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V photometry of Titania, Oberon, and Triton
ICARUS77, 239-247 (1989)
V Photometry of Titania, Oberon, and Triton J. D. G O G U E N ~ AND H. B. H A M M E L 2 Institute for Astronomy, University of Hawaii, Honolulu, Hawaii 96822
AND R. H. B R O W N MS: 183-501, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
Received October 30, 1984; revised June 29, 1988 V filter photometry with the 2.2-m University of Hawaii telescope on Manna Kea obtained during 1982-1983 is analyzed to determine the phase angle and orbital brightness variations of Titania, Oberon, and Triton. The unit distance opposition magnitudes and phase coefficients (a < 3*) are Titania, V(1,0) = 1.016 --+ 0.042, ~ = 0.102 --. 0.021 mag/deg; Oberon, V(1,0) = 1.231 - 0.035,/~ = 0.103 - 0.018 mag/deg; Triton V(1,0) = - 1.236 - 0.041; ~ = 0.027 --. 0.035 mag/deg. The phase coefficients for Titania and Oberon are comparable to those observed for asteroids at similar small phase angles. Measurements made at ot = 0.*06 show an ~0.2-mag additional increase in brightness similar to that reported in the near-infrared by R. H. Brown and D. P. Cruikshank ((1983), Icarus 55, 83-92). The small phase coefficient for Triton indicates the light may not be scattered from a Iow-albedo, porous regolith, but suggests a high-albedo surface, a significant atmosphere, or a smooth surface, e.g., an ocean. Orbital lightcurves are less than 0.1 mag in amplitude for Titania, Oberon, and Triton. The Titania data agree well with photometry at phase angles ~'0.'8 from the Voyager 2 imaging experiment (J. Veverka, P. Thomas, P. Helfenstein, R. H. Brown, and T. V. Johnson, 1987, J. Geophys. Res. 92, 14,895-14,904). © 1989AcademicPress,Inc.
I. INTRODUCTION V filter p h o t o m e t r y of the large satellites of U r a n u s and N e p t u n e during 1982-1983 is reported. Although there are several studies of the reflection spectra of these satellites at visible and near-IR wavelengths (e.g., Cruikshank et al. 1977, J o h n s o n et al. 1978, Bell et al. 1979, Cruikshank 1980, Soiffer et al. 1981, Cruikshank and B r o w n 1981, B r o w n and Cruikshank 1983, B r o w n 1983), the variation of the absolute flux with 1 Current address: MS: 183-501, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109. 2 Current address: MS: 169-237, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109.
p h a s e angle and orbital longitude has received relatively little attention. B r o w n and Cruikshank (1983) report evidence for a large opposition surge for the Uranian satellites in the near-infrared. The V p h o t o m e try was u n d e r t a k e n partly to confirm this report and to investigate the p h a s e variation at a c o m m o n l y used wavelength for c o m p a r i s o n with other Solar S y s t e m bodies. E v e n though the range of phase angle variation is only 3 ° for Uranus and 2 ° for N e p t u n e , p h a s e coefficients are well determined b y the data and show significant distinctions b e t w e e n satellites. During the dates of observation, Uranus was o b s e r v e d nearly pole-on so that equatorial satellites w h o s e rotational poles are normal to their orbital planes should show 239
0019-1035/89 $3.00 Copyright © 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.
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GOGUEN, HAMMEL, AND BROWN
no orbital variation in brightness. Peale (1977) points out that Titania and Oberon are two of the most prominent candidates for satellites that have not yet completed the tidal evolution of their spin state and may still exhibit nonzero obliquity and nonsynchronous rotation. No evidence of significant obliquity was found in the Voyager observations of these satellites (Davies et al. 1987). If. OBSERVATIONS
The observations were made with the UH 2.2-m telescope on Mauna Kea, Hawaii, during 1982 and 1983. The V filter (central wavelength 0.55/~m, FWHM 0.06 /~m) from the Arizona eight-color filter set (Tedesco et al. 1982) was used in the Tinsley pulse-counting photometer, whose detector is a dry-ice cooled RCA C31034A photomultiplier. Observation dates, geometries, and results are summarized in Table I. Accurate photometry of faint satellites close to a bright planet is limited by the problem of sky brightness subtraction. The sky brightness decreases radially from the planet and is largest when the apparent satellite-planet separation is smallest. In 1983, the sky observations were made with a special "occulting disk" aperture that allows the sky to be measured at all azimuths around the satellite simultaneously by simply changing from a clear aperture to a similar one with a central occulting disk (aperture dia. -12"; occ. disk dia. -8"). The advantages of this technique are twofold: the telescope is not moved between the object and sky measurements so that the sky is measured at effectively the same location as the object, and only one sky measurement per object measurement is necessary. The usual technique of measuring two skies on opposite sides of the satellite was used for the 1982 observations (see Table I). In general, the agreement between the two techniques is within the errors determined for each separately. Because the dominant source of error is accurate sky subtraction
(and not photon counting statistics), each satellite was observed several times per night and the errors quoted are the standard deviation of the distribution of measures about the mean. This should be a generous error estimate, a factor of Xfnn larger than the standard deviation of the mean. Typically, the sky brightness was 20-30% of satellite plus sky signal. Standard stars were selected from Landolt (1973) to sample a range of air mass spanning those of the observations and for B - V color similar to that of satellites. At least one Landolt standard was measured immediately before and after each set of satellite and sky measurements; no intermediate comparison stars were used. III. PHASE RELATIONS
The V magnitudes, reduced to a distance from the earth and Sun of 1 AU, are plotted vs phase angle in Fig. 1. The lines are the nonlinear least-squares best fits to the flux
-1.4 -1.2I -1.0 0.8I o > 1.0 [.2 1.4 1.6 1.8
clldeg}
FIG. 1. Variation of the unit distance V magnitudes of Triton, Titania, and Oberon over the range of phase angles obtainable from Earth. Small squares, circles, and triangles are the data from Table I of this paper for Triton, Titania, and Oberon, respectively. The corresponding large symbols circumscribing a letter show previously published results taken from (A) Degewij, Andersson and Zellner (1980), (F) Franz (1981), (J) Johnson, Green and Shorthill (1978).
