
Properties MORRISON
Institute for
Astronomy,
Received
July
of the
Galilean
AND DALE
University 1, 1972;
of Hawaii, revised
Satellites
P. CRUIKSHANK Honolulu,
September
11,
Hawaii
96822
1972
Radiometry in the 20-pm band of eclipses of each of the four Galilean satellites of Jupiter provides information about the thermal properties of the uppermost surface layers of these bodies. Their thermal inertias are all smaller than those of the Moon or of Mercury ; there is no evidence for atmospheres, and where the data are of high quality vertically homogeneous thermal properties are excluded. Numerically computed two-layer models reproduce the observed eclipse curves if the following values are adopted for the thermal inertia [erg crnm2 s-1/z OK-‘] and the surface density [gcm-2] of the low-conductivity upper layer: Callisto, (1.1 f 0.1) x lo4 and 0.11 iO.02; Canymede, (1.4f 0.2) x lo4 and 0.15+0.03; 10, (1.3+ 0.4) x lo4 and 0.10 f 0.04. Uncertainties in the variation of temperature with orbital phase preclude a model fit for Europa. Such thermal properties, together with other observational evidence, suggest that the surfaces of these satellites are largely composed of ices. A thin coating of frost provides the upper, lowconductivity layer, while the subsurface material maintains a high thermal conductivity by fusion of a mixture of ice and rock. Difficulties with this model, such as its failure to explain the low albedo of Callisto, are discussed ; however, a structure of this type with a discontinuity in thermal properties a few millimeters below the surface appears to be required by the eclipse observations.
I. INTRODUCTION Observations of the thermal response of a planetary surface to changing insolation provide a means of determining the thermophysical properties of the uppermost surface layers. In the solar system, there are two mechanisms for varying the insolation : the diurnal cycle and the more rapid changes associated with eclipses. From Earth it is not possible to observe the diurnal variations on the Galilean satellites (maximum phase angle 12’), but eclipses are common, especially for the inner three satellites. This paper reports an analysis of the thermophysical properties of the surface layers of the four Galilean satellites based on eclipse radiometry in the 20-p” band obtained in 1971 and 1972. The first measurements of the thermal emission of a satellite during eclipse were made in 1963 by Murray et al. (1965), who observed an eclipse of Ganymede (J III) in the 8- to 14-pm spectral band. Since they were able to detect the satellite only during the initial cooling and final heating phases Copyright All rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
of the eclipse, they could not determine a minimum temperature or make a quantitative determination of the thermal properties of the satellite. They did note, however, that the rapid changes in the 8- to 14-pm flux indicated a low thermal conductivity like that of the Moon. In 1971, 0. Hansen at Caltech began a program of observations at 8-14pm, while we made similar observations in the 20-pm spectral window; at 20pm the flux during eclipse is substantially larger than at 8-14pm, and the signal-to-noise ratio is correspondingly higher. Some of the observations have been discussed elsewhere (Morrison et al., 1971). In this paper we analyze all of our eclipse observations, which include one complete eclipse of Callisto (J IV), five disappearances or reappearances of Ganymede, seven of 10 (J I) and six of Europa (J II). II.
OBSERVATIONS
The observations infrared photometer 224
were made with our (Simon et al., 1972) at
GALILEAN
225
SATELLITES
the Cassegrain focus of the 2.24-m telescope of Mauna Kea Observatory. The detector was a pumped liquid helium-cooled germanium bolometer manufactured by Infrared Laboratories, Inc. The bolometer was located at the focus of the f/l0 beam (plate scale lOarcsec/mm); the only optical elements in the light path were a KRS-5 window on the Dewar and the cooled 20-pm interference filter. An electromagnetically driven, linear-throw dichroic diagonal mirror chopped the field of view between two tangent beams of diameter IOarcsec at a frequency of 10Hz. The signal from the bolometer was synchronously amplified by a PAR phase-lock amplifier, which interfaced with the IBM 1800 computer for data acquisition. The spectral band pass of the instrument was defined by the cooled interference filter and by the transmission of the atmosphere. The observations were made under dry conditions; we estimate that the zenith water vapor content of the atmosphere was normally between 0.5 and 1.0 precipitable millimeters. The extinction coefficients measured on the nights in which eclipses were observed, as well as on other nights of the same observing period, ranged from 0.25 to 0.50mag/air mass, consistent with our estimates of atmospheric water vapor. Figure 1 gives the measured transmission of the filter, the
calculated atmospheric transmission for lmm of H,O (V. Kunde, private communication, 1971), and the product of these two curves. The effective wavelength for a 150°K source is about 21pm, and the band pass is 17-28pm. The object of eclipse radiometry is to determine the change of flux on the time scale of the eclipse, about 2-4 hr; absolute photometry is not required. Observations of other satellites served to verify the stability of the atmospheric transparency and of the system sensitivity. In our standard observing procedure, each data point represents approximately 30sec of integration on the satellite in each of the two north-south-oriented tangent beams. In the few cases (primarily eclipses of 10) where the sky contribution, including scattered radiation from Jupiter, was significant, we determined this sky background by reobserving the same position when the satellite was no longer there. In most of the 1971 observations, we did not use this observing technique, but instead alternately placed one beam on the satellite and both beams on the sky about IOarcsec E or W of the satellite. The sky values are less well determined in these cases, making the 1971 observations of 10 and Europa less accurate. The internal errors in each observation, caused by sky or system noise or by
(a)
4
(b)
.2
(b)
.2 Cc) 0 50
40
30 26 26
24
22
20
IS
16~";
Wovelength
FIG. 1. Transmission of the atmosphere with
curves 1 mm
for the precipitable
20-c”
band
: (a), transmission
Hz0 ; (c), the product
of the filter; of curves (a) and
(b), transmission (b).
226
MORRISONANDCRUIKSHANK
imprecise positioning of the satellite in the aperture, were generally about 2-4% for Callisto and Ganymede and about twice as large for 10 and Europa. Often, however, systematic errors introduced a greater uncertainty into the observations. Such errors can arise from incomplete subtraction of the sky background or from incorrect choice of normalization factor, especially in reappearance observations of 10 and Europa, where the final flux level that represents equilibrium with the insolation must be assumed. Both sources of error are important for the inner satellites ; for this reason we will discuss primarily the data on Callisto and Ganymede in this paper and defer a more complete analysis of 10 and Europa until more observations are available. In order to interpret the radiometric data, we need to know the variation of insolation with time on the satellite. The eclipse times given in the American Ephemeris and Nautical Almanac can differ from the half-intensity point of the visual light curve by up to &2min, and the exact time from first fading to disappearance, or from first reappearance to full brightness, depends on the eclipse geometry. We obtain this information from simultaneous photoelectric photometry with a 61-cm telescope at Mauna Kea.
inhomogeneous models, which require three parameters for specification : the thermal inertias of the two layers and the thickness of the upper layer in units of surface density, e.g., gcmP2. Such a twolayer model is a first approximation to a case where the thermal properties vary continuously with depth. As a special case, we shall assume the thermal inertia of the lower layer to be much greater than that of the upper; then only two parameters, the thermal inertia and thickness of the upper layer, are needed to calculate the thermal flux. Third, we consider twoinhomogeneous component laterally models, also specified by three parameters : the thermal inertias of the two components and the fraction of the surface covered by each. Such models are a first approximation to a heterogeneous surface, such as one consisting of a dusty material with interspersed rocks. Here, also, an interesting special case exists, in which the thermal inertia of the less common component is much larger: again, the computed fluxes depend on only two parameters, the thermal inertia of the dominant component and the fraction of the surface covered by that component. The temperature of a point on the surface of the satellite is calculated from the onedimensional equation of heat conduction : aT -=--
Ka2T
THERMOPHYSICALMODELS
at pi ax2
For comparison with the observations, we compute the expected flux during eclipse for specified thermal properties of the satellites. We assume that the satellites are spherica,l, nonrotating, smooth, and uniform in albedo and infrared emissivity. First, we consider models with horizontally and vertically homogeneous subsurfaces characterized by the thermal inertia, where K is the thermal conWpW’, ductivity and pc is the heat capacity per unit volume. The units of the thermal inertia are [erg crnp2 s-i’2 OK-i], usually omitted in the text Multiplying by 2.4 x lo-* converts these values to the more common units of [calcm-2s-1/2 “K-i]. Second, we consider two-layer vertically
The numerical solution uses the approach described by Morrison (1969). In deriving the numerical values presented below, we have used a constant heat capacity c of i 9 x lo6 ergg-’ “K-l. To specify the bound- ( ary condition at the upper surface we need to know the variation of the insolation throughout the eclipse. Since the width of the penumbra of the shadow of Jupiter is less than the width of the satellite, the insolation at any point varies more rapidly than does the total photometric brightness of the satellite. As a first approximation, we consider the satellite to be in two parts, with the leading half entering eclipse before the trailing half by a time that is exactly half of the time for the total satellite brightness t,o fall to zero. Within
III.
