Six-color photometry of lapetus, Titan, Rhea, Dione and Tethys

ICXRUS 2 3 , 334--354 (1974)

Six-Color Photometry of lapetus, Titan, Rhea, Dione and Tethys M. IqOLAIXrD I,*, J. VEVERKA*, D. MORRISONt, D. P. CRUIKSHAIVK~, A. R. LAZAREWICZ~, IXl. D. MORRISON¢, J. L. ELLIOT ~,*, J. GOGUEN

~'*

BURNS I'$

AND J . A .

* Laboratory for Planetary Studies, Cornell University, Ithaca, New York 14850 ¢ Institute for Astronomy, University of Hawaii, Honolulu, Hawaii 96822 Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14850 Received April 30, 1974 Six-color photometric observations made during Saturn's 1972/73 opposition enable us ¢o separate the solar phase and orbital phase contributions to the observed light variations of Iapetus, Titan, Rhea, Dione and Tethys. Titan shows no orbital variations, but has phase coefficients which range from negligible values in the infrared to 0.014mag/deg in the ultraviolet. Rhea has a bright leading side, a light curve amplitude of about 0.2mag, which increases toward short wavelengths, and surprisingly large phase coefficients, which increase from 0.025mag/ deg in the red to 0.037mag/deg in the ultraviolet. Combined with other available information, this behavior suggests a very porous, texturally complex surface layer. Dione also has a leading side which is a few tenths of a magnitude brighter than the trailing side, but the light curve amplitude has little wavelength dependence and the phase coefficients are significantly smaller than those of Rhea, suggesting a less intricate surface texture. The leading side of Tethys is probably a few tenths of a magnitude brighter than the trailing side. Our Iapetus observations generally supplement the earlier work by Millis. The phase coefficients of the bright (trailing) side are typically ~0.03 mag/deg and are not strongly wavelength dependent; the dark (leading) side coefficients are large (~0.05 mag/deg) and increase at shorter wavelengths, indicating a very porous and intricate surface texture. The light curve amplitude shows a slight increase at shorter wavelengths, suggesting an increasing contrast between the dark and bright materials. The spectral reflectance curves we derive for the satellites are in agreement with the spectrophotometry of McCord, Johnson, and Elias.

I. INTRODUCTION

Previous photometric observations of the satellites of Saturn have been insufficient to permit a clear separation of the solar phase and orbital phase contributions to the observed light variations. The former quantity gives information on the surface microstructure of bodies without atmospheres, while the latter quantity yields information on the global distribution of albedo features, which in some cases m a y be related to interactions between the satellite and its environment. In order to determine the solar and orbital phase coefficients and to establish their wave-

length dependence, we undertook a program of six-color photometry of Iapetus, Titan, Rhea, Dione and Tethys during Saturn's 1972/1973 apparition. The observations cover solar phase angles from +6.4 ° to -4.8 ° and wavelengths from 0.35 to 0.75pm. II. OBSERVATIONS

The observations were made with the 61-cm telescope and standard photoelectric photometer of the Mauna Kea Observatory. This photometer uses an EMI 9558B (S-20) photomultiplier, thermoelectrically cooled to -20°C, together with photon-counting electronics and teletype data recording. We observed in six colors:

1 Guest Observer, Mauna Kea Observatory, University of Hawaii. Copyright © 1974by Academic Press, Inc. 334 All rights of reproduction in any formreserved. Printed in Great Britain

SATURN'S SATELLITES PHOTOMETRY

the standard four StrSmgren filters (u, v, b, y), an interference filter centered at 6239 • (here called the r' filter), and a wideband Schott RG 715 (here called the i' filter) that, in combination with the photomultiplier, provided a broad passband between 0.7 and 0.8~m. The central wavelengths and bandwidths of these filters are given in Table I. Each observation normally consisted of three consecutive integrations in each of the six colors, followed by measurements of the sky. The integration times were 8 sec for standard stars, either 8 or 16 sec for Titan, and 16 sec for the other satellites. An aperture 15-arc sec in diameter was most suitable for the outer satellites (Iapetus, Titan, and sometimes Rhea). For the inner satellites, however, the high background level of light scattered from Saturn necessitated the use of a 7-arc sec aperture. Standard stars were observed approximately once per hour, usually with both the 15- and 7-arc sec apertures. For Iapetus and the standard stars, the sky signal was measured by simply off. setting the telescope north or south by 15-20 arc sec. A more careful procedure was required for the inner satellites, however, in which the sky was measured on both sides of the satellite at the same radial distance from Saturn as the satellite. Errors in positioning the aperture in the presence of a strong gradient in the scattered light are the source of most of the uncertainty in the measurements of Dione, and especially of Tethys. A discussion of these effects, together with a plot of scattered light as a function of distance from Jupiter obtained with this same

335

telescope and photometer, has been presented by Cruikshank and ~ u r p h y (1973). For each observation we averaged the number of counts, computed a standard deviation, and subtracted the average of the sky readings. Where several sequences were taken on the same satellite within a short period of time, all of these measurements were combined to generate a single 6-color set of observations. Numerous observers have measured extinction in the uvby system at ~ a u n a Kea and have demonstrated t h a t the mean coefficients are highly reproducible (Wolff and Wolff 1971 ; )/[orrison et al. 1973). The uvby extinction coefficients t h a t we measured for our standard comparison star (37 Tau = H R 1256) generally agreed with the mean values (Table I). For the r' and i' filters, we determined extinction coefficients of 0.09 4- 0.02 and 0.07 4- 0.02 mag/airmass, respectively. Since we did not normally observe at airmasses greater than 2 and we reduced the magnitudes relative to 37 Tau, the uncertainties in these coefficients are insignificant. Differential magnitudes, expressed relative to our primary standard, 37 Tau, are sufficient for the determination of phase coefficients and amplitudes of light curves. These magnitudes, reduced to mean opposition distance from Earth and Sun (r = 9.54 AU and A = 8.54 AU), are tabulated in Tables I I - V I . In a later section, we will derive a transformation between our instrumental y magnitudes and the V magnitudes of the UBV system and between our instrumental colors and those of the standard uvby system. However, since these transformations introduce un-

TABLE I FILTER CHA.RACTERISTICS AND EXTII~CTIOI~ COEFFICIENTS Filter (A) Full-width at half-maximum

u

v

b

y

r"

i'

3500 300

4110 190

4670 180

5470 230

6239 256

~7500 N500

0.47

0.24

0.15

0.11

0.09

0.07

(h) N o m i n a l e x t i n c t i o n coefficient ( m a g / a i r m a s s )

S e p t . 15 16 17 18 19 20 22 23 25 Oct. 2 3 12 13 14 15 16 17 18 Nov. 1 19 2O 21 25 29 3O Dec. 1 2 13 14 J a n . 16

D a t e 1972--1973

13 12 12 13 11 12 12 15 11 13 12 13 12 10 12 11 11 10 9 9 8 10 21 9 9 8 8 11 6 6

UT

Hours

Orbital phase 8 (deg) 348 10 31 54 74 96 140 166 209 12 32 212 258 280 304 326 349 11 327 14 35 58 157 239 263 284 307 196 215 243

Solar phase (deg) 6.4 6.4 6.4 6.4 6.4 6.3 6.3 6.3 6.2 6.0 6.0 5.6 5.5 5.5 5.4 5.4 5.3 5.2 4.1 2.4 2.2 2.1 1.7 1.2 1.1 1.0 0.9 0.5 0.6 4.1

__ .07 __ .04 ____..07 +__ .04 __ .04 + .07

+_ .04 __ .05 ____..02 __ .02 + .02 +__.02 +___.05 +__ .03 __ .02 __ .05 +__ .02 __+ .04 __+ .03 +__.03 ____..02 +___.03 __ .03 +__ .02 __ .02 + .02 __ .02 + .03

3.96 3.98 4.00 3.95 3.99 3.96

3.94 4.03 3.95 3.95 3.97 3.95 3.96 3.95 3.97 3.96 3.92 3.92 3.94 3.93 3.91 3.89 3.90 3.90 3.90 3.89 3.86 3.91

TrrAN

TABLE

II

__+.05 __+.07 __+ .04 __ .03 +__.03 +__ .03 ____..06 __ .03 __+.02 +__ .03 __ .02 +___.02 _____.02 +__ .01 +__ .03 __ .02 __ .02 __ .02 ____..02 +__.02 __ .02 +__ .02 __ .04 __+ .01 __ .01 __ .01 + .02 _____.04

4.16 4.14 4.11 4.13 4.13 4.12 4.21 4.11 4.12 4.11 4.12 4.12 4.13 4.12 4.12 4.13 4.16 4.10 4.12 4.10 4.08 4.08 4.11 4.08 4.08 4.08 4.04 4.08

v 4.21 4.26 4.22 4.20 4.21 4.22 4.23 4.26 4.22 4.20 4.19 4.2I 4.17 4.21 4.21 4.21 4.22 4.23 4.19 4.18 4.22 4.19 4.17 4.19 4.18 4.17 4.18 4.18 4.16 4.18

__+ .03 + .04 __+.03 __+.03 +__ .01 +___.02 __ .02 __+.04 __ .03 +__ .03 __ .01 ____..02 +___.02 +__ .03 __ .02 __+.02 +___.02 +__ .02 ____..02 +__ .02 +__.03 __ .01 __ .02 + .02 __-/-.03 +__.02 __ .01 __ .01 _____.02 +__ .03

b 3.96 3.99 3.98 3.95 3.95 3.97 3.96 3.99 3.98 3.95 3.95 3.95 3.91 3.92 3.95 3.95 3.95 3.96 3.93 3.94 3.96 3.94 3.92 3.93 3.94 3.93 3.93 3.93 3.93 3.92