TABLE I UT date
Object
r(AU)
A(AU)
a(deg)
n
(V(I, a)) -+ o-
05/23.435 05/23.458 06/02.386 06/02.426 06/04.477 06/18.448 06/18.446 06/18.503
Oberon Titania Oberon Titania Oberon Oberon Titania Triton
18.880
1982 Observations 17.867
0.06
18.881
17.879
0.48
18.882 18.884
17.885 17.957
0.58 1.29
30.272
29.256
0.05
3 2 5 3 2 6 6 6
1.047 0.822 1.330 1.203 1.405 1.383 1.174 -1.266
_+ 0.038 - 0.016 --- 0.062 -+ 0.013 ± 0.073 -+ 0.045 _+ 0.011 +- 0.039
03/31.857 03/31.571 04/01.566 04/01.574 04/04.516 04/04.521 04/05.572 04/05.578 05/01.483 05/01.493 05/02.535 05/02.542 05/02.395 06/15.478 06/15.486 06/16.475 06/16.481 06/16.527 06/17.447 06/17.456 06/17.500 07/30.383 07/30.390 07/30.420 07/31.362 07/31.368 07/31.395 08/01.369 08/01.366 08/01.392 08/23.288 08/23.295 08/23.343 08/25.306
Oberon Titania Oberon Titania Oberon Titania Oberon Titania Oberon Titania Oberon Titania Triton Oberon Titania Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Triton
18.936
1983 Observations 18.405
2.60
18.391
2.57
18.937
18.349
2.49
18.937
18.335
2.46
18.942
18.047
1.44
18.942
18.039
1.39
30.267 18.950
29.583 17.976
1.42 0.90
18.950
17.981
0.95
30.267 18.950
29.253 17.986
0.13 1.00
30.267 18.958
29.252 18.447
0.10 2.69
30.266 18.958
29.475 18.462
1.22 2.71
30.266 18.958
29.486 18.477
1.25 2.74
30.266 18.962
29.497 18.834
1.27 3.04
30.266 30.266
29.790 29.820
1.70 t.73
1.497 1.239 1.445 1.259 1.453 1.259 1.449 1.271 1.361 1.149 1.332 1.149 -1.250 1.356 1.167 1.330 1.114 - 1.161 1.442 1.176 -1.296 1.572 1.388 - 1.081 1.481 1.240 -1.209 1.529 1.263 -1.203 1.543 1.312 -1.166 -1.252
± 0.008 -+ 0.007
18.936
3 4 1 1 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 3 4 4 6 3 4 6 3 3 6 6
± 0.029 +- 0.029 ± 0.016 ± 0.026 -+ 0.008 ± 0.018 ± 0.015 ± 0.018 --- 0.009 +- 0.014 ± 0.029 +- 0.006 ± 0.005 ± 0.022 --- 0.006 -+ 0.031 --- 0.021 ± 0.021 --- 0.074 -+ 0.071 ± 0.017 _+ 0.027 -+ 0.021 ± 0.024 ± 0.026 ± 0.038 --- 0.036 ± 0.011 ± 0.069 ± 0.026
Note. Table I summarizes the observations. F r o m left to right, the columns give the UT date and time of the observation in the format month/day.decimal day, the satellite name, the Sunto-planet distance (r), the Earth-to-planet distance (A), the phase angle (a), the n u m b e r (n) of independent satellite, sky measurement pairs used to determine the mean V magnitude, the mean V-filter magnitude reduced to r = A = l AU at the phase angle of the measurements (V(1, a)), and the estimated error (tr) in the mean magnitude. The 1982 observations measured the sky brightness offset radially from the planet interior and exterior to the satellite when possible. The 1983 observations used on occulting disk aperture to measure the sky brightness circumscribing the satellite. During 1983, the extinction coefficients were consistently 0.18 -+ 0.01 mag/air mass. During 1982, the El Chicon eruption dust cloud caused increased atmospheric extinction. The 1982 extinction coefficients were 0.76 ± 0.09 mag/air mass on 5/23; 0.30 -+ 0.02 mag/air mass on 6/2-4; and 0.50 -+ 0.02 mag/air mass on 6/18. 241
242
GOGUEN, HAMMEL, AND BROWN TABLE
II
OPPOSITION MAGNITUDES V(1,0), PHASE COEFFICIENTS fl, AND THEIR STANDARD DEVIATIONS Object Titania Titania h Oberon Oberon b Triton
V( 1,0) 1.016 1.097 1.231 1.293 -1.236
- 0.042 _+ 0 . 0 2 9 _+ 0 . 0 3 5 _+ 0 . 0 2 5 -+ 0.041
/3(mag/deg)" 0.102 0.066 0.103 0.075 0.027
-+ +-+ -+ -+
0.021 0.014 0.018 0.012 0.035
" Values of/3 for the U r a n i a n s a t e l l i t e s r e f e r to ~ < 3" a n d f o r T r i t o n to o~ < 177. ~' E x c l u d i n g ~ - 0?06 d a t a p o i n t o n 5/23/82 U T .
for an opposition magnitude V(1,0) and phase coefficient/3. Values of these parameters and their standard deviations, weighing each night equally, are given in Table II. Absolute photometry from previous investigations by Degewij et al. (1980), Johnson et al. (1978), and Franz (1981) are shown for comparison in Fig. 1. Titania and Oberon have nearly identical phase coefficients of 0.10 -+ 0.02 mag/deg with Titania 0.22 -+ 0.06 mag brighter than Oberon, in reasonable agreement with Reitsema et al. (1978), who report V(Oberon) V(Titania) = 0.15 + 0.02. V phase coefficients of 0.1 mag/deg are typical of asteroids for a < 3° (Scaltriti and Zappal~ 1980, Gehrels and Tedesco 1979, Bowell and Lumme 1979) and suggest that the scattering layer may be a particulate regolith of low to moderate albedo. This is consistent with Voyager results (Veverka et al. 1987). The data of Degewij et al. (1980) agree well with our results for Titania and Oberon. The points from Johnson et al. (1978) refer to a narrow bandpass (80 A) centered at 5660 ,~ and suggest both satellites are fainter. Observations reported by Harris (1961--dates not specified) would agree with those given here if they were made near maximum phase angle. Brown et al. (1982) based their opposition V magnitudes on a preliminary reduction of the 23 May 1982 data of this study because these
data were taken nearly simultaneously with their radiometry. The final analysis indicates that the opposition magnitudes are about 0. ! mag fainter than those quoted by Brown et al. (1982). The discrepancy may be related to nonphotometric conditions created by the El Chicon eruption dust cloud, which was responsible for large extinction coefficients on this date (see Table I), or may be due to a real, nonlinear surge in brightness in the last few tenths of a degree of phase angle (see below). In Fig. 2 the V phase relations for Titania and Oberon are compared to the !.5- to 2.5t~m observations of Brown and Cruikshank (1983). In both data sets, the point at the smallest phase angle (a < 071) is - 0 . 2 mag brighter than the linear extrapolation to a = 0°. The V and IR data sets were obtained by different instruments, in different years, on different telescopes, by different observers, and were reduced independently; but both show this large surge precisely at opposition. These data suggest this effect is real. Hapke (1983) argues that the IR data can be fit by an interparticle shadowing model in which the number density of particles varies from close packed at depth to zero at the surface over a distance scale - 3 0 times the mean particle size. Other mechanisms that may give rise to this effect are particles or surface structures that backscatter strongly, such as crystal face "corner cubes" (Trowbridge 1978) or large dielectric spheres (Hansen and Travis 1974). It is also possible that other satellite and asteroid surfaces exhibit similar surges precisely at opposition, but observations at the extremely small phase angles required for detection are lacking. The phase relation for Triton is also shown in Fig. 1. In contrast to the asteroidlike phase coefficients determined for Titania and Oberon, Triton's best fit/3 = 0.027 _+ 0.035 (c~ < 177) indicates no significant decrease in brightness with increasing phase angle. Small phase coefficients are characteristic of high-albedo surfaces, such as those of the Saturnian satellites Rhea (r
V PHOTOMETRY OF TITANIA, OBERON, AND TRITON a
i
i
i
i
f
i
i
i
b
i
0.45
0. 40
0. 40
o. 35
i
i
i
i
243 ]
]
i
H H O. 35
K
K H
~0.30
V
v
o. 30
H H
A
V
K
0,25 K
0.25
H
Iv
v
. . . . ~'0
0. 20 L
[
vw K
o~'(, Kv 'v
,
I
0. 20
H
vv ~
I
I
l
"Q~ i
I
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ot (deg)
H
~ 'v0 v'
Kv
0.15 ~
I
0.15 1.0 1.15 2.0 2.15 3.I0 3.15 4.10 ct (deg)
FIG. 2. (a) (I)/F vs p h a s e angle for Titania. (I) is the disk-averaged intensity and IrF is the incident solar flux; (I)/F at ~ = 0 is the geometric albedo. V s y m b o l s are the V-filter m e a s u r e m e n t s from this paper, H and K are the near-IR m e a s u r e m e n t s from Brown and Cruikshank (1983) averaged over the 1.6- and 2.2-~m b a n d s o f the H and K filters, respectively, and c, g and u are V o y a g e r 2 data from V e v e r k a et al. (1987). (b) S a m e as (a), but for Oberon.