GALILEANSATELLITES
227
each part, variation of insolation with time IV. RESULTS is constrained by the requirement that the Relative Fluxes and Temperatures light curve of the satellite follow the essentially linear decline observed photoIn addition to the observations of metrically. All of the models presented in satellite eclipses, we have measured the this paper were calculated with this ap20-p” fluxes of the Galilean satsllites on proximation. For the inner three satellites, numerous other occasions during 197 1 and the resulting flux differs by less than 2% 1972. Mean temperatures derived from a from that calculated on the zeroth ap- part of these observations have been proximation, in which the insolation is published (Morrison et al., 1972) ; here we assumed to fall off simultaneously at all present revised values based on more compoints on the satellite, but for the eclipse of plete data. The relative fluxes are needed Callisto on August 11 1972, the zeroth ap- to interpret the eclipse data, both to proximation is inadequate. Heating of the establish the equilibrium surface temperasatellite surface during eclipse by the tures and to permit accurate normalization thermal radiation of Jupiter has not been of eclipse reappearances of 10 and Europa. included, since even for 10 this radiation is Neither Callisto nor Ganymede shows a only about 1% of the out-of-eclipse solar variation in flux with orbital phase as large insolation. The thermal skin depth as- as *lo%. The mean flux ratio (J III/J IV) sociated with the rotation of the satellite is is 0.72 * 0.02; however, there is evidence several times the eclipse skin depth; that near superior conjunction of Ganyconsequently, the subsurface temperature mede this ratio is 0.67. Calibrated against gradients produced by the diurnal insolathe 20-pm standards given by Simon et al. tion cycle do not affect the eclipse tempera(1972) and corrected for color-temperature ture variations, and our assumption that effects (Morrison, 1973), the 20-pm monothe subsurface before the start of the chromatic flux from Callisto at mean eclipse is isothermal is justified. In these opposition is (1630 5 250) x 10-‘8Wcm-2 models, we held the lower boundary pm-‘. Adopting the radii given by temperature, many skin depths below the Morrison et al. (1972), the 20-p” brightness surface, constant. temperatures for Callisto and Ganymede The initial temperatures on the il- are then 149&5’K and 136rf3’K, luminated hemisphere of the satellite are respectively. assumed in these models to be in equiBoth of the inner satellites show a large librium with the insolation. For Callisto dependence of 20-pm flux on orbital phase, and Ganymede we take the temperature with a maximum between western elongaat the subsolar point to be 160°K and for tion and superior conjunction and a 10 and Europa 150°K (see, e.g., Morrison minimum between superior conjunction et al., 1972, and the discussion in Section and eastern elongation. Preliminary data IV). The computed flux variations depend indicate that the variation for 10 is about *12% and for Europa is about f25%. The only weakly on these initial temperatures. We divide the surface of the satellite into transition from maximum to minimum a central disk and four annuli and obtain flux takes place near the time of eclipse. numerical solutions of the heat-conduction There is a strong suggestion that this equation for the five different surface change is essentially discontinuous, but regions. The corresponding fluxes are more observations are needed, especially computed on the assumption that each for phase angles between 10 and 60”, to surface area radiates as a black body, and verify this remarkable effect. We expect the fluxes are averaged over the surface to discuss the phase variations of these and over the transmission band illustrated satellites more fully in a later publication, in Fig. 1. The time interval for computabut we note here that these variations tions is 1 min, which is approximately the seriously complicate the interpretation of same as the effective time resolution of the the eclipse observations. If similar variaobservations. tions take place at lOpm, Hansen’s (1972b)
228
MORRISON
AND
conclusions, reached on the assumption that each satellite returned to its preeclipse brightness within an hour after reappearance, may also need revision. The mean 20-pm temperatures of these two satellites are essentially those given by Morrison et al. (1972): 127°K for 10 and 119” K for Europa. Eclipse of Callisto The inner three Galilean satellites are eclipsed once per orbit; however, Callisto is so far from Jupiter that it is eclipsed only in those years when the inclination of the orbit plane to the solar direction is small. The first eclipses in 3 years took place in
CRUIKSHANK
July and August 1972, with the satellite passing through the shadow of the planet at near-grazing incidence. These eclipses were characterized by slow fall and rise in visual brightness and by short totality. We present here data on the eclipse of I1 August 1972, which was observable in its entirety from Hawaii. The photoelectric photometry indicated a duration, measured between the halfintensity points of the light curve, of 107min (from 0730 to 0917 UT). The approximately linear decline and rise in brightness each lasted 28 min. The satellite could be seen at a low light level (less than 1%) for much longer, however, and only
TABLE I OBSERVATIONSOFCALLISTOANDGANYMEDE Callisto
20lm
11 August UT
Callisto
1972
10pl
11 August
1972
F
0
UT
F
0
0703 0709
IrO?O c-J.982 0.915 O*R7A 0.827 0.761 0.715 0.583 0.516 0.44h 0.336 0.287 0.258
.025 .025 .025 .025 .020 .020 .020 .020 ,020 ,020 .020 .020 ,015 .015
0705 0713 0747 0813 OS55 0908 0923 0945 0958
0.990 0.928 0.078 0.025
,050 .050
0716
3.018
,003 .005 .030 .040 .050
UT
F
0
.OlO .OlO ,010 .OlO
1441 1443 1445 1447 1449 1451 1453 1455 1457 1459 1500 1504 1505 15’38 1509 1511 1513 1515 1518 1519 1521 1531 1542 1544 1553
1.002
,040 .040 .040 .040 ,040 .040 ,040 .040 .035 .033 .040 .060 .OhO ,050 ,040 ,040 .040 .040 ,040 .040 .040 .030 ,030 ,030 ,030
0720 0722 0724 0725 0727 0731 0733 c735 0739 0742 0743 0749
0751
lrOO2
3.182 0.169
0752 0754 0756 0805 0809 c901 C902
01168 0*155 0.146 0.117 0.106 0.088
0904 c911 0912 0919
0.096
0921 0923 0925 0930 0932 0934 0941 0943 0947 0949 0955
c.1q1
.015 r030 .030 .OlO
0.161 0.190
.OlO ,010 .OlO ,010
0.391 0.440 0,495 0.560 0.716 0.742 0.755 0.821 0.834 O.R68 O*R54 0.902
.020 .020 ,020 .020 ,020 .020 .025 ,030 .030 .030 ,030 .040
0.035 0.500 0.770 0.823
Ganymede
,010 ,010
20pm
17 March
1.010 0.980 1.086 0.997 1.003 0.795 C.705 0.655 0.497 0.371 0.242 0.344 0.288 0.309 0.334 0.312 0.376 0.322 0.279 0.236 0.270 0.246 0.296 0.176
1971
1555
00235
1606 1621 1631 1642 1644 1658 1701 170R 1709 1711 1713 1717 1718 1723 1722 1724 1727 1729 1732 173’1 1737
0.243 0.216 0.233 0*171 Oa234 0.166 0.145 0.276 0.369 D.378 0.541 0.713 0.622 Oe725 0.790 01865 0.850 O.Atl5 0.870 0.930 c.975
,030 .030 l 030 .030 .030 .030 ,040 .040 ,040 .040 .040 ,040 .050 ,050 .060 .060 ,060 .070 .070 .ORO ,080
0647 0649 0651 0653 0655 0712 0715 0717 0721 0834 0838 0840 0842 0844 0844 OS49 0852 OR54 0856 0902 0935
0.277 O-263 0.292 C.273 0.240 0.225 0.214 0.230 0.212 0.123
0.110 0.154 0.220 0.277 0.333 0.378 0.620 0.640 0.718 0.895
UT 0606 0609 0612 C615 0617 0619 0621 0623 0625 0627 0629 0631 0633 0635 0637 C639
F 1.000 1.030 1.040 0.920 0.935 0.R46 0.855 0.650 0.536 0.436 0.410 0.345 0.303 Oa292 0.290 0.255
,100
.lOO 31 July
10 Julv
,100
0.880
Ganymede
Ganymede
.050 .050 ,050 ,050 ,050 ,030 .03O .030 .030 ,025 ,025 .025 .030 ‘035 .040 ,040 ,040 .040 ,040
20pm
1972
20um
1971 0 .040 .040 ,040 .040 ,040 ,040 .040 ,030 .030 .040 .040 .050 .050 ,050 b050 ,060
0804 0805 0807 OS09 0810 OR12 OS13 0815 0817 0822 0823 0832 0838 0844 OS50 OR59 0905 0912 0918
0.143 0.146 0.157
0.188 0.247 Oe316 0.425 0.525 0.6’35 0.705 0.730 0.805 0.825 O*RSO 0.850 0.850 0.840 0.830 0.875
.020 .020 ,020 .020 ,020 ,030 .030 ,030 ,040 .050 .050 ,060 ,060 ,060 ,060 ,070 .070 .070 .070
GALILEAN
229
SATELLITES
1.0 II August 1972
.9 .6 .7 .6 .5
Homogeneous
.4
model
.3 .2 _I 0
.3
w-layer
model
.2 _I 0700
0600
0900 TIME
1000
(UT)
FIG. 2. Observations of the eclipse of Callisto of 11 August 1972. Filled circles open circles are at 1Opm. The arrows mark the photometric haif-intensity times. the figure illustrates the best-fitting homogeneous model, characterized by II2 = 1.2 x 104ergcm-2s-1/20K-1. Th e 1ower part illustrates the best-fitting VW characterized by a thermal inertia of 1.0 x lo4 and a surface density of 0.12gcm-2.
between 0758 and 0852 was it invisible through the 2.24-m telescope. In addition to the 20-pm observations, we took advantage of the slowness of the eclipse to obtain a few observations in the 8- to 14-pm region. The data at both wavelengths are tabulated in Table I and plotted in Fig. 2. Ganymede was observed several times before and nine times during the eclipse to verify system stability and to provide an extinction standard. An important source of error during most of the eclipse is the 2% uncertainty in the preeclipse ratio J III/J IV at 20pm (0.72) and the 5% uncertainty in this ratio at 1Op.m (0.50). The uncertainties in individual points calculated from internal scatter ranged from 2% at high flux levels to 4% near minimum. An additional source of uncertainty arises from the extinction correction near the end of the eclipse, where the air mass approached a value of 2.1. The three main parameters that characterize the eclipse curves are the initial rate of decline, the minimum value, and the initial rate of increase of the observed flux. 9
are 20-pm The upper a thermal two-layer
points; part of inertia model,
These values are listed in Table II. The general form of the lo- and 20-pm eclipse curve is that expected for a homogeneous subsurface of very low thermal conductivity, as illustrated in the upper part of Fig. 2, where best-fitting homogeneous model curves are plotted together with the observations. The model thermal inertia that matches the observed 20-pm minimum flux of 0.09 f 0.01 is (K~c)l’~ = 1.2 x 104. However, this curve does not match the large slopes in the heating and cooling phases of the eclipse. To fit these data, a model is required in which at least a part of the surface has a lower thermal inertia. It is significant that the homogeneous model that fits the 20-pm minimum also fits the lo-pm minimum of 0.018 f 0.003. This fact implies that there can be no important lateral inhomogeneities in thermal properties on the surface. Areas of high thermal inertia, being relatively hot during totality, would increase the 10-p” flux relative to that at 20pm. From the observed ratios at the two wavelengths we can set an upper limit of 1% on the fraction
230
MORRISON
AND
T-BLE PARAMETERS Photometric slope [min-‘1
IR wavelength (W
Callisto
0.036
Ganymede
0.083
Europa 10
0.17 0.25
20 10 20 10 20 20
Satellite
a Values
taken
from
Hansen
(197213,
CRUIKSHANK
II
OF ECLIPSE
CURVES
Cooling slope (min-‘) 0.036 f 0.001 0.037 f 0.003 0.054 5 0.002 -0.067’ 0.07 f 0.02 0.12 f 0.02 Fig.