+ .02 __+ .03 + .05 + .02 __+.02 +__ .03 __ .02 __ .04 __+ .03 __ .03 +__ .02 __ .02 +___.02 __ .03 __ .02 __ .02 __ .02 __ .02 +__ .02 +__ .01 __ .03 +__.01 +_ .01 __ .01 ____..02 __ .02 +__ .01 __ .02 + .02 __+.04

y 3.88 3.88 3.87 3.88 3.89 3.88 3.90 3.93 3.89 3.88 3.88 3.91 3.85 3.91 3.89 3.88 3.90 3.89 3.88 3.88 3.93 3.89 3.87 3.88 3.89 3.88 3.88 3.87 3.90 3.87

__+ .03 __+.05 __+ .04 + .02 __+ .01 4- .03 __ .01 __ .02 __+ .04 __ .03 __ .03 __ .02 -4- .02 + .03 __ .02 +__ .02 __ .03 __ .03 __ .02 -I- .01 +__ .03 __+ .01 __ .02 +..01 __ .02 +__ .02 __ .01 __ .03 __ .02 __.+.05

r"

M a g n i t u d e s r e l a t i v e t o 37 T a u a t m e a n o p p o s i t i o n

4.09 4.08 4.08 4.02 4.03 4.06 4.07 4.08 4.06 4.03 4.05 4.07 4.04 4.08 4.05 4.03 4.06 4.05 4.O3 4.04 4.08 4.04 4.03 4.05 4.05 4.04 4.05 4.05 4.04 4.05

_ .03 + .03 _+ .05 __..03 _+ .01 _ .03 _+ .04 _+ .02 + .04 _+ .03 _ .02 _ .02 +_ .02 _ .03 _ .01 +_ .02 __..03 _+ .01 + .02 + .01 +_..03 + .01 _+ .01 _+ .02 _+ .02 _ .02 +_ .01 _+ .03 _+ .02 _+ .04

i"

o

S e p t . 19 22 25 O c t . 12 13 14 15 15 16 16 17 17 17 18 18 18 N O V • 19 20 25 25 30 Dec. 1 1 1 2 2 10 13 13 14

D a t e 1972-1973

12.5 12.9 12.2 15.1 12.9 11.9 14.6 12.2 13.5 10.9 10.4 12.8 14.2 10.0 12.3 13.7 11.4 10.4 8.9 13.0 11.2 8.3 10.1 11.4 10.3 11.5 11.6 10.0 13.8 7.2

Hours UT 6.4 6.3 6.2 5.6 5.5 5.5 5.4 5.4 5.4 5.4 5.3 5.3 5.3 5.2 5.2 5.2 2.4 2.2 1.7 1.7 1.1 1.0 1.0 1.0 0.9 0.9 0.3 0.5 0.5 0.6

Solar phase a (deg) 147 27 265 189 261 337 66 58 142 134 210 219 224 290 297 302 327 43 77 9O 124 194 200 204 280 284 203 76 89 148

Orbital phase 0 (dog)

HI

+_ .08 _+ .01 -I- .05 _+ .02

4.59 4.57 4.56 4.59

4.25 +_ .02

4.44 + .02

4.45 + .06 4.30 _+ .01

_+ .03 + .04 +_ .08 _ .02 +_ .02 _ .05 _+ .02 +_ .02 + .01

4.43 4.49 4.66 4.54 4.65 4.66 4.39 4.38 4.40 _ .01 _+ .05 + .03 -_V_.02 + .05 4- .03 _+ .05 __..04 + .02 _+ .05 +__.02 _+ .02

_+ .05 -I- .06 _+ .05 _ .01 + .03

4.72 _+ .02

4.95 4.91 4.73 4.66 4.73

5.04 _+ .03

4.83 4.88 5.06 4.88 5.05 4.95 4.77 4.80 4.84 4.81 4.96 4.95

v

_+ .03 +_ .02 +_ .06 _ .02 _+ .01 +__.02 +__.02 + .01 +__.01 +__.01 + .01

_+ .01 _+ .05 + .03 -I- .01 _+ .07 + .04 _+ .03 + .01 --I-.01 _+ .04 +_ .03 _+ .06 +_ .02 + .03

5.12 +_ .03

5.04 _+ .01

5.38 5.26 5.22 5.15 5.06 5.04 5.30 5.20 5.22 5.22 5.22

5.21 5,26 5,42 5,27 5.55 5.37 5,21 5.20 5.21 5.21 5.35 5.37 5.37 5.40

b _ .01 +_ .02 +_ .05 -t- .03 _+ .05 -I- .02 _+ .04 4- .03 + .02 -I- .02 + .02

_ .02 +_-.03 + .01 _+ .03 + .01 +_ .02 +__.02 + .01 + .01 + .01 __+ .05 + .01 5.22 +_ .02 5.21 _+ .02 5.24 +__.02

5.52 5.50 5.40 5.31 5.22 5.24 5.23 5.35 5.36 5.36 5.43 5.37

5.52 _ .01

5.35 5.42 5.55 5.47 5.63 5.48 5.35 5.37 5.35 5.38 5.52

y

5.61 5.69 5.70 5.48 5.41 5.32 5.32 5.35 5.45 5.45 5.53 5.59 5.47 5.44 5.29 5.33 5.35

5.44 5.53 5.67 5.49 5.61 5.52 5.44 5.47 5.45 5.47 5.55 5.60

+_ .05 _+ .O3 +_ .02 +_ .03 _+ .04 + .01 _ .02 + .04 + .01 + .02 +__.01 + .05 +__ .01 _+ .03 _+ .02 _+ .02 +_ .02

_+ .02 + .O1 _+ .03 + .03 _+ .07 _ .03 + .03 + .02 +__.02 + .02 + .05 _+ .02

r'

M a g n i t u d e s r e l a t i v e t o 37 T a u a t m e a n o p p o s i t i o n

RHEA (7" APERTURE)

TABLE

5.40 _+ .02 5.38 + .02 5.47 ___ .02

_ .02 + .04 _+ .02 _ .02 + .04 _+ .02 4-_ .01 _+ .02 ___ .01 + .01 + .02 +_ .02 +_ .02

+ .02 ___ .10 + .10 ___ .01

5.57 5.61 5.66 5.67

5.72 5.92 5.77 5.62 5.53 5.50 5.45 5.46 5.63 5.57 5.57 5.63 5.60

+__.02 + .02 + .05 + .04 + .03 + .02

5.56 5.65 5.77 5.71 5.87 5.70

i'

o o

5~

5~

Jan.

Dec.

30 30 30 2 2 14 16

29 29 29

2 2 2 N o v . 21 21 25 25

Oct.

D a t e 1972-1973

11.0 12.7 14.2 9.5 12.1 10.7 I3.9 7.7 9.4 11.4 7.8 8.2 9.8 7.1 8.0 8.1 6.1

Hours UT

1.7 1.7 1.2 1.2 1.2 1.1 1.1 1.1 0.9 0.9 4.0 4.1

2.1

6.0 6.0 6.0 2.1

Solar phase (deg) 98 104 109 120 129 83 94 32 37 44 113 114 119 270 273 103 256

Orbital phase (deg) 4.39 4.43 4.37 4.34 4.27 4.23 4.25 4.35 4.29 4.31 4.15 4.21 4.21 4.40 4.47 4.35 4.54 _ .02 _+ .02 _+ .09 _+ .02 + .02 +_ .02 _ .02 +_ .02 +_ .02 _+ .02 + .07 + .02 _ .02 -4- .02 -4- .02 + .02 -4- .02

4.81 4.85 4.79 4.76 4.75 4.63 4.67 4.79 4.72 4.74 4.67 4.66 4.68 4.79 4.85 4.78 4.93

_ .02 _+ .02 + .04 _ .02 + .02 _ .02 + .02 _ .02 _ .02 + .02 + .02 _ .02 _+ .02 -4-_.02 _+ .02 _ .02 + .02

v 5.24 5.27 5.21 5.15 5.14 5.01 5.06 5.14 5.12 5.14 5.07 5.08 5.06 5.18 5.26 5.20 5.30

_ .02 _ .02 _ .02 _ .02 +_ .02 +_ .02 + .02 _ .02 +_ .02 +_ .02 _ .02 _ .02 +_ .02 + .02 _+ .02 +_ .02 + .02

b 5.29 5.39 5.37 5.30 5.29 5.16 5.21 5.31 5.32 5.32 5.24 5.23 5.24 5.35 5.42 5.36 5.44

+ .02 _ .03 _ .03 _ .02 +_ .02 +_ .02 _ .02 _ .02 _+ .02 _ .02 _ .02 _+ .02 + .02 _ .02 _+ .02 _+ .02 _ .02

y 5.40 5.51 5.47 5.40 5.40 5.24 5.31 5.44 5.44 5.39 5.34 5.38 5.33 5.44 5.53 5.47 5.52

_ .02 ___ .05 _ .02 _ .03 +_ .02 +__ .02 _ .02 +_ .02 +_ .02 _ .02 _ .02 _ .02 _ .02 + .02 + .02 _ .02 + .02

r"

M a g n i t u d e s r e l a t i v e t o 37 T a u a t m e a n o p p o s i t i o n

l~m~A (15" ~Xl~TUI~E )

T A B L E III----eontinued

5.50 5.49 5.33 5.42 5.54 5.55 5.55 5.45 5.44 5.43 5.55 5.65 5.61 5.62

+ .02 _ .02 + .02 +_ .02 +__ .02 + .02 + .02 +_ .02 _ .02 _ .02 + .02 _ .02 + .02 + .02