0.6, fl - 0.025 -+ 0.02 mag/deg), Dione (r 0.55, fl - 0.031 -+ 0.007 mag/deg), and Tethys (r ~ 0.8, fl ~ 0.019 -+ 0.007 mag/ deg). Values of the normal reflectance r are from Smith et al. (1982) and phase coefficients are from Noland et al. (1974), except for Dione where both are from Buratti and Veverka (1984). The high albedo asteroid 44 Nysa (p - 0.48, Morrison and Zellner 1979;/3 ~ 0.026 --- 0.01 mag/deg, Birch et al. 1983) also fits this scenario. Another possibility is that Triton has an optically thick atmosphere like Titan for which/3 0.005 mag/deg (Noland et al. 1974). Cruikshank et al. (1984) report spectroscopic evidence for abundant nitrogen on Triton and discuss the possibilities of a significant atmosphere and ocean. Similar comments also apply to the small phase coefficient reported for Pluto by Tholen and Tedesco (1983). Although Triton was also observed at a = 0.°05, no significant brightness surge, as observed for Titania and Oberon, was found. Observations of Triton by other investigators are also shown in Fig. 1. The data of Harris (1961), Degewij et al. (1980), and Johnson et al. (1978) are in good agreement
with our results. The observations of Franz (1981) agree precisely with ours and suggest his technique and conclusions are valid. IV. R O T A T I O N A L V A R I A T I O N
The variation of the brightness of Titania, Oberon, and Triton with orbital longitude is shown in Fig. 3. The coverage is inadequate and the variation too small to independently determine a rotational period, and the lightcurves shown in Fig. 3 assume synchronous rotation. The residuals to the best linear phase relation reported in the previous section are plotted against the fraction of an orbital period that has elapsed since northern elongation for Titania and Oberon and since superior conjunction for Triton. The orbits of these satellites are nearly circular so the abcissa is also orbital longitude. Neither of these three satellites shows an orbital variation larger than 0.1 mag amplitude. Within the accuracy of the data, Titania shows no significant variation as expected for a nearly pole-on satellite. Oberon's lightcurve suggests it may be a few percent brighter at southern elongation than at northern elongation.
244
GOGUEN, HAMMEL, AND BROWN a
0.2
I
I
I
I
Titania
-0.2 _ {
-0.1
I
I
Oberon
0.1
>
0.0
+ '4'*
'
0.0
0.1
0.1
m
1
J
0.2
0.4
I 0.6
I
I
I
I
I
I
0.8
0.2
0.4
0.6
0.8
Fraction of P
Fraction of P
I
-0.2
+
_
I
I
I
Triton
0.1 '
i
0.0
+ 0.1
I
I
I
0.2
0.4
0.6
0.8
Fraction of P
FIG. 3. Residuals to the phase relations shown in Fig. 1 plotted against orbital longitude: (a) Titania, (b) Oberon, and (c) Triton. The dashed line in (c) shows the variation reported by Franz (1981).
The scatter in the Triton p h o t o m e t r y is too large to confirm the 0.06-mag variation reported by F r a n z (1981). V. A P O S T - V O Y A G E R P E R S P E C T I V E
Since the submission of this manuscript, the V o y a g e r 2 flyby of the Uranus system has contributed m u c h new information on the Uranian satellites (Smith et al. 1986). Of particular relevance to this work are the dia m e t e r s of Titania and Oberon, for which geometric albedos can now be calculated, and a nearly c o m p l e t e p h a s e curve for Titania ( V e v e r k a et al. 1987) that overlaps some of the phase angle c o v e r a g e reported here and sample p h a s e angles as small as 0.8 ° . The radius of Titania of 790 _+ 4 km
(Davies et al. 1987) and V(1,0) from Table II give a geometric albedo p = 0.27 -+ 0.01 (p = 0.25 + 0.01 excluding the 5/23/82 point). The radius of O b e r o n of 762 + 4 km and V(1,0) f r o m Table II give p = 0.23 _+ 0.01 (p = 0.22 -+ 0.01 excluding the 5/23/82 point). Because the definition of geometric albedo refers to the brightness of the disk at e x a c t l y zero phase, we note that the true geometric albedo m a y be as m u c h as 2 0 30% larger than the values quoted a b o v e which are based on a linear magnitude vs phase angle extrapolation to zero, if the extreme brightness surges o b s e r v e d at phase angles less than 0.5 ° are definitely confirmed. In Fig. 2a, the p h o t o m e t r y based on Voy-
V PHOTOMETRY OF TITANIA, OBERON, AND TRITON ager 2 images adapted from Veverka et al. (1987) is compared with the V photometry reported here and with the near-IR photometry from Brown and Cruikshank (1983). Similar data from the Voyager 2 photopolarimeter experiment (Nelson et al. 1987) are not shown. In all cases, the values plotted are n o t normalized; they are the absolute calibration of the disk-averaged intensity and cover wavelengths from 0.41 to 2.2 tzm. Both the absolute level and slope of the ground-based and spacecraft measurements agree well at phase angles larger than 0.8 ° . Only the ground-based data extend to smaller phase angles, and both the near-IR and V photometry show a significant brightness surge at phase angles <0.5 °. Figure 2b is a similar plot for Oberon, except there are no Voyager data available for these small phase angles. As for Titania, the independent data sets agree and show a similar large brightness surge at phase angles <0.5 °. The Voyager data extend the photometric coverage to large phase angles and resolution of the disk for all of the large satellites. Thomas et al. (1987) show that both high and low albedo areas on Titania have similar (but not identical) opposition surges. Veverka et al. (1988) give an analysis in terms of the Minneart albedo and limb-darkening parameters. Veverka et al. (1987) and Nelson et al. (1987) give diskintegrated phase curves and colors from the imaging and photopolarimeter experiments, respectively. Helfenstein et al. (1988) fit Hapke's photometric function to the diskintegrated phase curves. The V photometry from this paper provides a useful check on the absolute calibration of the Voyager data as well as extension of the photometry to phase angles <0.8 °. In planning the upcoming Voyager encounter with Neptune, considerable attention has been paid to the small phase coefficient of Triton reported here. Although an optically thick atmosphere would result in a small phase coefficient for Triton (Thompson 1987), there are several other possibili-