Heating slope (Knin-‘) 0.027 0.025 0.037
f 0.001 f 0.001 * 0.003 -
Minimum IR flux 0.09 0.018 0.14 t0.06” 0.2 0.24
z!T 0.01 f 0.003 f 0.01 ,I 0.1 5 0.04
15).
of the surface that could consist of exposures of materials of large thermal inertia. In two-layer models, the slope of the cooling curve is sensitive primarily to the thermal inertia of the upper layer. However, for this slow eclipse, the slope of the cooling curve is the same as that of the photometric curve, indicating that the surface maintained approximate equilibrium with the changing insolation for the first 20min of the eclipse. With this information we can set only an upper limit to the thermal inertia of this layer. In order to change temperature as rapidly as indicated, the thermal inertia must be no greater than 1.0 x 104. Further constraints on this thermal inertia must come from the heating part of the curve. We consider two-layer models in which the thermal inertia of the lower layer is high; the best-fitting model curve is illustrated in the lower part of Fig. 2. The thermal inertia of the upper layer is 1.0 x lo4 and the surface density is 0.12gcm-2. No significant improvement is obtained with models in which the temperature of the lower layer is allowed to change ; however, essentially similar curves are derived from such models so long as the thermal inertia of this layer is no less than 3 x 105. We conclude from experimentation with both types of two-layer models that the possible range of thermal parameters for the upper layer that is consistent with the data is: thermal inertia
(1.0 & 0.1) x lo4 0.11 5 0.02gcme2.
and
surface
density
Eclipses of Ganymede Complete eclipse curves at 20p.m were obtained on March 17 and July 10 1971, and an additional reappearance was observed July 31 1972. These observations are listed in Table I and the averages at 2-min intervals plotted in Fig. 3. The eclipses were not of exactly the same length, but in Fig. 3 we adjusted them to a standard duration of 130min and separately aligned the disappearance and reappearance data on the basis of the visual photometry. To normalize the observations of July 10, 1971 and July 31, 1972, we assumed, based on preeclipse observations, that the ratio J III/J IV = 0.67. For the eclipse of 17 March 1971, we relied on the stability of the system and did not normalize on the basis of observations of Callisto. The uncertainties in the figure are estimated standard errors. The curve in Fig. 3 is notable for the rapid cooling and heating of the surface. A best fit to the observed minimum flux of 0.14 & 0.01 is obtained with a homogeneous model with thermal inertia 2.0 x 104, as illustrated by the dashed curve in Fig. 3. However, such a model clearly is not consistent with the observed cooling and heating slopes. The cooling curve requires a thermal inertia of (1.4 f 0.2) x 104, a value intermediate between that of Callisto and the Moon.
GALILEAN
For Callisto, the ratio of the lo- and 20-pm minimum fluxes allowed us to reject models with large lateral inhomogeneities. We did not observe Ganymede at lOpm, but Hansen (1972b and private communication, 1972) has made available to us his observations at this wavelength. While he did not observe the minimum flux directly, his data for the cooling curve indicate that the lo-pm minimum was less than 0.06, yielding an upper limit for exposures of high-conductivity material on Ganymede of about 5%. A two-layer model similar to that for Callisto matches the 20-pm data for Ganymede if the upper layer has thermal inertia 1.4 X lo4 and surface density 0.15gcm-2, as illustrated by the solid curve in Fig. 3. The only important discrepancy between this curve and the observations occurs at the end of the eclipse, where the 20-pm flux appears to approach a level that is lower than its preeclipse value. Even larger effects of this sort take place for 10 and Europa and will be discussed below. Eclipses of IO and Europa During 1971 and 1972 we observed at 2Opm seven disappearances or reappearances of 10 and five of Europa. The average .
I ’
”
”
”
TIME
eclipse curves for these satellites are shown in Fig. 4. In obtaining these averages, we normalized each data set to the preeclipse ratios J I/J IV = 0.21 and J II/J IV = 0.12, determined from numerous measurements at orbital phase angles between 340 and 355”. The observations were aligned along the time axis so that the photometrically observed half-intensity points coincided. The uncertainties are estimated standard errors. The rapid variations of 20-pm flux with orbital phase discussed at the beginning of Section V are apparent in Fig. 4. The posteclipse flux for 10 is only about 85% of the preeclipse value, and for Europa the posteclipse value is only about 60% of that measured an hour before eclipse. Under such conditions, the boundary conditions for simple thermal models are uncertain, and it is impossible to discuss quantitatively the thermal properties of these satellites as we did for Callisto and Ganymede. Provisionally, we can fit a model to the cooling curve and the minimum flux for 10 while ignoring the heating curve. Since the data show a rapid cooling but a relatively large minimum flux of 0.24 f 0.04, homogeneous models cannot match the observations. In Fig. 4 is illustrated a two-layer
”
FROM HALF
FIG. 3. Average of the 20-pm observations aligned to correspond to photometric half-intensity fitting homogeneous model, with thermal inertia two-layer model, with upper layer characterized 0.15gcm-2.
231
SATELLITES
““““‘I
INTENSITY
(mid
of three eclipses of Ganymede. The data have been at time = 0. The dashed curve illustrates the best2.0 x 104. The solid curve illustrates the best-fitting by thermal inertia 1.4 x lo4 and surface density
232
MORRISON
AND
CRUIKSHANK
V.
.6
E
=
.6I tt
?)-
1
t I
.2 -
t
-5
1
I
0 TIME
t
+ +-
t
t
I
,“A
I
,
I
5
IO”
-5
0
5
FROM HALF-INTENSITY
(mid
FIG. 4. Average 20-pm eclipse curves for 10 and Europa. The data have been aligned to correspond to photometric half-intensity at time = 0. The curve plotted with the 10 data illustrates a two-layer model with upper layer characterized by thermal inertia 1.3 x lo4 and surface density 0.1. In view of the obvious variations with orbital phase in the flux of Europa, no model has been fit to these data.
model that does fit the data; the upper layer has a thermal inertia of 1.3 x lo4 and a surface density of 0.1gcmm2. The thermal properties of this satellite appear to be similar to those of Callisto and Ganymede. We have not attempted to fit any thermal model to the observations of Europa, but the 20-pm minimum flux of 0.2 f 0.1 clearly indicates that this satellite also has a small thermal inertia. TABLE
DISCUSSION
The observations of the Galilean satellites demonstrate that, in spite of the varied albedos, colors, and temperatures of these objects, they all have similar thermophysical properties as measured by eclipse radiometry. The thermal inertias of the upper layers are in the range 1.0 x 1041.5 x 104ergcmm2 s-II2 OK-‘, smaller than those measured for any other objects in the solar system. Further, the data for Callisto, Ganymede, and 10 indicate that these satellites have a material of much higher thermal conductivity only a few millimeters below the surface. The numerical results are summarized in Table III. Given are the average 20-pm brightness temperature, the change in the center-of-disk temperature during eclipse, and (based on the range of two-layer models consistent with the observations) the thermal inertia (Kpc)‘12, the thermal parameter y = (Kpc)-‘12, and the surface density of the upper layer. Before discussing the interpretation of these results, we compare our conclusions with those obtained contemporaneously by Hansen (1972a, b) from IO-pm eclipse radiometry of 10, Europa, and Ganymede. His conclusions regarding the need for two-layer thermal models and his values for the thermal inertias of the upper layers are generally consistent with our own. There are significant differences in our conclusions regarding 10, however. Hansen finds a thermal inertia for this satellite of (3.8 * 0.3) x 104, while we obtain (1.3 & 0.4) x 104. His minimum flux at 10pm is 0.38, while ours at 20pm is 0.24 3 0.04; yet III
SUMNARYOFRESIJLTS
Td2OW Satellite
WI
Callisto Ganymede Europa
149 i 136 f -119
10
-127
AT,,,
Thermal (ergcm-2s-1/2
[OKI 5 3
62 f 3 50f3 >30
(1.0 (1.4
38 f
(1.3
6
inertia “K-i)
f 0.1) x 104 * 0.2) x 104 <4 x 104 f 0.4)
x 104
y = (Kpc)-“2 (Cal-’ cm2s1/2 420dk400 3000f400 >lOOO 32OOh
“K)
Surface density (gcmW2) 0.11 0.15
f 0.02 f 0.03 -
1000
0.10
f 0.04
&4LILEANSATELLTl!ES
for the two-layer models we both use one would expect the lo-pm minimum to be substantially lower than that at 20pm. In view of these apparent inconsistencies and of the remarkable behavior of this satellite in other respects, we prefer to defer final judgement on the thermal properties of 10 until more observations are available. We now wish to explore the question of the physical nature of the surfaces of the Galilean satellites. We conclude from this study : (1) the uppermost few millimeters of the surface are composed of material of very low thermal inertia and, therefore, low thermal conductivity; (2) the immediate subsurface has high thermal conductivity ; and (3) there are no large regions in which the high-conductivity subsurface is exposed. In view of the laboratory studies by Wechsler and Glaser (1965) we note that the low thermal inertias require that the atmospheric pressure must be less than lmb, consistent with the upper limit of 10e4mb found for 10 by other means (Taylor et al., 1972). The spectral reflectivities of the four Galilean satellites vary considerably (Gillett etal., 1970; JohnsonandMcCord, 1971; Pilcher et al., 1972). 10 is unusually red, with a very high reflectivity beyond 0.5pm and spectral features that may indicate a partial covering of water frost ; Europa and Ganymede have lower albedos than 10 beyond 1.5pm and clearly show spectral features of low-temperature water frost at 1.6 and 2.0 pm ; and Callisto has a uniformly low albedo throughout this spectral interval with some weak features that may be due to a partial cover of water frost. Prior to the discovery by P&her et al. (1972) of water frost absorptions in the spectra of the satellites, the presence of this substance had been inferred principally from the solar phase functions of 10, Europa, and Ganymede, which show the “opposition effect” indicative of loosely packed surface structures (Stebbins and Jacobsen, 1928). Polarimetric evidence (Veverka, 1971) is also consistent with a largely transparent, multiply scattering surface layer on the same three satellites. However, the polarimetry of Callisto shows
233