5.62 + .03 5.58 + .02

5.45 + .O3

i"

o

Qo

e.m

S e p t . 15 Oct. 13 14 15 15 16 16 17 17 17 18 18 18 :Nov. 1 1 25 29 29 3O 30 :Dee. 1 1 1 1 1 1 2 2 2 2 13 13

D a t e 1972-1973

13.5 14.5 12.3 12.5 14.9 11.4 13.8 10.7 13.1 14.5 10.3 12.6 14.0 9.4 9.9 12.3 8.6 11.6 10.6 10.9 8.2 8.5 9.9 10.3 11.2 11.7 8.2 9.6 10.0 11.3 7.3 14.3

Itours UT 6.4 5.5 5.5 5.4 5.4 5.4 5.4 5.3 5.3 5.3 5.2 5.2 5.2 4.1 4.1 1.7 1.2 1.2 1.1 1.I 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.5 0.5

Solar Phase a (deg) 207 170 283 56 69 182 195 309 322 33O 77 92 99 116 119 51 197 213 339 341 98 100 108 110 115 117 230 237 240 247 233 271

Orbital phase (deg)

_ .04 + .05 -4- .08 -4- .08 -4- .05

-4- .02 -4- .04 -4- .04 -4- .03 -4- .04

5.11 -4- .06 4.98 -4- .02

4.88 4.91 4.94 4.86 5.11

5.04 -4- .03

5.40 4.89 4.88 4.99 5.01

DIo~

TABLE

-4- .04 -4- .02 _ .02 -4- .02

-4- .02 -4- .02 ___ .02 -4- .04 -4- .02 -4- .03 -4- .06 _ .03 -4- .03 -4- .02 -4- .02 -4- .02

5.50 5.45 5.81 5.42

5.45 5.66 5.62 5.53 5.33 5.43 5.42 5.32 5.32 5.36 5.51 5.45

v

_ .03 -4- .06 _ .02 -4- .04 -4- .02 -4- .03 -4- .02

+ .02 -4- .06 -4- .02 -4- .02 -4- .02 + .02 + .02 -4- .02 -4- .02 + .02

5.67 5.68 5.69 5.71 5.70 5.78 5.83 5.92 5.96 5.93

_ .02 _+ .02 -4- .03 -4- .02 -4- .03

5.77 5.85 6.07 6.03 5.97 5.81 5.79 5.78 5.73 5.76 5.85 5.82

-4- .02 -4- .02 -4- .04 -4- .02

5.91 5.76 6.28 5.86

b

-4- .06 -4- .04 -4- .02 -4- .05 -4- .02 -4- .04 -4- .14 -4- .14

6.07 -4- .02

-4- .02 -4- .06 -4- .07 -4- .03 -4- .03 + .02 -4- .02 -4- .02 -4- .02 -4- .02 -4- .05 -4- .04 -4- .03

6.00 5.91 5.98 6.02 6.06 6.03 6.04 6.25 6.27 6.24 6.35 6.30 6.14

-4- .02 -4- .02 -4- .02 -4- .02 -4- .02 -4- .02 -4- .03 -4- .02 -4- .02 -4- .03 -4- .02

5.96 5.89 5.89 5.91 5.93 5.92 5.99 6.11 6.18 6.13 6.13

6.08 -4- .03 5.89 -4- .02 6.05 -4- .02

6.05 -4- .02 6.04 -4- .02

6.01 6.52 6.19 5.98 6.03 5.93 6.51 6.47

6.29 -4- .06

-4- .05 -4- .02 -4- .02 -4- .04 -4- .02

-4- .04 -4- .02 -4- .05 -4- .02 -4- .02 -4- .02 -4- .02 -4- .02 -4- .03

r'

6.12 -4- .07

6.02 6.01 5.98 5.92 6.01

6.06 5.96 6.39 6.02 6.08 5.92 5.93 6.24 6.21

y

M a g n i t u d e s r e l a t i v e t o 37 T a u a t m e a n o p p o s i t i o n

IV

6.11 6.12 6.10 6.13 6.16 6.13 6.19 6.38 6.41 6.38 6.41 6.44 6.33

6.20 6.05 6.06 6.48 6.40 6.35 6.17 6.18 6.22 6.04 5.86 6.27

± .02 -4- .02 _4- .02 -4- .02 -4- .02 +_ .03 _ .04 -4- .02 _+ .02 _+ .02 _+ .02 -4- .02 .05 -+ -

_ .02 +__.02 + .04 ±_ .03 + .03 _ .13 .03 -+ ± .02 _+ .05 ± .02 ± .02 _+ .02

5.93 + .03 6.69 -4- .06

i'

¢D

09 09

O O g

P~

~. ~

13 14 15 15 16 16 17 17 17 18 18 18 Nov. 29 29 3O 3O 3O 3O Dee. 1 1 1 1 2 2 2 2 2 13

Oct.

Date 1972-1973

13.3 12.7 12.9 15.1 11.8 14.1 11.0 13.4 14.8 10.6 12.9 14.3 11.8 12.0 11.1 11.5 11.7 12.0 10.5 11.1 11.5 11.8 9.8 10.1 10.4 11.1 11.5 12.6

Hours UT 5.5 5.5 5.4 5.4 5.4 5.4 5.3 5.3 5.3 5.2 5.2 5.2 1.2 12 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.5

Solar phase (deg) 270 96 282 300 llO 128 294 313 324 122 140 151 224 226 5O 53 54 56 235 240 243 246 61 63 65 71 74 22

Orbital phase O (deg)

± ± ± _ ± ± ±

.03 .09 .03 .04 .09 .02 .02

4.84 ± .02 4.79 ± .05

4.87 4.90 4.93 4.92 4.88 4.79 4.82

5.14 ± .03 4.72 _ .03 4.95 ± .03

TET]~YS

TABLE

V

5.43 5.35 5.32 5.28 5.47 5.36 5.50 5.28 5.27 5.29 5.32 5.28

± ± ± ± ± ± ± ± ± ± ± ±

.02 .05 .02 .02 .02 .03 .08 .02 .04 .06 .02 .02

5.38 _+ .03

v ± .02 ± .02 ± .02 ± .04 __ .02 ± .02 ± .02

6.12 5.88 5.76 5.64 5.55 5.57 5.66 5.58 5.60 6.04

± .02 ± .05 ± .02 ± .02 ± .02 ± .02 ± .02 ± .02 ± .02 +_ .05

5.72 ± .02 5.65 ± .02 5.68 ± .02

5.73 ± .02 5.69 ± .02 5.73 + .02

5.73 5.61 5.84 5.76 5.77 5.74 5.87

b 5.90 5.75 6.05 6.05 6.00 5.92 6.05 6.05 5.91 5.87 5.94 5.95 5.99 5.93 5.99 5.90 6.02 5.80 6.10 6.04 6.00 5.82 5.76 5.73 5.87 5.79 5.82 5.77

± .02 ± .02 ± .03 ± .03 ± .02 ± .02 ± .02 ± .02 ± .05 ± .02 ± .02 ± .05 ± .02 ± .02 __ .02 ± .02 ± .02 ± .02 __ .02 ± .02 ± .02 ± .02 ± .02 ± .02 ± .02 ± .02 _ .02 _ .12

y 5.95 5.77 6.22 6.08 6.12 6.04 6.22 6.22 6.13 6.08 5.98 6.15 6.04 5.98 6.27 6.07 6.16 5.97 6.31 6.28 6.10 5.92 5.85 5.88 6.06 5.89 5.86 6.34

± .03 ± .05 ± .02 ± .02 ± .02 ± .05 ± .04 +__.05 ± .13 ± .09 ,,, .04 ± .07 ± .02 ± .03 ± .04 ____.03 ± .06 ± .09 ± .02 ± .03 __ .02 ± .02 ± .02 ± .02 ± .03 ± .02 ± .02 ± .17

r'

M a g n i t u d e s relative t o 37 Tau a t m e a n opposition

6.50 6.50 6.38 5.98 5.99 5.95 6.23 6.03 6.06 5.73

6.01 5.92 6.35 6.22 6.21 6.29 6.30 6.20 6.28 6.25 6.18 6.09 6.19 6.32 6.32

± ± ± ± ± ± ± ± _ ±

.02 .06 .04 .02 .03 .02 .03 .02 .02 .02

± .04 ± .03 ± .03 ± .06 ± .02 ± .11 +_ .02 ± .02 ± .02 ± .05 ± .03 ± .08 + .05 ± .10 ± .11

i'

o

~D

~O

Sept. 16 17 18 19 20 22 23 25 2 Oct. 3 12 13 14 15 16 17 18 N o v . 19 20 21 25 29 30 Dec. 1 2 10 13 14 22 J a n . 14 15 24

D a t e 1972-1973

12 12 14 12 12 12 13 11 13 13 13 12 11 12 12 11 10 10 9 11 13 9 8 8 9 11 12 7 11 7 7 7

Hours UT 6.4 6.4 6.4 6.4 6.3 6.3 6.3 6.2 6.0 6.0 5.6 5.5 5.5 5.4 5.4 5.3 5.2 2.4 2.2 2.1 1.7 1.2 1.1 1.0 0.9 0.3 0.5 0.6 1.5 4.0 4.0 4.8

Solar phase a (deg) 261 265 270 275 279 289 294 303 336 341 21 26 30 34 39 43 47 190 195 199 219 238 243 248 253 289 304 309 35O 9O 95 135

Orbital phase O (deg)