245
ties. A smooth surface, instead of a particulate regolith, or a high-albedo surface or regolith would show a small phase coefficient. But even a very-low-albedo surface has been shown to exhibit a similarly small phase coefficient. French (1987) has measured the phase coefficient of the Trojan asteroid 1173 Anchises over phase angles from 0.3 ° to 2.0 ° and obtains a value of 0.023 --- 0.008 mag/deg, even though Anchises is a P-type asteroid with a geometric albedo of 0.03 ! Lark et al. (1987) have reported a methane-band (0.89 --- 0.02 /zm) lightcurve of Triton that shows no amplitude >0.02 mag. VI. SUMMARY
Titania and Oberon show variation in magnitude with phase angle similar to lowto-moderate albedo asteroids observed within a few degrees of opposition. Observations made at extremely small phase angles (~ = 0.°06) in both V and near-infrared wavelengths show both satellites to be - 0 . 2 mag brighter than the linear extrapolation of the phase coefficient found from all the data. None of these satellites shows orbital variation greater than 0. I mag. Where measurements were made at similar phase angles, the photometry reported here is in good agreement with photometry from Voyager 2. Triton's phase variation is distinctly different from Titania's and Oberon's. Triton's small phase coefficient is consistent with a high-albedo regolith or an optically thick nonparticulate scattering layer, such as an atmosphere or ocean, but a low-albedo regolith cannot be ruled out. Orbital brightness variation is <0.1 mag.
ACKNOWLEDGMENTS Part of this work was done while Jay Goguen held a National Research Council Research Associateship at JPL. The Jet Propulsion Laboratory, California Institute of Technology, is under contract to the National Aeronautics and Space Administration. We thank S. Peale for helpful discussions, and C. Blanco and B. J. Buratti for careful reviews of this
246
GOGUEN, HAMMEL, AND BROWN
manuscript. This work was supported in part by NASA Grant NGL 12-001-057.
HARRIS, D. L. 1961. Photometry and colorimetry ot planets and satellites. In The Solar System II1: Planets and Satellites (G. P. Kuiper and B. M. Middlehurst, Eds.), pp. 272-342. Univ. of Chicago Press, REFERENCES Chicago. BELL, J. F., R. N. CLARK, T. B. McCoRD, AND D. P. HELFENSTEIN, P., J. VEVERKA,AND P. THOMAS 1988. CRUIKSHANK 1979. Reflection spectra of Pluto and Uranus satellites: Hapke parameters from Voyager three-distant satellites. Bull. Amer. Astron. Soc. 11, disk-integrated photometry. Icarus 74, 231-239. 570. [Abstract] JOHNSON, P. E., T. F. GREENE, AND R. W. BIRCH, P. V., E. F. TEDESCO, R. C. TAYLOR, R. P. SHORTHILL 1978. Narrow-band spectrophotometry BINZEL, C. BLANCO, S. CATALANO, P. HARTIGAN, of Ariel, Umbriel, Titania, Oberon and Triton. F. SCALTRITI, O. J. THOLEN, AND V. ZAPPALA h'arus 36, 75-81. 1983. Lightcurves and phase function of asteroid 44 LANDOLT, A. U. 1973. UBV photoelectric sequences Nysa during its 1979 apparition. Icarus 54, I-12. in the celestial equatorial selected areas 92-115. AsBOWELL, E., AND K. LUMME 1979. Colorimetry and tron. J. 78, 959-981. magnitudes of asteroids. In Asteroids (T. Gehrels, LARK, N. L., H. B. HAMMEL, M. A. RIGLER, D. P. Ed.), pp. 132-167. Univ. of Arizona Press, Tucson. CRUIKSHANK, AND D. J. THOLEN 1987. Triton: OrBROWN, R. H. 1983. The Uranian satellites and Hypebital brightness variations, June 1987. Bull. Amer. rion: New spectrophotometry and compositional Astron. Soc. 19, 858. [Abstract] implications. Icarus 56, 414-425. MORRISON, D., AND B. ZELLNER 1979. Polarimetry BROWN, R. H., AND D. P. CRUIKSHANK 1983. The and radiometry of the asteroids. In Asteroids (T. Uranian satellites: Surface compositions and oppoGehrels, Ed.), pp. 1090-1097. Univ. of Arizona sition brightness surges. Icarus 55, 83-92. Press, Tucson. BROWN, R. H., D. P. CRUIKSHANK, AND D. MORal- NELSON, R. M., B. J. BURATTI, B. D. WALLIS, A. L. SON 1982. Diameters and albedos of satellites of LANE, R. A. WEST, K. E. SIMMONS, C. W. HORD, Uranus. Nature 300, 423-425. AND l.. W. ESPOSlTO 1987. Voyager 2 photopolaBURATTI, B., AND J. VEVERKA 1984. Voyager phorimeter obserwttions of the Uranian satellites. J. tometry of Rhea, Dione, Tethys, Enceladus and Geophys. Res. 92, 14,905-14,910. Mimas. Icarus 58, 254-264. NOLAND, M., J. VEVERKA, D. MORRISON, D. P. CRUIKSHANK, D. P. 1980. Near-infrared studies of the CRUIKSHANK, A. R. LARZAREWlCZ, N. D. MORRIsatellites of Saturn and Uranus. h:arus 41, 246-258. SON, J. L. ELLIOTT, J. D. GOGUEN, AND J. A. CRUIKSHANK, D. P,, AND R. H. BROWN 1981. The BURNS 1974. Six-color photometry of Iapetus, TiUranian satellites: Water ice on Ariel and Umbriel. tan, Rhea, Dione and Tethys. Icarus 23, 334-354. Icarus 45, 607-611. PEAt.E, S. J. 1977. Rotation histories of the natural CRUIKSHANK, D. P., R. H. BROWN, AND R. N. CLARK satellites. In Planetary Satellites (J. Burns, Ed.), pp. 1984. Nitrogen on Triton. Icarus 58, 293-305. 