no strong evidence for a loosely packed, transparent surface material. The low albedo suggests rock powder instead of frost, in which case Callisto is more nearly like the Moon than the other three Galilean satellites. The low reflectivity of all the satellites in the ultraviolet is not characteristic of ice but is comparable to that of silicate rock powders. Lebofsky et al. (1970) have considered these problems in a study of the rings of Saturn, which have some optical properties in common with the Galilean satellites. More recently, Lebofsky (1972) has shown that short-wavelength irradiation of several chemical compounds can produce ultraviolet absorptiona similar to those observed in the spectra of many solar system objects, but the effect on the infrared reflectivity is unknown. To summarize the spectral evidence : (1) the reflectivity of all four satellites in the ultraviolet is similar to that of some rock powders but different from that of simple frosts of H,O, CH,, and NH, ; (2) the infrared reflectivity of 10 is inconsistent with common silicate powders, but may show some features attributable to H,O frost ; (3) Europa and Ganymede show infrared spectral features attributable to H,O frost; and (4) the infrared reflectivity of Callisto is very low but may show H,O frost absorption features. Several rock powders have sufficiently low thermal conductivity at ambient gas pressures of less than 1 mb to give thermal inert& of (2 x 104. Thus, the simplest thermal model for the surfaces of the satellites is a layer of rock powder a few millimeters thick overlying a solid rock subsurface. We question, however, whether such a structure could withstand meteoritic bombardment. Conservative estimates, based on the number of Apollo asteroids projected back in time (E. Shoemaker, private communication, 1972) indicate that the upper several tens of centimeters of the Galilean satellites have been fragmented or “gardened” by repeated impacts. Unless the subsurface rocks “heal,” or resolidify, after a fragmentation event, their thermal properties will not show the discontinuity a few millimeters
234
MORRISON
AND
below the surface indicated by our observations. Since the evidence from impact studies in nature and in the laboratory indicates that rock melting upon impact is not great, some composition other than rock is suggested. In order to understand how the observed thermal properties could be sustained even with repeated deep fragmentation of the satellite surfaces, we consider a surface mantle of ices with an admixture of rocky debris (Lewis, 1971). An icy surface can heal after fragmentation in two ways. First, slow fusion and crystallization of ice fragments will increase the thermal conductivity to that of solid ice, whether or not rock inclusions occur in the matrix. Second, impact melting and vaporization of the icy matrix would be expected. The melted ice would immediately refreeze, healing some of the fragmentation, while the vapor would quickly condense, presumably as a frosty surface layer. This frost could provide the thin insulating layer required by the thermal data. Laboratory studies of H,O frosts show that in conditions of low humidity, dendritically structured layers having density as low as 0.06gcmP3 are deposited (Smith et al., 1964; Reid et al., 1966). The thermal conductivity of these low-density frosts at temperatures comparable to those on the Galilean satellites, but at atmospheric pressure, is in the vicinity of 1‘ x 10P3 Wcm-’ “K-l. If we scale the thermal conductivity at atmospheric pressure to vacuum conditions in the same way that rock powder conductivities are observed to scale, the frost conductivity is decreased by a factor of approximately 103. With the specific heat of water ice c= 1.08 x 107erg”K-‘g-1, the thermal conductivity scaled to vacuum K = 1 x 10v6 W cm-’ “K-l, and density p = O.O6gcm-), the thermal inertia is 2.5 x lo3 ergcmh2 S-I/~ ‘K-l, lower than that required for the surface layers of the Galilean satellites. Even if densification of the frost or increase of conductivity (as with a millibar or so of gas pressure) occurs, the thermal inertia will still be in an acceptable range to match the observations. With a uniform frost density of 0.06gcm-3, the thickness of the upper
CRULKSHANK
layers on Callisto and Ganymede would be about 2 cm. The simple model of an ice and frost mantle on the satellites, while not entirely in agreement with all the observational data, seems most compatible with the thermal models that we propose. The model appears most directly applicable to Ganymede while each of the other three satellites displays some anomalous physical property presently not understood: (1) 10 has anomalously high infrared reflectivity; (2) Europa has erratic posteclipse warming properties ; and (3) Callisto has very low reflectivity throughout the spectrum, suggestive of rock powder, although the thermal properties require some healing of the subsurface such as is provided in the frost and ice model. VI.
CONCLUSIONS
Observations at 20pm of eclipses of the Galilean satellites indicate that the surfaces of these objects have very low conductivity (thermal inertias of 1 .O x 1041/20K-1, or values of 1.5 x 104ergcmp2sy = (KPc)-‘/~ of 3000-4500cal-’ cm2 s1j2 “K). Models fitted to the data for Callisto, Ganymede, and 10 further indicate that the subsurface is not vertically homogeneous, but that the low-conductivity material is superficial, amounting to less than 0.2g cmM2. Beneath this coating, the thermal inertia is much higher, perhaps as high as that of solid rock or ice. However, combined lo- and 20-p” eclipse radiometry of Callisto and Ganymede indicates that no more than a few percent of the surface consists of uncoated outcroppings of this high-conductivity material. The numerical results obtained from fits of two-layer thermal models to the data are summarized in Table III. The exact values of the parameters depend on the assumptions inherent in these rather idealized models ; a thermal probe inserted into the surface of one of these satellites would not necessarily obtain the same values as those tabulated. However, even idealized models such as these are capable of matching the data with only two free parameters, and the results obtained
GALILEAN
permit a reasonable comparison among these four objects and between these observations and similar eclipse radiometry that has been done for the Moon. A plausible physical model with the required thermal properties is ice or frost, perhaps mixed with rock and rock powder. It is not improbable that low-density frost deposited in near-vacuum conditions would have the low thermal inertia required for the thin upper layer, while a few millimeters below the surface this material could compact and fuse to form a solid, high-conductivity layer. Ices are the only materials we know that could heal themselves after fragmentation and thus maintain a high thermal conductivity. The spectral reflectivity of the satellites is largely consistent with this hypothesis, but the low reflectivity of all four satellites in the ultraviolet and the high reflectivity of 10 in the infrared are not characteristic of any known frosts. Laboratory studies of the thermal and optical properties of frosts in vacuum and at temperatures below 150°K are needed for comparison with the satellite data. ACKNOWLEDGMENTS We express our sincere thanks to 0. L. Hansen for several stimulating discussions, and for permission to use his data in advance of publication. R. E. Murphy kindly supplied some of the photometric eclipse data. We are indebted to D. S. Dillard and R. V. Smith for directing our attention to laboratory studies of the properties of frosts, and to V. Kunde for providing models of atmospheric transmission. We thank Mauna Kea Observatory night assistants F. Cheigh and P. Hendricks for their help in obtaining the observations. The infrared radiometer was constructed with the assistance of J. G. Beery of the Los Alamos Scientific Laboratory (supported by the A.E.C.). This research was supported in part by NASA Grant NGL 12-001057 to the University of Hawaii.
REFERENCES
GILLETT,
F. C., MERRILL, K. M., W. A. (1970). Albedo and thermal Jovian satellites I-IV. Astrophyrl. 247-249.
AND STEIN, emission Lett.
235
SATELLITES
of 6,
HANSEN, 0. L. (1972a). the
Galilean
satellites.
Infrared Bull.
sot., 4, 367. HANSEN, 0. L. (1972b).
Thermal the Galilean satellites measured microns. Ph.D. Thesis, California Technology ; also submitted to JOHNSON, T. V., AND MCCORD, Spectral geometric albedo of satellites, 0.3 to 2.5 microns.
observations of Amer. A&row radiation from at 10 and 20 Institute of Icarus. T. B. (1971). the Galilean Astrophys. J.
169,589-594. LEWIS, J. S. (1971).
Satellites of the outer Their physical and chemical nature. Icarus 15, 174-185. LEBOESKY, L. A. (1972). Refleotivities of ammonium hydrosullldes: Application to the interpretation of reflection spectra of outer solar system bodies. Bull. Amer. Astron. Sot., planets:
4, 362. LEBOFSKY, L. A., JOHNSON, T. B. tivity
(1970). Saturn’s and compositional
T. V., AND MCCORD, rings: Spectral reflecimplication. Icorms
13, 226-230. MORRISON, D.
(1969). Thermal models and temperatures of the planet Smithson. Astrophp. Obs. Spec. 292. MORRISON, D. (1973). Determination of radii of satellites and asteroids from radiometry and photometry. In preparation. MORRISON, D., CRUIKSHANE, D. P., MURPHY, R. E., MARTIN, T. Z., BEERY, J. G., AND SHIPLEY, J. P. (1971). Thermal inertia of Ganymede from 20-micron eclipse radiometry. Astrophys. J. 167, L107-Llll. MORRISON, D., CRUIKSRANK, D. P., AND MURPHY, R. E. (1972). Temperatures of Titan and the Galilean satellites at 20 microns. Astrophys. J. 173, L143-L146. MURRAY,B.C.,WESTPHAL, J.A., ANDWILDEY, R. L. (1965). The eclipse cooling of Ganymede. Astrophys. J. 141, 1590-1591. PILCBER, C.? RIDGWAY, S. T., AND MCCORD, T. B. (1972). Galilean satellites: Identification of water frost. Submitted to Science. R,EID, R.C., BRIAN, P.L.T., ANDWEBER, M.E. (1966). Heat transfer and frost formation inside a liquid nitrogen-cooled tube. Amer. Inst. Chem. Eng. J. 12, 1190-1195. SIMON, T., MORRISON, D., AND CRUI~SHANK, D. P. (1972). Twenty-micron fluxes of bright stellar standards. Astrophy8. J. 177, L17microwave Mercury. Rep. No.
L20. SIVIITH, R. V., EDMONDS, D. K., BRENTARI, E. G. F., AND RICHARDS, R. J. (1964). Analysis of the frost phenomena on “Advances in Cryogenic pp. 8898, Plenum Press.
a cryo-surface. Engineering,”
In 9,
236
MORRISON
AND
STEBBINS, J., ANDJACOBSEN, photometric and Uranus,
measures with tests
T.(1928).Further of Jupiter’s satellites of the solar constant.
Lick 06s. Bull. 13, 180. TA~LOR,G. E., O'LEARY, B.T.,VAN FLANDERN, T. C., BARTHOLDI, P., OWEN, F., HUBBARD, W. B., SMITH, B. A., SMITH, S. A., FALLON,
CRUIKSHANK F. W., DEVINNEY, E. J., AND (1971). Occultation of beta Scorpii May 14, 1971. Nature, London
OLMXR,
J. C by 10 on
234,
405-
406. VEVERKA, J. (1971). of the
Gal&an
355-359.