VI

4.91 4.90 4.85 4.85 4.92 4.90 5.00 4.96 5.28 5.35 5.99 6.17 6.22 6.19 6.25 6.51 6.40 5.34 5.30 5.26 5.07 4.86 4.81 4.77 4.75 4.70 4.82 4.81 5.23 6.85 6.68 6.50

.4-- .04 .4-- .14 ± .03 .4-- .07 ± .12 .4-- .14 .4-- .01 .4-- .04 .4-- .04 ± .03 + .05 .4-- .06 .4-- .05 ± .08 + .11 .4-- .06 ± .08 .4-- .03 .4,, .04 4- .04 .4-- .04 ± .01 ± .03 .4-- .04 .4-- .03 .4-- .02 .4-- .03 .4-- .10 .4-- .06 ± .12 ± .09 _+_.07

IAPETUS

TABLE

5.39 5.41 5.37 5.40 5.40 5.36 5.45 5.55 5.78 5.81 6.51 6.58 6.63 6.79 6.80 6.90 6.95 5.83 5.79 5.74 5.50 5.35 5.32 5.29 5.24 5.20 5.31 5.34 5.74 7.31 7.27 6.97 4-- .03 +_ .03 4-- .05 4-- .02 4-- .06 _ .10 4-- .01 4-- .03 4-- .04 4-- .04 4-- .02 4-- .04 4-- .04 4-- .04 4-- .05 4-- .05 4-- .05 4-- .03 4-- .01 4-- .03 4-- .02 4-- .02 4-- .02 4-- .02 4-- .03 4-- .02 4-- .03 4-- .10 4-- .02 4-- .03 + .02 4-- .03

v 5.87 5.81 5.80 5.82 5.86 5.89 5.89 5.89 6.21 6.27 6.96 7.00 7.15 7.17 7.24 7.32 7.40 6.28 6.21 6.19 5.95 5.80 5.77 5.72 5.70 5.67 5.75 5.81 6.17 7.70 7.68 7.40

_ .02 .4-- .06 .4-- .02 .4-- .05 .4-- .05 .4--.02 .4-- .02 .4-- .04 ± .03 .4--.02 .4-- .02 .4-- .03 .4--.10 ± .06 ± .05 ± .05 .4-- .05 ± .04 .4-- .01 .4-- .03 .4-- .01 ± .02 .4-- .02 + .03 .4--.02 .4-- .02 .4-- .01 .4-- .10 .4-- .02 .4-- .03 + .03 _+ .03

b 6.06 6.03 6.03 6.06 6.01 6.11 6.13 6.13 6.39 6.47 7.16 7.21 7.24 7.34 7.36 7.56 7.58 6.49 6.45 6.40 6.15 6.00 5.97 5.95 5.91 5.90 5.94 5.97 6.39 7.86 7.93 7.57

.4-- .02 .4-- .03 .4--.06 .4-- .02 ± .07 .4-- .03 _ .01 .4-- .04 .4-- .04 ± .03 .4-- .01 .4-- .01 ± .03 .4--.10 ± .14 .4--.05 .4-- .06 .4-- .03 .4-- .01 .4--.02 ± .02 .4--.01 .4-- .04 .4-- .02 .4-- .02 .4-- .02 .4--.02 .4-- .04 .4-- .02 .4-- .03 +_ .02 .4-- .04

y 6.11 6.10 6.15 6.14 6.18 6.23 6.26 6.30 6.52 6.59 7.22 7.23 7.33 7.41 7.49 7.50 7.67 6.60 6.54 6.49 6.26 6.11 6.08 6.05 6.03 6.04 6.06 6.14 6.49 7.80 7.87 7.71 ± .08 4-- .09 .4-- .03 4-- .04 4-- .07 4-- .05 ± .05 4-- .07 4-- .03 + .03 4-- .02 4-- .04 + .07 .4-- .06 ± .04 4-- .04 ± .05 -4-_.02 4- .02 + .03 + .02 4-- .02 + .03 + .04 .4-- .02 -4- .02 4-- .04 + .04 + .02 .4-- .10 + .04 + .04

r'

M a g n i t u d e s r e l a t i v e to 37 T a u a t m e a n o p p o s i t i o n

6.26 6.33 6.23 6.26 6.32 6.30 6.32 6.38 6.59 6.67 7.29 7.34 7.52 7.58 7.60 7.62 7.79 6.73 6.66 6.62 6.37 6.23 6.18 6.15 6.13 6.07 6.16 6.24 6.61 7.98 8.04 7.71

± .04 ± .09 _ .03 ± .02 ± .03 ± .05 ± .10 ± .07 ± .05 .4-- .04 _ .02 ± .03 .4-- .06 .4-- .07 .4-- .05 ± .04 ± .09 .4-- .03 ± .02 ± .04 .4-- .03 .4-- .02 ± .03 .4-- .05 .4-- .01 .4-- .02 .4-- .02 .4-- .10 .4-- .02 ± .03 .4-- .03 ± .03

i'

o o

342

NOLAND

certainties in addition to those inherent in the basic differential photometry, we will base most of our physical conclusions on the instrumental relative values. Estimates of the uncertainty in each satellite magnitude (relative to 37 Tau) can be obtained in at least two ways. First, we compute the internal standard error obtained in averaging the three or more integrations t h a t make up each observation point. Second, observations made during the same night at similar solar and orbital phase angles can be checked for consistency. For the inner satellites, the errors estimated in the second way are usually greater than the internal errors, a result in agreement with our expectation t h a t the main source of uncertainty is the nonreproducibility of the sky readings. The larger of the two errors is adopted for each point and quoted in the tables. III. METHOD OF ANALYSIS

for the case of Iapetus (Morrison et al., 1975). Several assumptions and approximations are implicit in Eq. (1). First, a linear dependence on the solar phase angle is assumed, whereas over the range of phase angles of interest (0°-6 ° ) opposition effects are important for dark, texturally complex surfaces, and a phase angle dependent phase coefficient can be expected. Second, the orbital variation assumes t h a t the period of rotation of the satellite equals its orbital period. This assumption seems to be well founded, and only in the case of Tethys has it been questioned (Franz and Millis, 1973). Finally, the orbital sinusoid is only the first term in the general expansion of the brightness variation, and, in fact, the brightness, not the magnitude, is the quantity which varies sinusoidally with orbital phase. Only when ~JM < 0.3 mag is it true t h a t LJM~= o = --2.512 log [1 -- (/~ sin 0/I0) ]

Mean opposition magnitudes of the satellites relative to 37 Tau are given in Tables I I - V I . Assuming the magnitudes vary linearly with solar phase angle and sinusoidally with orbital phase angle, we perform a four-parameter least-squares fit to the data for each satellite with the equation : M=Mo+~O~+~osin(O--Oo),

et al.

(1)

where M 0 = mean magnitude relative to 37 Tau, ~ = solar phase angle, fi = phase coefficient, 0 = orbital phase angle, measured in the prograde sense from superior conjunction, 0o = orbital phase angle at which Mo occurs, and 2/~0 = peak to peak amplitude of the orbital phase variation. Except in the case of Tethys, points are weighted as 1/a 2, where a is the error assigned to an individual point according to the procedure outlined in Section II. In the case of Tethys, a more subjective weighting procedure is used (see Section VII). Note that, because of our interest in the wavelength dependence of phase coefficients and amplitudes, we reduce the magnitudes from each filter separately. Separate fits to colors are not attempted except

1.1 (~l sin 0/I0) ~- ~0 sin0, where ~ = half amplitude of the brightness variation and I 0 = b r i g h t n e s s at 0 = 0 ° and 180 ° for a = 0 ° (see Section VIII). For Iapetus this approximation is invalid, and the brightness version of Eq. (1) must be used. The philosophy adopted here is to regard Eq. (1), or its brightness equivalent in the case of Iapetus, as a suitable starting point for our analysis. For each satellite we shall determine the four parameters from the data and then comment upon the meaning and validity of the solutions in each particular case.

IV. TITAN When the thirty available observations (Table II) are fitted for all four parameters in Eq. (1), it is found t h a t the light curve amplitude (2/~0) is less than 0.02 mag at all wavelengths, in agreement with the earlier observations by Harris (1961), Blanco and Catalano (1971) and McCord, Johnson and Elias (1971). Since there is no observable orbital

SATURN'S SATELLITESPHOTOMETRY

343

TABLE VII TITAN: DERIVEDLIGHT-CURVEPAttAMETERS u ~(raag/deg) Mo (mag)

v

b

y

r'

.014 _+ .OO1 .010 _ .001 .006 _..001 .005 _ .OO1 .002 __ .001 .001 _..001 3.88 _+ .01 4.07 __ .01 4.17 +_ .01 3.93 _+ .01 3.88 _+ .O1 4.04 __.01

variation, the d a t a m a y be a n a l y z e d b y m e a n s of a t w o - p a r a m e t e r fit, M

=

M 0 + fl~,

t o determine the w a v e l e n g t h dependence of the phase coefficients. The results, shown in Table V I I a n d Figs. 1 a n d 2, range from 0.014 m a g / d e g in the ultraviolet to negligible values in the infrared. The only previous d e t e r m i n a t i o n of a phase coefficient for T i t a n is t h a t of Blanco a n d Catalano (1971). A l t h o u g h these a u t h o r s fit their d a t a to a q u a d r a t i c expression for a, a linear e q u a t i o n yields an equally good fit with fl(V) - 0.006 ± 0.001mag/deg, a result in a g r e e m e n t with our y value. R e c e n t models of T i t a n (Pollack, 1973 ; Danielson et al., 1973; Veverka, 1973;

B a r k e r a n d Trafton, 1974) postulate various a m o u n t s of a t m o s p h e r e a n d aerosols on Titan. Some involve optically t h i c k clouds, while others require only a t h i n aerosol haze over a partially obscured surface. The ability of these models to reproduce the observed phase coefficients is discussed in detail in N o l a n d a n d V e v e r k a (1974).