87-112. Univ. of Arizona Press, Tucson. CRUIKSHANK, D. P., C. B. PILCHER, AND D. MORRI- RIETSEMA, H. J., B. A. SMITH, AND D. E. WEISTROP SON 1977. Identification of a new class of satellites in 1978. Visual and near-lR photometry of the Uranian the outer Solar System. Astrophys. J. 217, 1006satcllitcs. B,II. Amer. Astron. Soc. 10, 585. [Ab1010. stractl DAVIES, M. E., T. R. COLVIN, F. Y. KATAYAMA,AND SCALTRITI, F., AND V. ZAPPALA 1980. The similarity P. C. THOMAS 1987. The control networks of the of the opposition effect among asteroids. Astron. satellites of Uranus. Icarus 71, 137-147. Astrophys. 83, 249-251. DEGEWIJ, J., L. E, ANDERSSON, AND B. ZELLNER SMITH, B. A,, L. SODERBLOM, R. BATSON, P. 1980. Photometric properties of outer planet satelBRIDGES, J. 1NGE, H. MASURSKY,E. SHOEMAKER. lites. Icarus 44, 520-590. R. BEEBE, J. BOYCE, G. BRIGGS, A. BUNKER, S. A. FRANZ, O. G. 1981. UBV photometry of Triton. COLLINS, C. J. HANSEN, T. V. JOHNSON, J, L. Icarus 45, 602-606. MITCHELL, R. J. TERRILE, A. F. COOK 11, J. Cuzzl, FRENCH, L. M. 1987. Rotation properties of four L5 J. B. POLLACK, G. E. DANIELSON, A. INGERSOLL, Trojan asteroids from CCD photometry. Icarus 72, M. E. DAVIES, G. E. HUNT, D. MORRISON, Z. 325-341. OWEN, C. SAGAN, J. VEVERKA,R. STRUM, AND V. GEHRELS, T., AND E. F. TEDESCO 1979. Minor planets E. SuoMl 1982. A new look at the Saturn system: and related objects. XXVIII. Asteroid magnitudes The Voyager It images. Science 215, 504-537. and phase relations. Astron. J. 84, 1079-1087. SMITH, B. A., L. A. SODERBLOM, R. BEEBE, D. HANSEN, J. E., AND L. D. TRAVIS 1974. LightscatBLISS, J. M. BOYCE, A. BRAHlC, G. A. BRIGGS, R. tering in planetary atmospheres. Space Sci. Rev. 16, H. BROWN, S. A. COLLINS, A. F. COOK, S. K. 527-610. CROFT, J. N. CUZZ1, G. E. DANIELSON, M. E. DAHAPKE, B. 1983. The opposition effect. Bull. Amer. VIES, T. E. DOWLING, D. GODFREY, C. J. HANES, Astron. Soc. 15, 856. [Abstract] C. HARRIS, G. E. HUNT, A. P. INGERSOLL. T. V.
V PHOTOMETRY
OF TITANIA, OBERON, AND TRITON
JOHNSON, R. J. KRAUS, H. MASURSKY, D. MORRISON, T. OWEN, J. B. PLESCIA, J. B. POLLACK, C. C. PORCO, K. RAGES, C. SAGAN, E. M. SHOEMAKER, L. A. SROMOVSKY,C. STOKER,R. G. STROM,V. E. SUOMI, S. P. SYNNOTT, R. J. TERRILE, P. THOMAS, W. R. THOMPSON, AND J. VEVERKA 1986. Voyager 2 in the Uranian system: Imaging science results. Science 233, 43-64. SOIFFER, B. T., G. T. NEUGEBAUER,AND K. MATTHEWS 1981. Near-infrared spectrophotometry of the satellites and rings of Uranus. Icarus 45, 612617. TEDESCO, E. F., D. J. THOLEN, AND B. ZELLNER 1982. The eight-color asteroid survey: Standard stars. Astron. J. 87, 1585-1592. THOLEN, D. J., AND E. F. TEDESCO. 1983. Pluto's lightcurve: Results from four apparitions. Bull. Amer. Astron. Soc. 15, 859. [Abstract]
247
THOMAS, P., J. VEVERKA, P. HELFENSTEIN, R. H. BROWN, AND T. V. JOHNSON 1987. Titania's opposition effect: Analysis of Voyager observations. J. Geophys. Res. 92, 14,911-14,917.
THOMPSON, W. R. 1987. Triton: Constraints on the atmosphere and surface. Bull. Amer. Astron. Soc. 19, 858. [Abstract] TR0WBRIDGE, T. S. 1978. Retro-reflection from rough surfaces. J. Opt. Soc. Amer. 68, 1225-1242. VEVERKA, J. P., HELFENSTEIN, A. SKYPECK, AND P. THOMAS 1988. Minneart photometric parameters for the satellites of Uranus. Icarus, in press. VEVERKA, J., P. THOMAS, P. HELEENSTEIN, R. H. BROWN, AND T. V. JOHNSON 1987. Satellites of Uranus: Disk-integrated photometry from Voyager imaging observations. J. Geophys. Res. 92, 14,89514,904.
V Photometry of Titania, Oberon, and Triton J. D. G O G U E N ~ AND H. B. H A M M E L 2 Institute for Astronomy, University of Hawaii, Honolulu, Hawaii 96822
AND R. H. B R O W N MS: 183-501, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
Received October 30, 1984; revised June 29, 1988 V filter photometry with the 2.2-m University of Hawaii telescope on Manna Kea obtained during 1982-1983 is analyzed to determine the phase angle and orbital brightness variations of Titania, Oberon, and Triton. The unit distance opposition magnitudes and phase coefficients (a < 3*) are Titania, V(1,0) = 1.016 --+ 0.042, ~ = 0.102 --. 0.021 mag/deg; Oberon, V(1,0) = 1.231 - 0.035,/~ = 0.103 - 0.018 mag/deg; Triton V(1,0) = - 1.236 - 0.041; ~ = 0.027 --. 0.035 mag/deg. The phase coefficients for Titania and Oberon are comparable to those observed for asteroids at similar small phase angles. Measurements made at ot = 0.*06 show an ~0.2-mag additional increase in brightness similar to that reported in the near-infrared by R. H. Brown and D. P. Cruikshank ((1983), Icarus 55, 83-92). The small phase coefficient for Triton indicates the light may not be scattered from a Iow-albedo, porous regolith, but suggests a high-albedo surface, a significant atmosphere, or a smooth surface, e.g., an ocean. Orbital lightcurves are less than 0.1 mag in amplitude for Titania, Oberon, and Triton. The Titania data agree well with photometry at phase angles ~'0.'8 from the Voyager 2 imaging experiment (J. Veverka, P. Thomas, P. Helfenstein, R. H. Brown, and T. V. Johnson, 1987, J. Geophys. Res. 92, 14,895-14,904). © 1989AcademicPress,Inc.