Polarization measurements satellites of Jupiter. Icaru.9
14,
l&224-236
(1973)
Thermal DAVID
Properties MORRISON
Institute for
Astronomy,
Received
July
of the
Galilean
AND DALE
University 1, 1972;
of Hawaii, revised
Satellites
P. CRUIKSHANK Honolulu,
September
11,
Hawaii
96822
1972
Radiometry in the 20-pm band of eclipses of each of the four Galilean satellites of Jupiter provides information about the thermal properties of the uppermost surface layers of these bodies. Their thermal inertias are all smaller than those of the Moon or of Mercury ; there is no evidence for atmospheres, and where the data are of high quality vertically homogeneous thermal properties are excluded. Numerically computed two-layer models reproduce the observed eclipse curves if the following values are adopted for the thermal inertia [erg crnm2 s-1/z OK-‘] and the surface density [gcm-2] of the low-conductivity upper layer: Callisto, (1.1 f 0.1) x lo4 and 0.11 iO.02; Canymede, (1.4f 0.2) x lo4 and 0.15+0.03; 10, (1.3+ 0.4) x lo4 and 0.10 f 0.04. Uncertainties in the variation of temperature with orbital phase preclude a model fit for Europa. Such thermal properties, together with other observational evidence, suggest that the surfaces of these satellites are largely composed of ices. A thin coating of frost provides the upper, lowconductivity layer, while the subsurface material maintains a high thermal conductivity by fusion of a mixture of ice and rock. Difficulties with this model, such as its failure to explain the low albedo of Callisto, are discussed ; however, a structure of this type with a discontinuity in thermal properties a few millimeters below the surface appears to be required by the eclipse observations.
I. INTRODUCTION Observations of the thermal response of a planetary surface to changing insolation provide a means of determining the thermophysical properties of the uppermost surface layers. In the solar system, there are two mechanisms for varying the insolation : the diurnal cycle and the more rapid changes associated with eclipses. From Earth it is not possible to observe the diurnal variations on the Galilean satellites (maximum phase angle 12’), but eclipses are common, especially for the inner three satellites. This paper reports an analysis of the thermophysical properties of the surface layers of the four Galilean satellites based on eclipse radiometry in the 20-p” band obtained in 1971 and 1972. The first measurements of the thermal emission of a satellite during eclipse were made in 1963 by Murray et al. (1965), who observed an eclipse of Ganymede (J III) in the 8- to 14-pm spectral band. Since they were able to detect the satellite only during the initial cooling and final heating phases Copyright All rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
of the eclipse, they could not determine a minimum temperature or make a quantitative determination of the thermal properties of the satellite. They did note, however, that the rapid changes in the 8- to 14-pm flux indicated a low thermal conductivity like that of the Moon. In 1971, 0. Hansen at Caltech began a program of observations at 8-14pm, while we made similar observations in the 20-pm spectral window; at 20pm the flux during eclipse is substantially larger than at 8-14pm, and the signal-to-noise ratio is correspondingly higher. Some of the observations have been discussed elsewhere (Morrison et al., 1971). In this paper we analyze all of our eclipse observations, which include one complete eclipse of Callisto (J IV), five disappearances or reappearances of Ganymede, seven of 10 (J I) and six of Europa (J II). II.
OBSERVATIONS
The observations infrared photometer 224
were made with our (Simon et al., 1972) at
GALILEAN
225
SATELLITES
the Cassegrain focus of the 2.24-m telescope of Mauna Kea Observatory. The detector was a pumped liquid helium-cooled germanium bolometer manufactured by Infrared Laboratories, Inc. The bolometer was located at the focus of the f/l0 beam (plate scale lOarcsec/mm); the only optical elements in the light path were a KRS-5 window on the Dewar and the cooled 20-pm interference filter. An electromagnetically driven, linear-throw dichroic diagonal mirror chopped the field of view between two tangent beams of diameter IOarcsec at a frequency of 10Hz. The signal from the bolometer was synchronously amplified by a PAR phase-lock amplifier, which interfaced with the IBM 1800 computer for data acquisition. The spectral band pass of the instrument was defined by the cooled interference filter and by the transmission of the atmosphere. The observations were made under dry conditions; we estimate that the zenith water vapor content of the atmosphere was normally between 0.5 and 1.0 precipitable millimeters. The extinction coefficients measured on the nights in which eclipses were observed, as well as on other nights of the same observing period, ranged from 0.25 to 0.50mag/air mass, consistent with our estimates of atmospheric water vapor. Figure 1 gives the measured transmission of the filter, the
calculated atmospheric transmission for lmm of H,O (V. Kunde, private communication, 1971), and the product of these two curves. The effective wavelength for a 150°K source is about 21pm, and the band pass is 17-28pm. The object of eclipse radiometry is to determine the change of flux on the time scale of the eclipse, about 2-4 hr; absolute photometry is not required. Observations of other satellites served to verify the stability of the atmospheric transparency and of the system sensitivity. In our standard observing procedure, each data point represents approximately 30sec of integration on the satellite in each of the two north-south-oriented tangent beams. In the few cases (primarily eclipses of 10) where the sky contribution, including scattered radiation from Jupiter, was significant, we determined this sky background by reobserving the same position when the satellite was no longer there. In most of the 1971 observations, we did not use this observing technique, but instead alternately placed one beam on the satellite and both beams on the sky about IOarcsec E or W of the satellite. The sky values are less well determined in these cases, making the 1971 observations of 10 and Europa less accurate. The internal errors in each observation, caused by sky or system noise or by
(a)
4
(b)
.2
(b)
.2 Cc) 0 50
40
30 26 26
24
22
20
IS
16~";
Wovelength
FIG. 1. Transmission of the atmosphere with
curves 1 mm
for the precipitable
20-c”
band
: (a), transmission
Hz0 ; (c), the product
of the filter; of curves (a) and
(b), transmission (b).
226
MORRISONANDCRUIKSHANK
imprecise positioning of the satellite in the aperture, were generally about 2-4% for Callisto and Ganymede and about twice as large for 10 and Europa. Often, however, systematic errors introduced a greater uncertainty into the observations. Such errors can arise from incomplete subtraction of the sky background or from incorrect choice of normalization factor, especially in reappearance observations of 10 and Europa, where the final flux level that represents equilibrium with the insolation must be assumed. Both sources of error are important for the inner satellites ; for this reason we will discuss primarily the data on Callisto and Ganymede in this paper and defer a more complete analysis of 10 and Europa until more observations are available. In order to interpret the radiometric data, we need to know the variation of insolation with time on the satellite. The eclipse times given in the American Ephemeris and Nautical Almanac can differ from the half-intensity point of the visual light curve by up to &2min, and the exact time from first fading to disappearance, or from first reappearance to full brightness, depends on the eclipse geometry. We obtain this information from simultaneous photoelectric photometry with a 61-cm telescope at Mauna Kea.
inhomogeneous models, which require three parameters for specification : the thermal inertias of the two layers and the thickness of the upper layer in units of surface density, e.g., gcmP2. Such a twolayer model is a first approximation to a case where the thermal properties vary continuously with depth. As a special case, we shall assume the thermal inertia of the lower layer to be much greater than that of the upper; then only two parameters, the thermal inertia and thickness of the upper layer, are needed to calculate the thermal flux. Third, we consider twoinhomogeneous component laterally models, also specified by three parameters : the thermal inertias of the two components and the fraction of the surface covered by each. Such models are a first approximation to a heterogeneous surface, such as one consisting of a dusty material with interspersed rocks. Here, also, an interesting special case exists, in which the thermal inertia of the less common component is much larger: again, the computed fluxes depend on only two parameters, the thermal inertia of the dominant component and the fraction of the surface covered by that component. The temperature of a point on the surface of the satellite is calculated from the onedimensional equation of heat conduction : aT -=--
Ka2T
THERMOPHYSICALMODELS
at pi ax2
For comparison with the observations, we compute the expected flux during eclipse for specified thermal properties of the satellites. We assume that the satellites are spherica,l, nonrotating, smooth, and uniform in albedo and infrared emissivity. First, we consider models with horizontally and vertically homogeneous subsurfaces characterized by the thermal inertia, where K is the thermal conWpW’, ductivity and pc is the heat capacity per unit volume. The units of the thermal inertia are [erg crnp2 s-i’2 OK-i], usually omitted in the text Multiplying by 2.4 x lo-* converts these values to the more common units of [calcm-2s-1/2 “K-i]. Second, we consider two-layer vertically
The numerical solution uses the approach described by Morrison (1969). In deriving the numerical values presented below, we have used a constant heat capacity c of i 9 x lo6 ergg-’ “K-l. To specify the bound- ( ary condition at the upper surface we need to know the variation of the insolation throughout the eclipse. Since the width of the penumbra of the shadow of Jupiter is less than the width of the satellite, the insolation at any point varies more rapidly than does the total photometric brightness of the satellite. As a first approximation, we consider the satellite to be in two parts, with the leading half entering eclipse before the trailing half by a time that is exactly half of the time for the total satellite brightness t,o fall to zero. Within
III.