V. RHEA F o r R h e a a n d the inner satellites sky brightness m e a s u r e m e n t s become progressively more difficult, with the result t h a t certain m e a s u r e m e n t s are n o t i c e a b l y discrepant a n d have to be excluded. There r e m a i n 17 m e a s u r e m e n t s m a d e with t h e 15-arc sec aperture a n d up to 30 measure-

T T IANI

T I T A N

L

3.80

~

I

filfe/~u

L

~

,

59 ,0 , =4

• oo

2

4.00

i'

,

j

;

i

'

.

0

,

0

~ l

filter=,

•9 °

,

,

,

'

,

~

4.30

(deg)

filferl = ¢,~

lit

f;Ttef = b

400 / 4.20

1

3.80

4.20 ,

filler .y

i

-o

4. I0

'

'

,

4.,otJliliI,

,

(2

,

(deg)

FIG. 1. Magnitude of Titan as a function of the solar phase angle ~. The meaning of the error bars is discussed in Section II. All magnitudes in this and subsequent figures are reduced to mean opposition (r = 9.54 AU; A = 8.54 AU).

344

~OLAZ~D

et al.

T A B L E VIII

RHEA: DERIVED LIGHT-CURvE PARAMETERS

fl(mag/deg)

.037 _ .003 .24 -+ .02 4.30 + .01 7 -+ 5

2/~o ( m a g ) J~ro ( m a g ) 0o (deg)

0.015

v

b

y

r'

i"

•031 +_ .003 •20 +_ .02 4.73 -+ .01 12____.8

.027 -+ .003 .18 + .02 5.13 + .01 0-+7

.025 + .002 .19 + . 0 2 5.29 -+.01 0_____5

.025 __+.003 .19 __+ .02 5.40 -+.01 --1__+7

.024 __+ .004 .20 --+.02 5.52 -+.01 3-+9

TLTAN

001(

E~ 0.005

Fro. 2. Wavelength dependence of Titan's phase coefficient.

ments (depending on the filter) made with the 7-arc sec aperture (Table III). No systematic difference between the two sets is evident, and they have been combined to determine the parameters given in Table VIII. A sinusoidal variation in magnitude with an amplitude of about 0.2 mag provides good fit to the data (Fig. 3). The rotation period appears to be completely synchronous, with maximum brightness occurring near 0 = 90 ° and minimum brightness near 0 = 270 °. It is therefore the leading side of Rhea which is brighter. These results are in agreement with earlier, less comprehensive measurements by Harris RHEA ]

,

=

,

i

,

I

'

i

,

i

,

i

,

i

,

i

filler

,

.y

RHEA

i

5

'

4 5 0 l ,4 "i . . ~0, 0 i~' / l - ' =i . ui .

i,

i,

.

0

0

~

i 5"50~ , I . . . . . . .

I,'

: .....

=

=

i

,

r

,

'~

i

,

.i

i

,

i

,

.l,l

4.50

~

~

.i

,

l

"i'

,

i

i,

i,

.

I

,~

['

1

i

r

i

*

~

,

[

,

j

,

i

,

i

i

i

,

~

filter

,

z •

LI

filter

=

v

6

"~ 5.00 ,

I

o

1

5.00

& =

.~ 5.5o

t

,

i

] '

,

i

,

i

,

'

i

.

.

.

i

, .

i

,

~ ,

L ,

i

i

,

i

,

•

5.o~,

5°°t |,

0

r

,

i

,

i

,

I

0 ,

i

,

i

,

i

.

i

r

40 80 120 160 ~00 L~.0 7.80 32.0 360 (deg}

, ~

t 0

40 80

120 160 ZOO 240 EBO ~ 0 360 0 {deg)

FIG. 3. Orbital magnitude variations of Rhea with solar phase angle effects removed. The fitted sinusoidal variation provides an adequate representation of the data.

345

S A T U R N ' S SATELLITES PHOTOMETRY

(1961), McCord, Johnson and Elias (1971), Blanco and Catalano (1971), and Blair and Owen (1974). In Fig. 4 we plot the derived light curve amplitude and phase coefficient against wavelength. The amplitude shows a sharp rise at wavelengths less than 0.5/xm. This behavior can be explained by a twocomponent model of the surface in which the relative contrast between the dark and bright areas increases strongly shortward of 0.5~m. The spectral reflectance data of McCord et al. (1971) show that, relative to the (trailing side)/(leading side) contrast ratio at 0.56/xm, the trailing (dark) side is darker than the leading side at shorter wavelengths, in agreement with our results, and possibly brighter at longer wavelengths, where our results are inconclusive. Such an effect can be explained if the spectral reflectance of the brighter material is flat over the wavelength range of interest (consistent with ice), while the spectral reflectance of the darker material increases from ultraviolet to red (consistent with carbonaceous or silicate material). The value of the phase coefficient increases from 0.025mag/deg in the red to 0.037mag/deg in the ultraviolet. We reiterate t h a t these are linear coefficients, determined at small phase angles, where opposition effects are likely to be important, and t h a t any comparison with phase RHEA

0.4C

!

0.3C

g

0.04C

-g o

•~ 0.03C o Q~- 0.02C 0.010

I.O0

*

2 . 0I 0

3.100

"Ix tYro'l)

FIG. 4. Wavelength dependence of Rhea's light curve amplitude (top) and phase coefficient (bottom).

coefficients of other bodies, determined at larger phase angles, must be made judiciously (see, for example, Morrison et al., 1975). Nevertheless, Rhea's phase coefficients are large, and these high coefficients, coupled with the very high geometric albedo in the visible (0.6-0.8 according to Morrison, 1974), imply a very porous and texturally complex surface layer. Such a surface layer is also needed to explain the relatively deep negative branch in the polarization curve of Rhea found by Zellner (1972). VI. DIOI~IE The available data are given in Table IV and plotted in Fig. 5. All measurements were made with the 7-are sec aperture. The data are fitted in two ways: (1) using a four parameter fit, as before; and (2) assuming 00 = 0 ° at all wavelengths, and solving for three parameters only. The parameters obtained by both methods are given in Table IX. Since the first method yields inconsistent values of 00 ranging from -21 ° (or 339 °) to +34 °, the assumption used in the second method appears justified. The main advantage of the second method is t h a t more reasonable values of fl and/~0 in the u are obtained. In what follows we will adopt the method (2) solution. The leading side of Dione is clearly brighter than the trailing side, consistent with the more fragmentary results of McCord, Johnson, and Elias (1971) and with the recent photometry of Franz and Millis (1973) and Blair and Owen (1974). I t is also clear, however, t h a t our sinusoidal fit to the data is not a very good one. Since the amplitude of the light curve appears to be larger between 180 ° and 360 ° than between 0 ° and 180 °, the amplitudes of 0.2-0.3mag indicated in Table I X m a y be underestimates. The measurements of Franz and Millis, for example, suggest an amplitude closer to 0.4 mag, and Blair and Owen claim an amplitude of 0.8mag. Unfortunately, we have too few data points to justify separate fits to the two sides. Within the error bars there is no wave

346

NOLA~D et al. DIONE I , i, I,I ' I' I ' I ' I' I'

"|1--

4.50t

h'lter

DIONE

. u

6.00

5

.

0

0

6 ,

5.501

I

,

I

,

i

.

i

,

,

I

,

i

,

L

•

i

•

i

'

I

'

'

I

'

I

'

5.0C

~

~ ~

,

I

~

'

I

filtor

.

5

0

~

1

, '

= v

o

o

o

5.5C

4 6.0(3

~

650

600 I

,

r

,

I

.

(

.

f

,

I

,

I

,

~

'

l

'

i

•

i

*

i

,

i

,

i

.

5.50

~

,

I

i

,

I

filter

,

,

i

,

i

,

~

,

E

I,, '

I

,

=b

.

i

,

i

,

i

,

i

,

i

I 32~

,

I 360

6.5C

I,

0

I.

~.

40

80

I.

I,

i,

i.

i.

i

r

I,

I ]

120 160 200 240 280 520 360

,40,_k,~.~

I

,

120 160 200

240

280

~

0 ca~)

FIG. 5. Orbital m a g n i t u d e variations of D i o n e w i t h solar p h a s e angle effects removed. The sinusoidal fit appears to u n d e r e s t i m a t e t h e light curve a m p l i t u d e near 8 = 270 °. This difficulty is discussed in Section V I .

length dependence to the derived light curve amplitudes. Unlike Rhea, Dione does not show a strongly wavelengthdependent contrast between the dark and bright areas, l~KcCord et al. (1971) report similar findings. Not much weight should be given to the precise values of the phase coefficients for Dione since the errors involved are large--

a fact underscored by the unphysical negative values of fl found in the i' filter. Nevertheless, the coefficients for Dione are significantly smaller than those for Rhea. The smaller phase coefficients and the comparable geometric albedo (0.6) given by Morrison (1974) indicate that Dione probably has a less intricate surface texture than Rhea.

TABLE IX D I O ~ V E

: D E R I V E D

L I G H T - C U r v E

P A I ~ A M : E T E R S .

SEE TEXT u

~(1) ( m a g / d e g ) fl(2) ( m a g / d e g ) 2~o(1)(mag) 2~o(2)(mag ) /~/o(1)(mag) Mo(2)(mag) 80 (1) (deg) 80 (2) (deg)

v

F O R

b

T w o

S O L U T I O N S

A R E

G I V E N .