I. INTRODUCTION V filter p h o t o m e t r y of the large satellites of U r a n u s and N e p t u n e during 1982-1983 is reported. Although there are several studies of the reflection spectra of these satellites at visible and near-IR wavelengths (e.g., Cruikshank et al. 1977, J o h n s o n et al. 1978, Bell et al. 1979, Cruikshank 1980, Soiffer et al. 1981, Cruikshank and B r o w n 1981, B r o w n and Cruikshank 1983, B r o w n 1983), the variation of the absolute flux with 1 Current address: MS: 183-501, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109. 2 Current address: MS: 169-237, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109.
p h a s e angle and orbital longitude has received relatively little attention. B r o w n and Cruikshank (1983) report evidence for a large opposition surge for the Uranian satellites in the near-infrared. The V p h o t o m e try was u n d e r t a k e n partly to confirm this report and to investigate the p h a s e variation at a c o m m o n l y used wavelength for c o m p a r i s o n with other Solar S y s t e m bodies. E v e n though the range of phase angle variation is only 3 ° for Uranus and 2 ° for N e p t u n e , p h a s e coefficients are well determined b y the data and show significant distinctions b e t w e e n satellites. During the dates of observation, Uranus was o b s e r v e d nearly pole-on so that equatorial satellites w h o s e rotational poles are normal to their orbital planes should show 239
0019-1035/89 $3.00 Copyright © 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.
240
GOGUEN, HAMMEL, AND BROWN
no orbital variation in brightness. Peale (1977) points out that Titania and Oberon are two of the most prominent candidates for satellites that have not yet completed the tidal evolution of their spin state and may still exhibit nonzero obliquity and nonsynchronous rotation. No evidence of significant obliquity was found in the Voyager observations of these satellites (Davies et al. 1987). If. OBSERVATIONS
The observations were made with the UH 2.2-m telescope on Mauna Kea, Hawaii, during 1982 and 1983. The V filter (central wavelength 0.55/~m, FWHM 0.06 /~m) from the Arizona eight-color filter set (Tedesco et al. 1982) was used in the Tinsley pulse-counting photometer, whose detector is a dry-ice cooled RCA C31034A photomultiplier. Observation dates, geometries, and results are summarized in Table I. Accurate photometry of faint satellites close to a bright planet is limited by the problem of sky brightness subtraction. The sky brightness decreases radially from the planet and is largest when the apparent satellite-planet separation is smallest. In 1983, the sky observations were made with a special "occulting disk" aperture that allows the sky to be measured at all azimuths around the satellite simultaneously by simply changing from a clear aperture to a similar one with a central occulting disk (aperture dia. -12"; occ. disk dia. -8"). The advantages of this technique are twofold: the telescope is not moved between the object and sky measurements so that the sky is measured at effectively the same location as the object, and only one sky measurement per object measurement is necessary. The usual technique of measuring two skies on opposite sides of the satellite was used for the 1982 observations (see Table I). In general, the agreement between the two techniques is within the errors determined for each separately. Because the dominant source of error is accurate sky subtraction
(and not photon counting statistics), each satellite was observed several times per night and the errors quoted are the standard deviation of the distribution of measures about the mean. This should be a generous error estimate, a factor of Xfnn larger than the standard deviation of the mean. Typically, the sky brightness was 20-30% of satellite plus sky signal. Standard stars were selected from Landolt (1973) to sample a range of air mass spanning those of the observations and for B - V color similar to that of satellites. At least one Landolt standard was measured immediately before and after each set of satellite and sky measurements; no intermediate comparison stars were used. III. PHASE RELATIONS
The V magnitudes, reduced to a distance from the earth and Sun of 1 AU, are plotted vs phase angle in Fig. 1. The lines are the nonlinear least-squares best fits to the flux
-1.4 -1.2I -1.0 0.8I o > 1.0 [.2 1.4 1.6 1.8
clldeg}
FIG. 1. Variation of the unit distance V magnitudes of Triton, Titania, and Oberon over the range of phase angles obtainable from Earth. Small squares, circles, and triangles are the data from Table I of this paper for Triton, Titania, and Oberon, respectively. The corresponding large symbols circumscribing a letter show previously published results taken from (A) Degewij, Andersson and Zellner (1980), (F) Franz (1981), (J) Johnson, Green and Shorthill (1978).
TABLE I UT date
Object
r(AU)
A(AU)
a(deg)
n
(V(I, a)) -+ o-
05/23.435 05/23.458 06/02.386 06/02.426 06/04.477 06/18.448 06/18.446 06/18.503
Oberon Titania Oberon Titania Oberon Oberon Titania Triton
18.880
1982 Observations 17.867
0.06
18.881
17.879
0.48
18.882 18.884
17.885 17.957
0.58 1.29
30.272
29.256
0.05
3 2 5 3 2 6 6 6
1.047 0.822 1.330 1.203 1.405 1.383 1.174 -1.266
_+ 0.038 - 0.016 --- 0.062 -+ 0.013 ± 0.073 -+ 0.045 _+ 0.011 +- 0.039
03/31.857 03/31.571 04/01.566 04/01.574 04/04.516 04/04.521 04/05.572 04/05.578 05/01.483 05/01.493 05/02.535 05/02.542 05/02.395 06/15.478 06/15.486 06/16.475 06/16.481 06/16.527 06/17.447 06/17.456 06/17.500 07/30.383 07/30.390 07/30.420 07/31.362 07/31.368 07/31.395 08/01.369 08/01.366 08/01.392 08/23.288 08/23.295 08/23.343 08/25.306
Oberon Titania Oberon Titania Oberon Titania Oberon Titania Oberon Titania Oberon Titania Triton Oberon Titania Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Oberon Titania Triton Triton
18.936
1983 Observations 18.405
2.60
18.391
2.57
18.937
18.349
2.49
18.937
18.335
2.46
18.942
18.047
1.44
18.942
18.039
1.39
30.267 18.950
29.583 17.976
1.42 0.90
18.950
17.981
0.95
30.267 18.950
29.253 17.986
0.13 1.00
30.267 18.958
29.252 18.447
0.10 2.69
30.266 18.958
29.475 18.462
1.22 2.71
30.266 18.958
29.486 18.477
1.25 2.74
30.266 18.962
29.497 18.834
1.27 3.04
30.266 30.266
29.790 29.820
1.70 t.73