GALILEANSATELLITES
227
each part, variation of insolation with time IV. RESULTS is constrained by the requirement that the Relative Fluxes and Temperatures light curve of the satellite follow the essentially linear decline observed photoIn addition to the observations of metrically. All of the models presented in satellite eclipses, we have measured the this paper were calculated with this ap20-p” fluxes of the Galilean satsllites on proximation. For the inner three satellites, numerous other occasions during 197 1 and the resulting flux differs by less than 2% 1972. Mean temperatures derived from a from that calculated on the zeroth ap- part of these observations have been proximation, in which the insolation is published (Morrison et al., 1972) ; here we assumed to fall off simultaneously at all present revised values based on more compoints on the satellite, but for the eclipse of plete data. The relative fluxes are needed Callisto on August 11 1972, the zeroth ap- to interpret the eclipse data, both to proximation is inadequate. Heating of the establish the equilibrium surface temperasatellite surface during eclipse by the tures and to permit accurate normalization thermal radiation of Jupiter has not been of eclipse reappearances of 10 and Europa. included, since even for 10 this radiation is Neither Callisto nor Ganymede shows a only about 1% of the out-of-eclipse solar variation in flux with orbital phase as large insolation. The thermal skin depth as- as *lo%. The mean flux ratio (J III/J IV) sociated with the rotation of the satellite is is 0.72 * 0.02; however, there is evidence several times the eclipse skin depth; that near superior conjunction of Ganyconsequently, the subsurface temperature mede this ratio is 0.67. Calibrated against gradients produced by the diurnal insolathe 20-pm standards given by Simon et al. tion cycle do not affect the eclipse tempera(1972) and corrected for color-temperature ture variations, and our assumption that effects (Morrison, 1973), the 20-pm monothe subsurface before the start of the chromatic flux from Callisto at mean eclipse is isothermal is justified. In these opposition is (1630 5 250) x 10-‘8Wcm-2 models, we held the lower boundary pm-‘. Adopting the radii given by temperature, many skin depths below the Morrison et al. (1972), the 20-p” brightness surface, constant. temperatures for Callisto and Ganymede The initial temperatures on the il- are then 149&5’K and 136rf3’K, luminated hemisphere of the satellite are respectively. assumed in these models to be in equiBoth of the inner satellites show a large librium with the insolation. For Callisto dependence of 20-pm flux on orbital phase, and Ganymede we take the temperature with a maximum between western elongaat the subsolar point to be 160°K and for tion and superior conjunction and a 10 and Europa 150°K (see, e.g., Morrison minimum between superior conjunction et al., 1972, and the discussion in Section and eastern elongation. Preliminary data IV). The computed flux variations depend indicate that the variation for 10 is about *12% and for Europa is about f25%. The only weakly on these initial temperatures. We divide the surface of the satellite into transition from maximum to minimum a central disk and four annuli and obtain flux takes place near the time of eclipse. numerical solutions of the heat-conduction There is a strong suggestion that this equation for the five different surface change is essentially discontinuous, but regions. The corresponding fluxes are more observations are needed, especially computed on the assumption that each for phase angles between 10 and 60”, to surface area radiates as a black body, and verify this remarkable effect. We expect the fluxes are averaged over the surface to discuss the phase variations of these and over the transmission band illustrated satellites more fully in a later publication, in Fig. 1. The time interval for computabut we note here that these variations tions is 1 min, which is approximately the seriously complicate the interpretation of same as the effective time resolution of the the eclipse observations. If similar variaobservations. tions take place at lOpm, Hansen’s (1972b)
228
MORRISON
AND
conclusions, reached on the assumption that each satellite returned to its preeclipse brightness within an hour after reappearance, may also need revision. The mean 20-pm temperatures of these two satellites are essentially those given by Morrison et al. (1972): 127°K for 10 and 119” K for Europa. Eclipse of Callisto The inner three Galilean satellites are eclipsed once per orbit; however, Callisto is so far from Jupiter that it is eclipsed only in those years when the inclination of the orbit plane to the solar direction is small. The first eclipses in 3 years took place in
CRUIKSHANK
July and August 1972, with the satellite passing through the shadow of the planet at near-grazing incidence. These eclipses were characterized by slow fall and rise in visual brightness and by short totality. We present here data on the eclipse of I1 August 1972, which was observable in its entirety from Hawaii. The photoelectric photometry indicated a duration, measured between the halfintensity points of the light curve, of 107min (from 0730 to 0917 UT). The approximately linear decline and rise in brightness each lasted 28 min. The satellite could be seen at a low light level (less than 1%) for much longer, however, and only
TABLE I OBSERVATIONSOFCALLISTOANDGANYMEDE Callisto
20lm
11 August UT
Callisto
1972
10pl
11 August
1972
F
0
UT
F
0
0703 0709
IrO?O c-J.982 0.915 O*R7A 0.827 0.761 0.715 0.583 0.516 0.44h 0.336 0.287 0.258
.025 .025 .025 .025 .020 .020 .020 .020 ,020 ,020 .020 .020 ,015 .015
0705 0713 0747 0813 OS55 0908 0923 0945 0958
0.990 0.928 0.078 0.025
,050 .050
0716
3.018
,003 .005 .030 .040 .050
UT
F
0
.OlO .OlO ,010 .OlO
1441 1443 1445 1447 1449 1451 1453 1455 1457 1459 1500 1504 1505 15’38 1509 1511 1513 1515 1518 1519 1521 1531 1542 1544 1553
1.002
,040 .040 .040 .040 ,040 .040 ,040 .040 .035 .033 .040 .060 .OhO ,050 ,040 ,040 .040 .040 ,040 .040 .040 .030 ,030 ,030 ,030
0720 0722 0724 0725 0727 0731 0733 c735 0739 0742 0743 0749
0751
lrOO2
3.182 0.169
0752 0754 0756 0805 0809 c901 C902
01168 0*155 0.146 0.117 0.106 0.088
0904 c911 0912 0919
0.096
0921 0923 0925 0930 0932 0934 0941 0943 0947 0949 0955
c.1q1
.015 r030 .030 .OlO
0.161 0.190
.OlO ,010 .OlO ,010
0.391 0.440 0,495 0.560 0.716 0.742 0.755 0.821 0.834 O.R68 O*R54 0.902
.020 .020 ,020 .020 ,020 .020 .025 ,030 .030 .030 ,030 .040
0.035 0.500 0.770 0.823
Ganymede
,010 ,010
20pm
17 March
1.010 0.980 1.086 0.997 1.003 0.795 C.705 0.655 0.497 0.371 0.242 0.344 0.288 0.309 0.334 0.312 0.376 0.322 0.279 0.236 0.270 0.246 0.296 0.176
1971
1555
00235
1606 1621 1631 1642 1644 1658 1701 170R 1709 1711 1713 1717 1718 1723 1722 1724 1727 1729 1732 173’1 1737
0.243 0.216 0.233 0*171 Oa234 0.166 0.145 0.276 0.369 D.378 0.541 0.713 0.622 Oe725 0.790 01865 0.850 O.Atl5 0.870 0.930 c.975
,030 .030 l 030 .030 .030 .030 ,040 .040 ,040 .040 .040 ,040 .050 ,050 .060 .060 ,060 .070 .070 .ORO ,080
0647 0649 0651 0653 0655 0712 0715 0717 0721 0834 0838 0840 0842 0844 0844 OS49 0852 OR54 0856 0902 0935
0.277 O-263 0.292 C.273 0.240 0.225 0.214 0.230 0.212 0.123
0.110 0.154 0.220 0.277 0.333 0.378 0.620 0.640 0.718 0.895
UT 0606 0609 0612 C615 0617 0619 0621 0623 0625 0627 0629 0631 0633 0635 0637 C639
F 1.000 1.030 1.040 0.920 0.935 0.R46 0.855 0.650 0.536 0.436 0.410 0.345 0.303 Oa292 0.290 0.255
,100
.lOO 31 July
10 Julv
,100
0.880
Ganymede
Ganymede
.050 .050 ,050 ,050 ,050 ,030 .03O .030 .030 ,025 ,025 .025 .030 ‘035 .040 ,040 ,040 .040 ,040
20pm
1972
20um
1971 0 .040 .040 ,040 .040 ,040 ,040 .040 ,030 .030 .040 .040 .050 .050 ,050 b050 ,060
0804 0805 0807 OS09 0810 OR12 OS13 0815 0817 0822 0823 0832 0838 0844 OS50 OR59 0905 0912 0918
0.143 0.146 0.157
0.188 0.247 Oe316 0.425 0.525 0.6’35 0.705 0.730 0.805 0.825 O*RSO 0.850 0.850 0.840 0.830 0.875
.020 .020 ,020 .020 ,020 ,030 .030 ,030 ,040 .050 .050 ,060 ,060 ,060 ,060 ,070 .070 .070 .070
GALILEAN
229
SATELLITES
1.0 II August 1972
.9 .6 .7 .6 .5
Homogeneous
.4
model
.3 .2 _I 0
.3
w-layer
model
.2 _I 0700
0600
0900 TIME
1000
(UT)
FIG. 2. Observations of the eclipse of Callisto of 11 August 1972. Filled circles open circles are at 1Opm. The arrows mark the photometric haif-intensity times. the figure illustrates the best-fitting homogeneous model, characterized by II2 = 1.2 x 104ergcm-2s-1/20K-1. Th e 1ower part illustrates the best-fitting VW characterized by a thermal inertia of 1.0 x lo4 and a surface density of 0.12gcm-2.
between 0758 and 0852 was it invisible through the 2.24-m telescope. In addition to the 20-pm observations, we took advantage of the slowness of the eclipse to obtain a few observations in the 8- to 14-pm region. The data at both wavelengths are tabulated in Table I and plotted in Fig. 2. Ganymede was observed several times before and nine times during the eclipse to verify system stability and to provide an extinction standard. An important source of error during most of the eclipse is the 2% uncertainty in the preeclipse ratio J III/J IV at 20pm (0.72) and the 5% uncertainty in this ratio at 1Op.m (0.50). The uncertainties in individual points calculated from internal scatter ranged from 2% at high flux levels to 4% near minimum. An additional source of uncertainty arises from the extinction correction near the end of the eclipse, where the air mass approached a value of 2.1. The three main parameters that characterize the eclipse curves are the initial rate of decline, the minimum value, and the initial rate of increase of the observed flux. 9
are 20-pm The upper a thermal two-layer
points; part of inertia model,
These values are listed in Table II. The general form of the lo- and 20-pm eclipse curve is that expected for a homogeneous subsurface of very low thermal conductivity, as illustrated in the upper part of Fig. 2, where best-fitting homogeneous model curves are plotted together with the observations. The model thermal inertia that matches the observed 20-pm minimum flux of 0.09 f 0.01 is (K~c)l’~ = 1.2 x 104. However, this curve does not match the large slopes in the heating and cooling phases of the eclipse. To fit these data, a model is required in which at least a part of the surface has a lower thermal inertia. It is significant that the homogeneous model that fits the 20-pm minimum also fits the lo-pm minimum of 0.018 f 0.003. This fact implies that there can be no important lateral inhomogeneities in thermal properties on the surface. Areas of high thermal inertia, being relatively hot during totality, would increase the 10-p” flux relative to that at 20pm. From the observed ratios at the two wavelengths we can set an upper limit of 1% on the fraction
230
MORRISON
AND
T-BLE PARAMETERS Photometric slope [min-‘1
IR wavelength (W
Callisto
0.036
Ganymede
0.083
Europa 10
0.17 0.25
20 10 20 10 20 20
Satellite
a Values
taken
from
Hansen
(197213,
CRUIKSHANK
II
OF ECLIPSE
CURVES
Cooling slope (min-‘) 0.036 f 0.001 0.037 f 0.003 0.054 5 0.002 -0.067’ 0.07 f 0.02 0.12 f 0.02 Fig.