DETAILS. y

r'

.045 ± .029 .016 _ .010 .012 ± .005 .009 ± .007 .003 ± .011 .029 ± .018 .021 ± .010 .015 ± .006 .009 ± .007 .003 _ .010 .32 + . 3 0 .36 ± . 0 8 .30 ± . 0 8 .24 ± . 1 2 .24 + . 1 0 -- .12 -- .06 .23 ± . 0 8 .33 ± . 0 6 .23 ± . 0 4 .19 ± . 0 4 .2~ ± . 0 6 4.82 ± . 1 3 5.43 ± . 0 5 5.83 ± . 0 2 6.02 ± . 0 2 6.12 ± . 0 3 4.90 ± .07 5.41 ± .05 5.80 ± . 0 2 6.01 ± .03 6.12 ± .03 --21 ± 32 16 _ 10 34_+ 19 32 ± 15 10 ± 22 0 0 0 0 0

i"

--.015 ± .011 --.015 ± .012 .32 + . 1 8 -- .08 .27 ± . 0 6 6.29 ± . 0 4 6.27 ± .04 29 ± 18 0

347

SATURN'S SATELLITES PHOTOMETRY TABLE X TETHYS : DERIVED

LIGHT-CURVE

PARAMETERS.

TWO SOLL'TIONS ARE GIVE~.

SEE TEXT FOR DETAILS.

u f~(l) ( m a g / d e g ) ~(2) ( m a g / d e g ) 2~o(l)(mag)

v

.066 _+ .015 .035 i .012 .40 + . 2 0 --

2~o (2)(mag) Mo(1)(mag) Mo (2)(mag) 0o (1) (deg) 0o (2) (deg)

.20 4.52 4.69 --35

b

.009 ± .014 .021 + .008 .11 + . 0 7

.12

--

+ .05 ± .08 ± .06 ___ 15 0

.12 5.29 5.22 54

.014 + .011 .015 ± .010 .12 + . 2 0

.15

--

i .03 ±.08 ± .04 ± 70 0

.12 5.66 5.66 --7

VII. TETHYS The observations of Tethys given in Table V are very noisy due to scattered light from Saturn. They are analyzed by the two methods used in the case of I)ione, with the most reproducible points weighted as i, and all others (whose reproducibility is bad or uncertain) weighted as 1/4. Since method (1) gives values of 00 ranging from - 4 1 ° (319 °) to +54 °, we adopt the method (2) solution, which sets 0o - 0 ° at all wavelengths. The derived parameters are shown in Table X, and a typical curve is given in Fig. 6. The leading side of Tethys is probably brighter than the trailing side. The formal values of the light curve amplitudes lie between 0.1 and 0.2 mag, which is not inconsistent with the results of Blair and

'

I

'

I

'

I

'

TETHYS I '

I

'

I

'

I

'

I

y

'

r'

.019 ± .007 .019 ± .007 .16 + . 0 6

.011 _ .012 .009 ± .012 .19 + . 3 0

.07

± .05 ± .04 ± .04 ± 50 0

--

.16 5.85 5.85 --1

± ,04 ± ,03 ± .03 ___25 0

i'

.15 6.00 6.00 33

.10

± .06 ± .04 ± .04 ± 30 0

.016 _ .014 .016 ± .014 .21 + . 4 8 - - .09 .16 ± .07 6.09 _ .05 6.09 + .05 --41 ± 30 0

Owen (1974), Franz and Millis (1973), and ~¢[cCord et al. (1971). However, Fig. 6 indicates that amplitudes up to 0.5 mag cannot be excluded. The phase coefficients are comparable to those for Dione, but, again, the uncertainties are large. Finally, since our Tethys observations extend over only two months, we cannot test the validity of the slightly nonsynchronous rotation period suggested b y Franz and ~¢[illis (1973). VIII. IAPETUS The basic data are given in Table VI, and the b filter magnitudes, uncorrected for solar phase effect, are plotted against orbital phase angle in Fig. 7. It is clear that: (1) 8 0 ~ 0 ° (in fact for all filters, Eq. (1) yields 8 o = 0 ° + 2 °) and (2) 2tz0 2 mag (which renders Eq. (1) inapplicable, as noted in Section III). Accordingly,

I

Filter • y 5.50 5C~

]APETU$ fH let • b

o

~r,lx 71r!

i

• 6.oc

i I 40

.

I 80

.

I

120

,

I

160

,

I

200

~

I

240

~

I 280

,

I 320

,

I

560

ti

8(deo)

FIG. 6. O r b i t a l m a g n i t u d e v a r i a t i o n of T e t h y s i n t h e y filter w i t h solar p h a s e a n g l e effect r e m o v e d . T h e s i n u s o i d a l fit is n o t good, as n o t e d i n Section V I I .

6{deul

FIO. 7. M a g n i t u d e v a r i a t i o n of I a p e t u s i n t h e b filter, u n c o r r e c t e d for solar p h a s e a n g l e effect.

348

~OLA~D et al.

we a s s u m e 8 0 = 0 ° a n d solve E q . w r i t t e n in t e r m s o f b r i g h t n e s s ,

(1),

....

,.,.

~.,

'n~°~. ~ . ~ . , . ~ . ,

Filter. b

M = M 0 + fla - 2.512 log [1 - / ~ 2 sin 8],

(2)

6.oc

for t h r e e p a r a m e t e r s : M0, fl and/~2. H e r e of the brightness variation and I o = brightness a t 8 = 0 ° a n d 180 °. I t s h o u l d also be n o t e d t h a t W i d o r n (1952) f o u n d a g o o d fit t o t h e t h e n a v a i l a b l e I a p e t u s m e a s u r e ments by using the equation t~2 - i ~ l / I o , w h e r e /~1 = h a l f a m p l i t u d e

g IE

,

I 40

,

I 80

,

I , 120

I

160

~

I

200

~

I

240

~

I

28O

~

I

32O

~

I

36O

,

l

O(deg )

I = 0.571 - 0.429 sin 0.

FIG. 8. Orbital magnitude variation of Iapetus in the b filter with solar phase angle effect removed. Since such a fit is unsatisfactory near 0 = 90 °, the two sides of Iapetus must be analyzed separately.

T h e f o r m o f this e x p r e s s i o n is e q u i v a l e n t t o (2) if solar p h a s e a n g l e effects are ignored. T h e r e s u l t o f fitting t h e whole light c u r v e t o E q . (2) is s h o w n in Fig. 8 for t h e b filter. W e find M 0 ( b ) = 6 . 2 8 ± .02 m a g (relative t o 37 T a u ) a n d fl = 0.025 ± 0.005 mag/deg, but the agreement between the c u r v e a n d t h e d a t a p o i n t s is n o t v e r y g o o d n e a r 0 = 90 ° or 270 °. F o r a n i m p r o v e d fit, we m u s t a n a l y z e t h e t w o sides o f I a p e t u s separately. T h e a n a l y s i s o f t h e b r i g h t side yields a v e r y g o o d fit t o t h e o b s e r v a t i o n s w i t h t h e p a r a m e t e r s s h o w n in T a b l e X I . N o t e t h a t in this t a b l e t h e m a g n i t u d e e q u i v a l e n t o f /~2 is given. F o r t h e b filter t h e b r i g h t side v a l u e o f M 0 is a b o u t 0.1 m a g g r e a t e r t h a n t h e v a l u e o b t a i n e d b y fitting t h e w h o l e light curve, b u t t h e v a l u e o f t h e p h a s e coefficient is a b o u t t h e s a m e in t h e t w o cases. A similar s i t u a t i o n holds for t h e p a r a m e t e r s o b t a i n e d w i t h t h e o t h e r filters. I f E q . (2) is a p p l i e d t o t h e d a r k side, t h e

f o r m a l fit yields n e g a t i v e v a l u e s o f fl w i t h large u n c e r t a i n t i e s a n d c o r r e s p o n d i n g l y large v a l u e s o f M 0. T h e r e a s o n for t h i s u n p h y s i c a l s i t u a t i o n is clear: since t h e r a n g e o f d a r k side o b s e r v a t i o n s is l i m i t e d to p h a s e angles b e t w e e n 4.0 ° a n d 5.6 °, a wide r a n g e o f fl's will give s t a t i s t i c a l l y e q u a l l y v a l i d fits. T h e r a n g e o f a c c e p t a b l e fl's for t h e d a r k side c a n be limited, h o w ever, b y m a k i n g t h e r e a s o n a b l e r e q u i r e ment that M 0 ( d a r k side) = M 0 ( b r i g h t side). Since t h e M o for t h e b r i g h t side is well d e t e r m i n e d (see above), t h e d a r k side a n a l y s i s can be r e d u c e d t o a t w o - p a r a m e t e r fit for fl a n d /~2. T h e r e s u l t s are s h o w n in Fig. 9 a n d T a b l e X I , w h e r e t h e t o t a l light c u r v e a m p l i t u d e / ~ 2 = tz2 (dark) +/~2 (bright) is also given.