1.497 1.239 1.445 1.259 1.453 1.259 1.449 1.271 1.361 1.149 1.332 1.149 -1.250 1.356 1.167 1.330 1.114 - 1.161 1.442 1.176 -1.296 1.572 1.388 - 1.081 1.481 1.240 -1.209 1.529 1.263 -1.203 1.543 1.312 -1.166 -1.252
± 0.008 -+ 0.007
18.936
3 4 1 1 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 3 4 4 6 3 4 6 3 3 6 6
± 0.029 +- 0.029 ± 0.016 ± 0.026 -+ 0.008 ± 0.018 ± 0.015 ± 0.018 --- 0.009 +- 0.014 ± 0.029 +- 0.006 ± 0.005 ± 0.022 --- 0.006 -+ 0.031 --- 0.021 ± 0.021 --- 0.074 -+ 0.071 ± 0.017 _+ 0.027 -+ 0.021 ± 0.024 ± 0.026 ± 0.038 --- 0.036 ± 0.011 ± 0.069 ± 0.026
Note. Table I summarizes the observations. F r o m left to right, the columns give the UT date and time of the observation in the format month/day.decimal day, the satellite name, the Sunto-planet distance (r), the Earth-to-planet distance (A), the phase angle (a), the n u m b e r (n) of independent satellite, sky measurement pairs used to determine the mean V magnitude, the mean V-filter magnitude reduced to r = A = l AU at the phase angle of the measurements (V(1, a)), and the estimated error (tr) in the mean magnitude. The 1982 observations measured the sky brightness offset radially from the planet interior and exterior to the satellite when possible. The 1983 observations used on occulting disk aperture to measure the sky brightness circumscribing the satellite. During 1983, the extinction coefficients were consistently 0.18 -+ 0.01 mag/air mass. During 1982, the El Chicon eruption dust cloud caused increased atmospheric extinction. The 1982 extinction coefficients were 0.76 ± 0.09 mag/air mass on 5/23; 0.30 -+ 0.02 mag/air mass on 6/2-4; and 0.50 -+ 0.02 mag/air mass on 6/18. 241
242
GOGUEN, HAMMEL, AND BROWN TABLE
II
OPPOSITION MAGNITUDES V(1,0), PHASE COEFFICIENTS fl, AND THEIR STANDARD DEVIATIONS Object Titania Titania h Oberon Oberon b Triton
V( 1,0) 1.016 1.097 1.231 1.293 -1.236
- 0.042 _+ 0 . 0 2 9 _+ 0 . 0 3 5 _+ 0 . 0 2 5 -+ 0.041
/3(mag/deg)" 0.102 0.066 0.103 0.075 0.027
-+ +-+ -+ -+
0.021 0.014 0.018 0.012 0.035
" Values of/3 for the U r a n i a n s a t e l l i t e s r e f e r to ~ < 3" a n d f o r T r i t o n to o~ < 177. ~' E x c l u d i n g ~ - 0?06 d a t a p o i n t o n 5/23/82 U T .
for an opposition magnitude V(1,0) and phase coefficient/3. Values of these parameters and their standard deviations, weighing each night equally, are given in Table II. Absolute photometry from previous investigations by Degewij et al. (1980), Johnson et al. (1978), and Franz (1981) are shown for comparison in Fig. 1. Titania and Oberon have nearly identical phase coefficients of 0.10 -+ 0.02 mag/deg with Titania 0.22 -+ 0.06 mag brighter than Oberon, in reasonable agreement with Reitsema et al. (1978), who report V(Oberon) V(Titania) = 0.15 + 0.02. V phase coefficients of 0.1 mag/deg are typical of asteroids for a < 3° (Scaltriti and Zappal~ 1980, Gehrels and Tedesco 1979, Bowell and Lumme 1979) and suggest that the scattering layer may be a particulate regolith of low to moderate albedo. This is consistent with Voyager results (Veverka et al. 1987). The data of Degewij et al. (1980) agree well with our results for Titania and Oberon. The points from Johnson et al. (1978) refer to a narrow bandpass (80 A) centered at 5660 ,~ and suggest both satellites are fainter. Observations reported by Harris (1961--dates not specified) would agree with those given here if they were made near maximum phase angle. Brown et al. (1982) based their opposition V magnitudes on a preliminary reduction of the 23 May 1982 data of this study because these
data were taken nearly simultaneously with their radiometry. The final analysis indicates that the opposition magnitudes are about 0. ! mag fainter than those quoted by Brown et al. (1982). The discrepancy may be related to nonphotometric conditions created by the El Chicon eruption dust cloud, which was responsible for large extinction coefficients on this date (see Table I), or may be due to a real, nonlinear surge in brightness in the last few tenths of a degree of phase angle (see below). In Fig. 2 the V phase relations for Titania and Oberon are compared to the !.5- to 2.5t~m observations of Brown and Cruikshank (1983). In both data sets, the point at the smallest phase angle (a < 071) is - 0 . 2 mag brighter than the linear extrapolation to a = 0°. The V and IR data sets were obtained by different instruments, in different years, on different telescopes, by different observers, and were reduced independently; but both show this large surge precisely at opposition. These data suggest this effect is real. Hapke (1983) argues that the IR data can be fit by an interparticle shadowing model in which the number density of particles varies from close packed at depth to zero at the surface over a distance scale - 3 0 times the mean particle size. Other mechanisms that may give rise to this effect are particles or surface structures that backscatter strongly, such as crystal face "corner cubes" (Trowbridge 1978) or large dielectric spheres (Hansen and Travis 1974). It is also possible that other satellite and asteroid surfaces exhibit similar surges precisely at opposition, but observations at the extremely small phase angles required for detection are lacking. The phase relation for Triton is also shown in Fig. 1. In contrast to the asteroidlike phase coefficients determined for Titania and Oberon, Triton's best fit/3 = 0.027 _+ 0.035 (c~ < 177) indicates no significant decrease in brightness with increasing phase angle. Small phase coefficients are characteristic of high-albedo surfaces, such as those of the Saturnian satellites Rhea (r
V PHOTOMETRY OF TITANIA, OBERON, AND TRITON a
i
i
i
i
f
i
i
i
b
i
0.45
0. 40
0. 40
o. 35
i
i
i
i
243 ]
]
i
H H O. 35
K
K H
~0.30
V
v
o. 30
H H
A
V
K
0,25 K
0.25
H
Iv
v
. . . . ~'0
0. 20 L
[
vw K
o~'(, Kv 'v
,
I
0. 20
H
vv ~
I
I
l
"Q~ i
I
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ot (deg)
H
~ 'v0 v'
Kv
0.15 ~
I
0.15 1.0 1.15 2.0 2.15 3.I0 3.15 4.10 ct (deg)
FIG. 2. (a) (I)/F vs p h a s e angle for Titania. (I) is the disk-averaged intensity and IrF is the incident solar flux; (I)/F at ~ = 0 is the geometric albedo. V s y m b o l s are the V-filter m e a s u r e m e n t s from this paper, H and K are the near-IR m e a s u r e m e n t s from Brown and Cruikshank (1983) averaged over the 1.6- and 2.2-~m b a n d s o f the H and K filters, respectively, and c, g and u are V o y a g e r 2 data from V e v e r k a et al. (1987). (b) S a m e as (a), but for Oberon.