Heating slope (Knin-‘) 0.027 0.025 0.037
f 0.001 f 0.001 * 0.003 -
Minimum IR flux 0.09 0.018 0.14 t0.06” 0.2 0.24
z!T 0.01 f 0.003 f 0.01 ,I 0.1 5 0.04
15).
of the surface that could consist of exposures of materials of large thermal inertia. In two-layer models, the slope of the cooling curve is sensitive primarily to the thermal inertia of the upper layer. However, for this slow eclipse, the slope of the cooling curve is the same as that of the photometric curve, indicating that the surface maintained approximate equilibrium with the changing insolation for the first 20min of the eclipse. With this information we can set only an upper limit to the thermal inertia of this layer. In order to change temperature as rapidly as indicated, the thermal inertia must be no greater than 1.0 x 104. Further constraints on this thermal inertia must come from the heating part of the curve. We consider two-layer models in which the thermal inertia of the lower layer is high; the best-fitting model curve is illustrated in the lower part of Fig. 2. The thermal inertia of the upper layer is 1.0 x lo4 and the surface density is 0.12gcm-2. No significant improvement is obtained with models in which the temperature of the lower layer is allowed to change ; however, essentially similar curves are derived from such models so long as the thermal inertia of this layer is no less than 3 x 105. We conclude from experimentation with both types of two-layer models that the possible range of thermal parameters for the upper layer that is consistent with the data is: thermal inertia
(1.0 & 0.1) x lo4 0.11 5 0.02gcme2.
and
surface
density
Eclipses of Ganymede Complete eclipse curves at 20p.m were obtained on March 17 and July 10 1971, and an additional reappearance was observed July 31 1972. These observations are listed in Table I and the averages at 2-min intervals plotted in Fig. 3. The eclipses were not of exactly the same length, but in Fig. 3 we adjusted them to a standard duration of 130min and separately aligned the disappearance and reappearance data on the basis of the visual photometry. To normalize the observations of July 10, 1971 and July 31, 1972, we assumed, based on preeclipse observations, that the ratio J III/J IV = 0.67. For the eclipse of 17 March 1971, we relied on the stability of the system and did not normalize on the basis of observations of Callisto. The uncertainties in the figure are estimated standard errors. The curve in Fig. 3 is notable for the rapid cooling and heating of the surface. A best fit to the observed minimum flux of 0.14 & 0.01 is obtained with a homogeneous model with thermal inertia 2.0 x 104, as illustrated by the dashed curve in Fig. 3. However, such a model clearly is not consistent with the observed cooling and heating slopes. The cooling curve requires a thermal inertia of (1.4 f 0.2) x 104, a value intermediate between that of Callisto and the Moon.
GALILEAN
For Callisto, the ratio of the lo- and 20-pm minimum fluxes allowed us to reject models with large lateral inhomogeneities. We did not observe Ganymede at lOpm, but Hansen (1972b and private communication, 1972) has made available to us his observations at this wavelength. While he did not observe the minimum flux directly, his data for the cooling curve indicate that the lo-pm minimum was less than 0.06, yielding an upper limit for exposures of high-conductivity material on Ganymede of about 5%. A two-layer model similar to that for Callisto matches the 20-pm data for Ganymede if the upper layer has thermal inertia 1.4 X lo4 and surface density 0.15gcm-2, as illustrated by the solid curve in Fig. 3. The only important discrepancy between this curve and the observations occurs at the end of the eclipse, where the 20-pm flux appears to approach a level that is lower than its preeclipse value. Even larger effects of this sort take place for 10 and Europa and will be discussed below. Eclipses of IO and Europa During 1971 and 1972 we observed at 2Opm seven disappearances or reappearances of 10 and five of Europa. The average .
I ’
”
”
”
TIME
eclipse curves for these satellites are shown in Fig. 4. In obtaining these averages, we normalized each data set to the preeclipse ratios J I/J IV = 0.21 and J II/J IV = 0.12, determined from numerous measurements at orbital phase angles between 340 and 355”. The observations were aligned along the time axis so that the photometrically observed half-intensity points coincided. The uncertainties are estimated standard errors. The rapid variations of 20-pm flux with orbital phase discussed at the beginning of Section V are apparent in Fig. 4. The posteclipse flux for 10 is only about 85% of the preeclipse value, and for Europa the posteclipse value is only about 60% of that measured an hour before eclipse. Under such conditions, the boundary conditions for simple thermal models are uncertain, and it is impossible to discuss quantitatively the thermal properties of these satellites as we did for Callisto and Ganymede. Provisionally, we can fit a model to the cooling curve and the minimum flux for 10 while ignoring the heating curve. Since the data show a rapid cooling but a relatively large minimum flux of 0.24 f 0.04, homogeneous models cannot match the observations. In Fig. 4 is illustrated a two-layer
”
FROM HALF
FIG. 3. Average of the 20-pm observations aligned to correspond to photometric half-intensity fitting homogeneous model, with thermal inertia two-layer model, with upper layer characterized 0.15gcm-2.
231
SATELLITES
““““‘I
INTENSITY
(mid
of three eclipses of Ganymede. The data have been at time = 0. The dashed curve illustrates the best2.0 x 104. The solid curve illustrates the best-fitting by thermal inertia 1.4 x lo4 and surface density
232
MORRISON
AND
CRUIKSHANK
V.
.6
E
=
.6I tt
?)-
1
t I
.2 -
t
-5
1
I
0 TIME
t
+ +-
t
t
I
,“A
I
,
I
5
IO”
-5
0
5
FROM HALF-INTENSITY
(mid
FIG. 4. Average 20-pm eclipse curves for 10 and Europa. The data have been aligned to correspond to photometric half-intensity at time = 0. The curve plotted with the 10 data illustrates a two-layer model with upper layer characterized by thermal inertia 1.3 x lo4 and surface density 0.1. In view of the obvious variations with orbital phase in the flux of Europa, no model has been fit to these data.
model that does fit the data; the upper layer has a thermal inertia of 1.3 x lo4 and a surface density of 0.1gcmm2. The thermal properties of this satellite appear to be similar to those of Callisto and Ganymede. We have not attempted to fit any thermal model to the observations of Europa, but the 20-pm minimum flux of 0.2 f 0.1 clearly indicates that this satellite also has a small thermal inertia. TABLE
DISCUSSION
The observations of the Galilean satellites demonstrate that, in spite of the varied albedos, colors, and temperatures of these objects, they all have similar thermophysical properties as measured by eclipse radiometry. The thermal inertias of the upper layers are in the range 1.0 x 1041.5 x 104ergcmm2 s-II2 OK-‘, smaller than those measured for any other objects in the solar system. Further, the data for Callisto, Ganymede, and 10 indicate that these satellites have a material of much higher thermal conductivity only a few millimeters below the surface. The numerical results are summarized in Table III. Given are the average 20-pm brightness temperature, the change in the center-of-disk temperature during eclipse, and (based on the range of two-layer models consistent with the observations) the thermal inertia (Kpc)‘12, the thermal parameter y = (Kpc)-‘12, and the surface density of the upper layer. Before discussing the interpretation of these results, we compare our conclusions with those obtained contemporaneously by Hansen (1972a, b) from IO-pm eclipse radiometry of 10, Europa, and Ganymede. His conclusions regarding the need for two-layer thermal models and his values for the thermal inertias of the upper layers are generally consistent with our own. There are significant differences in our conclusions regarding 10, however. Hansen finds a thermal inertia for this satellite of (3.8 * 0.3) x 104, while we obtain (1.3 & 0.4) x 104. His minimum flux at 10pm is 0.38, while ours at 20pm is 0.24 3 0.04; yet III
SUMNARYOFRESIJLTS
Td2OW Satellite
WI
Callisto Ganymede Europa
149 i 136 f -119
10
-127
AT,,,
Thermal (ergcm-2s-1/2
[OKI 5 3
62 f 3 50f3 >30
(1.0 (1.4
38 f
(1.3
6
inertia “K-i)
f 0.1) x 104 * 0.2) x 104 <4 x 104 f 0.4)
x 104
y = (Kpc)-“2 (Cal-’ cm2s1/2 420dk400 3000f400 >lOOO 32OOh
“K)
Surface density (gcmW2) 0.11 0.15
f 0.02 f 0.03 -
1000
0.10
f 0.04
&4LILEANSATELLTl!ES
for the two-layer models we both use one would expect the lo-pm minimum to be substantially lower than that at 20pm. In view of these apparent inconsistencies and of the remarkable behavior of this satellite in other respects, we prefer to defer final judgement on the thermal properties of 10 until more observations are available. We now wish to explore the question of the physical nature of the surfaces of the Galilean satellites. We conclude from this study : (1) the uppermost few millimeters of the surface are composed of material of very low thermal inertia and, therefore, low thermal conductivity; (2) the immediate subsurface has high thermal conductivity ; and (3) there are no large regions in which the high-conductivity subsurface is exposed. In view of the laboratory studies by Wechsler and Glaser (1965) we note that the low thermal inertias require that the atmospheric pressure must be less than lmb, consistent with the upper limit of 10e4mb found for 10 by other means (Taylor et al., 1972). The spectral reflectivities of the four Galilean satellites vary considerably (Gillett etal., 1970; JohnsonandMcCord, 1971; Pilcher et al., 1972). 10 is unusually red, with a very high reflectivity beyond 0.5pm and spectral features that may indicate a partial covering of water frost ; Europa and Ganymede have lower albedos than 10 beyond 1.5pm and clearly show spectral features of low-temperature water frost at 1.6 and 2.0 pm ; and Callisto has a uniformly low albedo throughout this spectral interval with some weak features that may be due to a partial cover of water frost. Prior to the discovery by P&her et al. (1972) of water frost absorptions in the spectra of the satellites, the presence of this substance had been inferred principally from the solar phase functions of 10, Europa, and Ganymede, which show the “opposition effect” indicative of loosely packed surface structures (Stebbins and Jacobsen, 1928). Polarimetric evidence (Veverka, 1971) is also consistent with a largely transparent, multiply scattering surface layer on the same three satellites. However, the polarimetry of Callisto shows
233