TABLE X I IAPETUS

: DERIVED

u J~/o (mag) 5.44 ± fl (dark side) .061 ± fl (bright side) .035 ± ~2 (dark)(mag) 1.13 ± /~2 (bright) (mag) 0.72 + /~2 (total)(mag)1.85 ±

LIGHT-CU][tVE

PARAMETERS.

v

b

.04 5.94 ___.02 6.37 .008 .055 _+ .005 .057 .003 .031 ± .003 .030 .10 1.14 ± .04 1.12 .04 .14

0.73 _+ .03 1.87 ± .07

± ± ± ±

SEE

TEXT

y

FOR DETAILS.

r'

.02 6.59 ± .02 6.66 _ .004 .048 _+ .002 .053 ± .003 .032 ± .003 .029 ± .04 1.15 ± .03 1.05 ±

0.71 ± .03 1.83 ± .07

0.72 ± .03 1.87 ± .06

i' .02 6.78 ± .03 .007 .046 ± .005 .003 .031 _ .003 .08 1.07 + .04

0.67 ~ .02 1.72 ± .10

0.71 ± .02 1.78 ± .06

SATURN'S IAPETUS

SATELLITES

IAPETUS

,i,+',i,+,L+l'+l~'L +

;,j,,,+,;

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

349

PHOTOMETRY

h7ler~y

6DO 6

D

0

7.~

~

l l l t i l , l r f i r t t l l i l r E ~ ,

]

,

I

,

I

,

L

i

L

~

I

I

I

I

I

, ' L ' t ' t ' ~ ' E ' L ' t ' + ' l ' l

5.00

~ller=r'

filter = v

o 6.00

o a

6,00

7.00 c

7.00

,l,t,l,T,l,t,l,l,ltl ,+,i,i,i,i,i,i,i,i,+i

~E

,

i

,

I

,

i

,

i

,

t

,

t

,

t

,

t

,

I

,

Z~

&Oc 7.0(

,°t

i

40

80

i

120 160 200 240 280 520 560 OtdeQ)

O ldeg)

Fro. 9. Orbital m a g n i t u d e variations of I a p e t u s w i t h solar phase angle effects r e m o v e d , o b t a i n e d b y analyzing t h e d a t a for t h e bright side (0°~< 8~< 180 °) and for t h e d a r k side (180 ° ~< 8 ~< 360 °) separa t e l y (see Section V I I I ) .

The wavelength dependence of the phase coefficients is shown in Fig. 10. Our phase coefficients for the dark side are large (~0.05mag/deg) and wavelength dependent, with the larger values occurring at shorter wavelengths. Although these are the best values for the dark side, they should be treated with caution, for changing M 0 b y 0.1 mag changes fl b y about 0.015mag/deg. The phase coefficients for the bright side are smaller (~0.03mag/ deg) and not noticeably wavelength dependent. These results agree well with the earlier work of ~¢Iillis ( 1973), who found the phase coefficients for the dark and bright sides to be 0.06 and 0.02 mag/deg, respectively, in the visible. The unusually large values of fl for the dark side are consistent with a very low albedo for this side (0.04 to 0.05 according to Murphy et al., 1972 and Morrison, 1973) and with the deep negative branch of the polarization curve (Zellner, 1972), all of

IAPETUS

O.O'~C

0.06(3

0.05C

~'

--

t}+tt

!

o.o4c -

0.030

0.020

- -

{{{{{

--

lJOO

I 2+<~

n/x( ~m'n )

I &O0

FIo. 10. W a v e l e n g t h dependence of the phase coefficients of I a p e t u s for : (a) the bright side ; and (b) the d a r k side.

350

NO~ND et aI.

which point to a very porous and intricate surface texture. The lower values of the phase coefficient on the bright side are consistent with a brighter surface, a less porous surface, or both. The light curve amplitudes for the dark and bright sides of Iapetus are plotted against wavelength in Fig. 11, along with the total amplitude. Since the brighter material dominates the average photometric behavior of the surface, it is not surprising t h a t the bright side amplitude, which is a measure of the bright/average spectral reflectance ratio, appears to be wavelength independent. The dark side and total amplitudes increase slightly towards the blue, suggesting t h a t the contrast between the dark and bright materials increases towards shorter wavelengths. :~Iorrison et al. (1975) show that, in fact, the spectral reflectance of the bright material is fairly flat, while the spectral reflectance of the dark material increases with wavelength. A great deal of additional physical information about Iapetus can be obtained from a comparison of light curves at different values of the tilt of the Saturn system and, especially, from simultaneous photometric and radiometric light curves. Such IAPETU$ 2.C

t'

l

Q.

E

,?, 1.0--

0.5 1.00

,

:

I

2.00

tb

I

~00

V x ( , m "I )

Fro. 1 I. Wavelength dependence of the light

curve amplitude of Iapetus : (a) bright side only; (b) dark side only ; and (c) combined amplitude.

analyses, based in part on the observations presented here, are to be found in )/Iorrison et al. (1975). In t h a t paper are derived values for the radius, the distribution of geometric albedo on the satellite, and the mean bolometric Bond albedo and mean phase integral for the bright (trailing) side. I X . V ~AGNITUDES, COLORS, AND ALBEDOS

Up to this point, we have considered only differential magnitudes and colors, expressed on the instrumental system. We now discuss the transformation to the standard system and derive absolute V magnitudes and colors for the satellites. On most nights, we observed, in addition to the satellites and 37 Tau (HR 1256), at least two additional standards, one of which was usually 47 Tau (HR 1311). On two nights in January, however, we performed a complete transformation, using seven u v b y standards. The V magnitudes and colors of a number of standard stars are listed in Table XII, together with the mean V magnitudes and colors of the satellites (taken from Tables VII to XI), transformed to the standard system. For the transformation of the satellite magnitudes and colors, we used the mean of transformation coefficients obtained on seven nights in December and January. The errors introduced in the transformation could be as great as ~=0.02 in V, although an examination of the residuals for the standard stars on the two nights on which the transformation was performed suggests that the standard error in V is probably only _0.01 mag. The uncertainties in the colors are less than ±0.01 mag. Since none of these satellites exhibits large variations in color, the transformation applied to the mean magnitudes and colors should apply equally well to the individual measurements. No standard system exists for the r' and i' filters, so we adopt our instrumental system as the standard and define the zero points of the color indices so t h a t (r' -- y) = (i' -- y) =- O for 37 Tau. The

351

SATURN'S SATELLITES PHOTOMETRY

TABLE X I I V MAGNITUDES AND COLORS OF STANDARD STARS AND OF SATELLITES

Object 37 Tau 47 Tau 64 Tau 68 Tall pGem oVir 29 Psc Titan Rhea Dione Tethys Iapetus

HR No.

V

u -- y

v -- y

b -- y

r' -- y

i ' -- y

1256 1311 1380 1389 2852 4608 9087 -

4.39 4.86 4.46 4.32 4.18 4.14 5.14 8.34 9.67 10.38 10.22 10.96

3.282 2.545 1.644 1.492 1.565 2.780 0.544 3.218 2.300 2.182 2.131 2.145

1.751 1.268 0.372 0.233 0.583 1.550 0.004 1.887 1.193 1.153 1.123 1.105

0.644 0.501 0.081 0.020 0.214 0.590 --0.041 0.882 0.485 0.435 0.455 0.426

0.00 a 0.07 0.33 0.37 0.24 0.02 0.44 --0.05 0.11 0.11 0.15 0.07

0.00 ° 0.13 0.69 0.77 0.48 0.03 0.92 0.11 0.23 0.26 0.24 0.19

a By definition. m e a n v a l u e s of t h e s e color indices for t h e s t a n d a r d s t a r s a n d s a t e l l i t e s a r e also g i v e n in T a b l e X I I . T h e m e a n V m a g n i t u d e s of t h e s a t e l l i t e s d e r i v e d f r o m o u r m e a s u r e m e n t s a r e compared with those obtained by other authors in T a b l e X I I I . F o r T i t a n , t h e e x c e l l e n t agreement with the magnitude obtained b y B l a n c o a n d C a t a l a n o (1971) a n d t h e difference of 0.05 m a g n i t u d e f r o m t h a t o b t a i n e d b y H a r r i s (1961) are s i m i l a r to the agreement between Mauna Kea magnitudes and those published by Harris and b y B l a n c o a n d C a t a l a n o for t h e G a l i l e a n s a t e l l i t e s (lViorrison et al., 1974). F o r t h e o t h e r s a t e l l i t e s , o u r V m a g n i t u d e s are consistently brighter than those published p r e v i o u s l y . These differences p r o b a b l y r e s u l t f r o m t h e f a c t t h a t we o b t a i n m a g nitudes at phase angle ~ = 0 ° using d e r i v e d p h a s e coefficients, w h e r e a s pre-

vious o b s e r v e r s d i d n o t c o r r e c t t h e i r m a g n i t u d e s for d e p e n d e n c e on p h a s e angle. In order to determine the spectral r e f l e c t a n c e o f t h e s a t e l l i t e s f r o m t h e colors g i v e n in T a b l e X I I , we m u s t k n o w t h e colors o f t h e S u n in our p h o t o m e t r i c s y s t e m . Morrison et al. (1974) h a v e d e r i v e d t h e solar v a l u e s of t h e t h r e e color i n d i c e s of t h e uvby s y s t e m f r o m a c o m p a r i s o n o f t h e published spectrophotometry of seven uvby s t a n d a r d s t a r s w i t h t h e solar s p e c t r a l energy distribution measured by Arvesen et al. (1969). W e will n o w use a s i m i l a r a p p r o a c h t o d e r i v e t h e (r' - y) a n d (i' - y) colors of t h e Sun. F o r t h r e e of t h e s e c o n d a r y s t a n d a r d s o b s e r v e d in t h i s p r o g r a m - - 6 4 T a u , 68 T a u , and p Gem--spectral energy distributions h a v e b e e n p u b l i s h e d b y Code (1960) or Oke a n d Conti (1966). W e h a v e a d j u s t e d

TABLE X I I I MEAN OPPOSITIONV MAGNITUDES Satellite Titan Rhea Dione Tethys Iapetus

V

Vo (Harris)

Vo (Blanco and Catalano)