no strong evidence for a loosely packed, transparent surface material. The low albedo suggests rock powder instead of frost, in which case Callisto is more nearly like the Moon than the other three Galilean satellites. The low reflectivity of all the satellites in the ultraviolet is not characteristic of ice but is comparable to that of silicate rock powders. Lebofsky et al. (1970) have considered these problems in a study of the rings of Saturn, which have some optical properties in common with the Galilean satellites. More recently, Lebofsky (1972) has shown that short-wavelength irradiation of several chemical compounds can produce ultraviolet absorptiona similar to those observed in the spectra of many solar system objects, but the effect on the infrared reflectivity is unknown. To summarize the spectral evidence : (1) the reflectivity of all four satellites in the ultraviolet is similar to that of some rock powders but different from that of simple frosts of H,O, CH,, and NH, ; (2) the infrared reflectivity of 10 is inconsistent with common silicate powders, but may show some features attributable to H,O frost ; (3) Europa and Ganymede show infrared spectral features attributable to H,O frost; and (4) the infrared reflectivity of Callisto is very low but may show H,O frost absorption features. Several rock powders have sufficiently low thermal conductivity at ambient gas pressures of less than 1 mb to give thermal inert& of (2 x 104. Thus, the simplest thermal model for the surfaces of the satellites is a layer of rock powder a few millimeters thick overlying a solid rock subsurface. We question, however, whether such a structure could withstand meteoritic bombardment. Conservative estimates, based on the number of Apollo asteroids projected back in time (E. Shoemaker, private communication, 1972) indicate that the upper several tens of centimeters of the Galilean satellites have been fragmented or “gardened” by repeated impacts. Unless the subsurface rocks “heal,” or resolidify, after a fragmentation event, their thermal properties will not show the discontinuity a few millimeters
234
MORRISON
AND
below the surface indicated by our observations. Since the evidence from impact studies in nature and in the laboratory indicates that rock melting upon impact is not great, some composition other than rock is suggested. In order to understand how the observed thermal properties could be sustained even with repeated deep fragmentation of the satellite surfaces, we consider a surface mantle of ices with an admixture of rocky debris (Lewis, 1971). An icy surface can heal after fragmentation in two ways. First, slow fusion and crystallization of ice fragments will increase the thermal conductivity to that of solid ice, whether or not rock inclusions occur in the matrix. Second, impact melting and vaporization of the icy matrix would be expected. The melted ice would immediately refreeze, healing some of the fragmentation, while the vapor would quickly condense, presumably as a frosty surface layer. This frost could provide the thin insulating layer required by the thermal data. Laboratory studies of H,O frosts show that in conditions of low humidity, dendritically structured layers having density as low as 0.06gcmP3 are deposited (Smith et al., 1964; Reid et al., 1966). The thermal conductivity of these low-density frosts at temperatures comparable to those on the Galilean satellites, but at atmospheric pressure, is in the vicinity of 1‘ x 10P3 Wcm-’ “K-l. If we scale the thermal conductivity at atmospheric pressure to vacuum conditions in the same way that rock powder conductivities are observed to scale, the frost conductivity is decreased by a factor of approximately 103. With the specific heat of water ice c= 1.08 x 107erg”K-‘g-1, the thermal conductivity scaled to vacuum K = 1 x 10v6 W cm-’ “K-l, and density p = O.O6gcm-), the thermal inertia is 2.5 x lo3 ergcmh2 S-I/~ ‘K-l, lower than that required for the surface layers of the Galilean satellites. Even if densification of the frost or increase of conductivity (as with a millibar or so of gas pressure) occurs, the thermal inertia will still be in an acceptable range to match the observations. With a uniform frost density of 0.06gcm-3, the thickness of the upper
CRULKSHANK
layers on Callisto and Ganymede would be about 2 cm. The simple model of an ice and frost mantle on the satellites, while not entirely in agreement with all the observational data, seems most compatible with the thermal models that we propose. The model appears most directly applicable to Ganymede while each of the other three satellites displays some anomalous physical property presently not understood: (1) 10 has anomalously high infrared reflectivity; (2) Europa has erratic posteclipse warming properties ; and (3) Callisto has very low reflectivity throughout the spectrum, suggestive of rock powder, although the thermal properties require some healing of the subsurface such as is provided in the frost and ice model. VI.
CONCLUSIONS
Observations at 20pm of eclipses of the Galilean satellites indicate that the surfaces of these objects have very low conductivity (thermal inertias of 1 .O x 1041/20K-1, or values of 1.5 x 104ergcmp2sy = (KPc)-‘/~ of 3000-4500cal-’ cm2 s1j2 “K). Models fitted to the data for Callisto, Ganymede, and 10 further indicate that the subsurface is not vertically homogeneous, but that the low-conductivity material is superficial, amounting to less than 0.2g cmM2. Beneath this coating, the thermal inertia is much higher, perhaps as high as that of solid rock or ice. However, combined lo- and 20-p” eclipse radiometry of Callisto and Ganymede indicates that no more than a few percent of the surface consists of uncoated outcroppings of this high-conductivity material. The numerical results obtained from fits of two-layer thermal models to the data are summarized in Table III. The exact values of the parameters depend on the assumptions inherent in these rather idealized models ; a thermal probe inserted into the surface of one of these satellites would not necessarily obtain the same values as those tabulated. However, even idealized models such as these are capable of matching the data with only two free parameters, and the results obtained
GALILEAN
permit a reasonable comparison among these four objects and between these observations and similar eclipse radiometry that has been done for the Moon. A plausible physical model with the required thermal properties is ice or frost, perhaps mixed with rock and rock powder. It is not improbable that low-density frost deposited in near-vacuum conditions would have the low thermal inertia required for the thin upper layer, while a few millimeters below the surface this material could compact and fuse to form a solid, high-conductivity layer. Ices are the only materials we know that could heal themselves after fragmentation and thus maintain a high thermal conductivity. The spectral reflectivity of the satellites is largely consistent with this hypothesis, but the low reflectivity of all four satellites in the ultraviolet and the high reflectivity of 10 in the infrared are not characteristic of any known frosts. Laboratory studies of the thermal and optical properties of frosts in vacuum and at temperatures below 150°K are needed for comparison with the satellite data. ACKNOWLEDGMENTS We express our sincere thanks to 0. L. Hansen for several stimulating discussions, and for permission to use his data in advance of publication. R. E. Murphy kindly supplied some of the photometric eclipse data. We are indebted to D. S. Dillard and R. V. Smith for directing our attention to laboratory studies of the properties of frosts, and to V. Kunde for providing models of atmospheric transmission. We thank Mauna Kea Observatory night assistants F. Cheigh and P. Hendricks for their help in obtaining the observations. The infrared radiometer was constructed with the assistance of J. G. Beery of the Los Alamos Scientific Laboratory (supported by the A.E.C.). This research was supported in part by NASA Grant NGL 12-001057 to the University of Hawaii.
REFERENCES
GILLETT,
F. C., MERRILL, K. M., W. A. (1970). Albedo and thermal Jovian satellites I-IV. Astrophyrl. 247-249.
AND STEIN, emission Lett.
235
SATELLITES
of 6,
HANSEN, 0. L. (1972a). the
Galilean
satellites.
Infrared Bull.
sot., 4, 367. HANSEN, 0. L. (1972b).
Thermal the Galilean satellites measured microns. Ph.D. Thesis, California Technology ; also submitted to JOHNSON, T. V., AND MCCORD, Spectral geometric albedo of satellites, 0.3 to 2.5 microns.
observations of Amer. A&row radiation from at 10 and 20 Institute of Icarus. T. B. (1971). the Galilean Astrophys. J.
169,589-594. LEWIS, J. S. (1971).
Satellites of the outer Their physical and chemical nature. Icarus 15, 174-185. LEBOESKY, L. A. (1972). Refleotivities of ammonium hydrosullldes: Application to the interpretation of reflection spectra of outer solar system bodies. Bull. Amer. Astron. Sot., planets:
4, 362. LEBOFSKY, L. A., JOHNSON, T. B. tivity
(1970). Saturn’s and compositional
T. V., AND MCCORD, rings: Spectral reflecimplication. Icorms
13, 226-230. MORRISON, D.
(1969). Thermal models and temperatures of the planet Smithson. Astrophp. Obs. Spec. 292. MORRISON, D. (1973). Determination of radii of satellites and asteroids from radiometry and photometry. In preparation. MORRISON, D., CRUIKSHANE, D. P., MURPHY, R. E., MARTIN, T. Z., BEERY, J. G., AND SHIPLEY, J. P. (1971). Thermal inertia of Ganymede from 20-micron eclipse radiometry. Astrophys. J. 167, L107-Llll. MORRISON, D., CRUIKSRANK, D. P., AND MURPHY, R. E. (1972). Temperatures of Titan and the Galilean satellites at 20 microns. Astrophys. J. 173, L143-L146. MURRAY,B.C.,WESTPHAL, J.A., ANDWILDEY, R. L. (1965). The eclipse cooling of Ganymede. Astrophys. J. 141, 1590-1591. PILCBER, C.? RIDGWAY, S. T., AND MCCORD, T. B. (1972). Galilean satellites: Identification of water frost. Submitted to Science. R,EID, R.C., BRIAN, P.L.T., ANDWEBER, M.E. (1966). Heat transfer and frost formation inside a liquid nitrogen-cooled tube. Amer. Inst. Chem. Eng. J. 12, 1190-1195. SIMON, T., MORRISON, D., AND CRUI~SHANK, D. P. (1972). Twenty-micron fluxes of bright stellar standards. Astrophy8. J. 177, L17microwave Mercury. Rep. No.
L20. SIVIITH, R. V., EDMONDS, D. K., BRENTARI, E. G. F., AND RICHARDS, R. J. (1964). Analysis of the frost phenomena on “Advances in Cryogenic pp. 8898, Plenum Press.
a cryo-surface. Engineering,”
In 9,
236
MORRISON
AND
STEBBINS, J., ANDJACOBSEN, photometric and Uranus,
measures with tests
T.(1928).Further of Jupiter’s satellites of the solar constant.
Lick 06s. Bull. 13, 180. TA~LOR,G. E., O'LEARY, B.T.,VAN FLANDERN, T. C., BARTHOLDI, P., OWEN, F., HUBBARD, W. B., SMITH, B. A., SMITH, S. A., FALLON,
CRUIKSHANK F. W., DEVINNEY, E. J., AND (1971). Occultation of beta Scorpii May 14, 1971. Nature, London
OLMXR,
J. C by 10 on
234,
405-
406. VEVERKA, J. (1971). of the
Gal&an
355-359.
Polarization measurements satellites of Jupiter. Icaru.9
14,