8.34 9.67 10.38 10.22 10.96

8.39 9.76 10.44 10.27

8.35 9.73

352

NOLAND et al.

these distributions to be on the scale defined for Vega by Oke and Schild (1970). The solar energy distribution published b y Arvesen et al. (1969) yields irradiance ratios in our filters of r'/y = 0.902 and i ' / y = 0.679. Table X I V gives the color indices derived for the Sun from the observations of these 3 standards. We also derive two independent calibrations of the colors of the Sun from our measurements of o Vir and 29 Psc and the ratios of the irradiance of these stars to t h a t of the Sun obtained b y Johnson (1971) and Chapman et al. (1973), respectively. Results for these two stars are also given in Table 14. We take a straight average to obtain the final color indices of the Sun, which are given in Table XV along with the uvby color indices derived by i~Iorrison et al. (1974). The uncertainties given are based on the uncertainties in the stellar observations b u t do not include an additional uncertainty of perhaps ±0.05 magnitude due to possible errors in the energy distributions of the Sun (Arvesen et al., 1969) and of Vega (Oke and Schild, 1970). Also listed in Table XV are the mean colors of the satellites, relative to the Sun, and the corresponding albedos, normalized to unity for the y filter (0.55Fm). These albedos are plotted as a function of wavelength in Fig. 12, together with the UBV colors obtained by Harris (1961) and the spectrophotometric colors of McCord et al. (197]). The agreement among the three sets of data is quite good, except for Harris' long wavelength data, which m a y be contaminated b y light from Saturn or its rings (!VicCord et al., 1971). The Titan reflectance curve displays its well-known ultraviolet dip. We also note the re-

1.6C

This Paper

•

A~. Harris(196t) .... McCordetol (1971}

I4C

..---J J

I.OC

",

/ TITAN

0.8 06 0.4 I00 ~

- ..........

~-'-'7r ......... RHEA

I (X)~-~ LO0~"

......

~

........

~ ...... TETHFS

I.OOt~~ ""'~ . . . . . . . . . . . . . . 08|

I

0.4

I

1

0.5

~DIONE

0.6

>.(Fro)

--~ IAPETUS I 0.7

FIo. 12. Wavelength dependence of the geometric albedos of Titan, Rhea, Dione, Tethys and Iapetus (at 0= 0°), normalized at 0.55 /~m (y filter). Measurements by Harris (1961) and McCord et al. (1971), similarly normalized, are shown for comparison. markable similarity in the colors of Rhea, Dione, Tethys, and Iapetus. (Although we have plotted the mean reflectance for lapetus, the high-albedo material is the source of most of the reflected light). X.

CONCLUSION

The extensive photometric observations of Titan, Iapetus, Rhea, ])lone and Tethys presented in this paper have made it possible to separate the solar phase and orbital phase contributions to the observed light variations of these satellites. For Titan, we have obtained the wavelength dependence of its solar phase coefficient. This dependence should prove useful in constructing future model atmospheres.

TABLE XIV SOLAR COLORS I N T H E r t AND i ' F I L T E R S , R E L A T I V E TO 37

(r' -- Y)o (i' -- Y)o

TAU

64 Tau

68 Tau

p Gem

o Vir

29 Psc

Average

+0.07 +0.23

+0.07 +0.22

+0.06 +0.15

+0.10 +0.22

+0.07 +0.22

+0.07 + .01 +0.21 + .02

2.03 _ .04

1.19 0.27 0.15 0.10 0.12

Sun

Titan Rhea Dione Tethys Iapetus

A (u - y)

0.34 0.78 0.87 0.91 0.90

p,,

0.86 0.16 0.12 0.09 0.08

1.03 _ .02

A (v - y)

0.45 0.86 0.90 0.92 0.93

Pv

0.47 0.08 0.03 0.05 0.02

0.41 _+ .01

A (b - y)

0.65 0.93 0.97 0.95 0.98

Pb

--0.12 0.04 0.04 0.08 0.00

0.07 _+.01

A (r' -- y)

1.12 0.96 0.96 0.93 1.00

p,,

--0.10 0.02 0.05 0.03 --0.02

0.21 _+ .02

A (i" -- y)

SOLAR COLORS, SATELLITE COLORS I~ELATIVE TO THE SUN~ AND NORMALIZED SATELLITE GEOMETRIC ALBEDOS

TABLE XV

1.10 0.98 0.95 0.97 1.02

p~,

© ©

5~

lq0LAND et al.

354

The other four satellites show a surprising array of different photometric behaviors. Rhea and Dione have similar high albedos, but differ in their phase coefficients and in the wavelength dependence of their light curve amplitudes. Rhea and the bright side of Iapetus have similar phase coefficients, but t h e y differ strongly in albedo. The inner satellites have bright leading sides and light curve amplitudes of a few tenths of a magnitude, while Iapetus has a dark leading side and an amplitude of almost two magnitudes. D3spite these differences, all four satellites have similar spectral reflectivities. Clearly Iapetus, Rhea, Dione and Tethys are complex objects, varying substantially from one another in surface structure and/ or composition. ACKNOWLEDGMENTS We wish to thank T. V. Johnson, F. Franklin, and C. Chapman for helpful comments and diseussions and the entire staff of the Mauna K e a Observatory for their assistance. This work was supported in part by NASA Grants NGR-033010-082 and NGL-12-001-057.

REFERENCES ARVESE~¢, J. C., GRIFFIN, R. N., AND PEARSON, B. D. (1969). Determination of extraterrestrial solar spectral irradiance from a research aircraft. App1. Opt. 8, 2215-2232. BARKER, E. S., AND TRAFTON, L. M. (1974). Ultraviolet rcflectivity and geometrical albedo of Titan. Icarus 20, 444-454. BLAIR, G. N., AND OWEN, F. N. (1974). The U B V orbital phase curves of Rhea, Dione, and Tethys. Icarus 22, 224-229. BLANCO, C., A N D CATALANO, S. (1971). Photoelectric observations of Saturn satellitesR h e a and Titan. Astron. Astrophys. 14, 43-47. CHAPMAN, C. R., McCORD, T. B., AND JOHNSON, T. V. (1973). Asteroid spectral reflectivities. Astron. J. 78, 126-140. CODE, A. D. (1960). Stellar energy distribution. I n "Stellar Atmospheres" (J. L. Greenstein, Ed.), pp. 50-87. University of Chicago, Chicago. CHUI~:SHANK,D. P., AND MURPHY, R. E. (1973). The post eclipse brightening of Io. Icarus 20, 7-17. DANIELSON, R. E., CALDWELL, J. J., AND LARACH, D. R. (1973). An inversion in the atmosphere of Titan. Icarus 20, 4 3 7 4 4 3 .

FRANZ, O. G., AND MI:LLIS, R. L. (1973). U B V photometry of Enceladus, Tethys, and Dionc. Bull. Amer. Astron. Soc. 5, 304. HARRIS, D. L. (1961). P h o t o m e t r y and polarimerry of planets and satellites. I n "Planets and Satellites" (G. P. Kuiper and B. M. Middlehurst, Eds.), pp. 272-342. University of Chicago, Chicago. JOHNSON, T. V. (1971). Galilean satellites: Narrowband photometry 0.30-1.10 microns. Icarus 14, 94-] 11. IV[cCORD, T. B., JOHNSON, T. V., A N D ELIAS, J. H. (l971 ).Saturn and its satellites:Narrowband spectrophotometry (0.3-1.I /~m). Astrophys. J. 165,413-424. MI:L:LIS, R. L. (1973). U B V photometry of Iapetus. Icarus 18, 247-252. I~IORRISON, D. (1973). Determination of radii of satellites and asteroids from radiometry and photometry. Icarus 19, 1-14. I~ORRISON, D. (1974). Albedos and densities of the inner satellites of Saturn. Icarus 22, 5156. ~IORRISON, D., MURPHY, R. E., CRUIKSHANK, D. P., SINTON, W. M., AND MARTIN, T. Z. (1973). Evaluation o f M a u n a Kea, Hawaii, as an observing site. P . A . S . P . 85, 255-267. MORRISON, D., MORRISON, N. D., AND LAZAREWICZ, A. R. (1974). Four-color photometry of the Galilean satellites. Icarus 23, 399-416. ~¢[ORRISON, D., JONES, T. J., CRUIKSHANK, D. P., AND MURPHY, R. E. (1975). The two faces of Iapetus. Icarus 24, in press. MURPHY, R. E., CRUIKSHANK, D. P., AND MORRISON, D. (1972). Radii, albedos, and 20-micron brightness temperatures of Iapetus and Rhea. Astrophys. J. 177, L93-L95. NO:LAND, M., AND VEVERKA, J. (1974). In preparation. OKE, J. S. AND CONT1, P. S. (1966). Absolute spectrophotometry of stars in the Hyades. Astrophys. J. 143, 134-145. OKE, J. B., AND SCHILD, R. E. (1970). The absolute spectral energy distribution of alpha Lyrae. Astrophys. J. 161, 1015-1023. PO:L:LACK,J. B. (1973). Greenhouse models of the atmosphere of Titan. Icarus 19, 43-58. VEVERKA, J. (1973). Titan: polarimetrie evidence for an optically thick atmosphere? Icarus 18, 657-660. WOLFF, R. J., AND WOLFF, S. C. (1971). uvby photometry of Ap stars : the nature of the light variations. Astron. J. 76, 422-430. WIDORN, T m (1952). Der Lichtwechsel des Saturn Satelliten Iapetus im Jah r e 1949. Mitt. Univ.-Sternw. Wien 5, 19-29. ZE:LLNER, B. (1972). On the nature of Iapetus. Astrophys. J. 174, L107-L109.