0.6, fl - 0.025 -+ 0.02 mag/deg), Dione (r 0.55, fl - 0.031 -+ 0.007 mag/deg), and Tethys (r ~ 0.8, fl ~ 0.019 -+ 0.007 mag/ deg). Values of the normal reflectance r are from Smith et al. (1982) and phase coefficients are from Noland et al. (1974), except for Dione where both are from Buratti and Veverka (1984). The high albedo asteroid 44 Nysa (p - 0.48, Morrison and Zellner 1979;/3 ~ 0.026 --- 0.01 mag/deg, Birch et al. 1983) also fits this scenario. Another possibility is that Triton has an optically thick atmosphere like Titan for which/3 0.005 mag/deg (Noland et al. 1974). Cruikshank et al. (1984) report spectroscopic evidence for abundant nitrogen on Triton and discuss the possibilities of a significant atmosphere and ocean. Similar comments also apply to the small phase coefficient reported for Pluto by Tholen and Tedesco (1983). Although Triton was also observed at a = 0.°05, no significant brightness surge, as observed for Titania and Oberon, was found. Observations of Triton by other investigators are also shown in Fig. 1. The data of Harris (1961), Degewij et al. (1980), and Johnson et al. (1978) are in good agreement
with our results. The observations of Franz (1981) agree precisely with ours and suggest his technique and conclusions are valid. IV. R O T A T I O N A L V A R I A T I O N
The variation of the brightness of Titania, Oberon, and Triton with orbital longitude is shown in Fig. 3. The coverage is inadequate and the variation too small to independently determine a rotational period, and the lightcurves shown in Fig. 3 assume synchronous rotation. The residuals to the best linear phase relation reported in the previous section are plotted against the fraction of an orbital period that has elapsed since northern elongation for Titania and Oberon and since superior conjunction for Triton. The orbits of these satellites are nearly circular so the abcissa is also orbital longitude. Neither of these three satellites shows an orbital variation larger than 0.1 mag amplitude. Within the accuracy of the data, Titania shows no significant variation as expected for a nearly pole-on satellite. Oberon's lightcurve suggests it may be a few percent brighter at southern elongation than at northern elongation.
244
GOGUEN, HAMMEL, AND BROWN a
0.2
I
I
I
I
Titania
-0.2 _ {
-0.1
I
I
Oberon
0.1
>
0.0
+ '4'*
'
0.0
0.1
0.1
m
1
J
0.2
0.4
I 0.6
I
I
I
I
I
I
0.8
0.2
0.4
0.6
0.8
Fraction of P
Fraction of P
I
-0.2
+
_
I
I
I
Triton
0.1 '
i
0.0
+ 0.1
I
I
I
0.2
0.4
0.6
0.8
Fraction of P
FIG. 3. Residuals to the phase relations shown in Fig. 1 plotted against orbital longitude: (a) Titania, (b) Oberon, and (c) Triton. The dashed line in (c) shows the variation reported by Franz (1981).
The scatter in the Triton p h o t o m e t r y is too large to confirm the 0.06-mag variation reported by F r a n z (1981). V. A P O S T - V O Y A G E R P E R S P E C T I V E
Since the submission of this manuscript, the V o y a g e r 2 flyby of the Uranus system has contributed m u c h new information on the Uranian satellites (Smith et al. 1986). Of particular relevance to this work are the dia m e t e r s of Titania and Oberon, for which geometric albedos can now be calculated, and a nearly c o m p l e t e p h a s e curve for Titania ( V e v e r k a et al. 1987) that overlaps some of the phase angle c o v e r a g e reported here and sample p h a s e angles as small as 0.8 ° . The radius of Titania of 790 _+ 4 km
(Davies et al. 1987) and V(1,0) from Table II give a geometric albedo p = 0.27 -+ 0.01 (p = 0.25 + 0.01 excluding the 5/23/82 point). The radius of O b e r o n of 762 + 4 km and V(1,0) f r o m Table II give p = 0.23 _+ 0.01 (p = 0.22 -+ 0.01 excluding the 5/23/82 point). Because the definition of geometric albedo refers to the brightness of the disk at e x a c t l y zero phase, we note that the true geometric albedo m a y be as m u c h as 2 0 30% larger than the values quoted a b o v e which are based on a linear magnitude vs phase angle extrapolation to zero, if the extreme brightness surges o b s e r v e d at phase angles less than 0.5 ° are definitely confirmed. In Fig. 2a, the p h o t o m e t r y based on Voy-
V PHOTOMETRY OF TITANIA, OBERON, AND TRITON ager 2 images adapted from Veverka et al. (1987) is compared with the V photometry reported here and with the near-IR photometry from Brown and Cruikshank (1983). Similar data from the Voyager 2 photopolarimeter experiment (Nelson et al. 1987) are not shown. In all cases, the values plotted are n o t normalized; they are the absolute calibration of the disk-averaged intensity and cover wavelengths from 0.41 to 2.2 tzm. Both the absolute level and slope of the ground-based and spacecraft measurements agree well at phase angles larger than 0.8 ° . Only the ground-based data extend to smaller phase angles, and both the near-IR and V photometry show a significant brightness surge at phase angles <0.5 °. Figure 2b is a similar plot for Oberon, except there are no Voyager data available for these small phase angles. As for Titania, the independent data sets agree and show a similar large brightness surge at phase angles <0.5 °. The Voyager data extend the photometric coverage to large phase angles and resolution of the disk for all of the large satellites. Thomas et al. (1987) show that both high and low albedo areas on Titania have similar (but not identical) opposition surges. Veverka et al. (1988) give an analysis in terms of the Minneart albedo and limb-darkening parameters. Veverka et al. (1987) and Nelson et al. (1987) give diskintegrated phase curves and colors from the imaging and photopolarimeter experiments, respectively. Helfenstein et al. (1988) fit Hapke's photometric function to the diskintegrated phase curves. The V photometry from this paper provides a useful check on the absolute calibration of the Voyager data as well as extension of the photometry to phase angles <0.8 °. In planning the upcoming Voyager encounter with Neptune, considerable attention has been paid to the small phase coefficient of Triton reported here. Although an optically thick atmosphere would result in a small phase coefficient for Triton (Thompson 1987), there are several other possibili-
245
ties. A smooth surface, instead of a particulate regolith, or a high-albedo surface or regolith would show a small phase coefficient. But even a very-low-albedo surface has been shown to exhibit a similarly small phase coefficient. French (1987) has measured the phase coefficient of the Trojan asteroid 1173 Anchises over phase angles from 0.3 ° to 2.0 ° and obtains a value of 0.023 --- 0.008 mag/deg, even though Anchises is a P-type asteroid with a geometric albedo of 0.03 ! Lark et al. (1987) have reported a methane-band (0.89 --- 0.02 /zm) lightcurve of Triton that shows no amplitude >0.02 mag. VI. SUMMARY
Titania and Oberon show variation in magnitude with phase angle similar to lowto-moderate albedo asteroids observed within a few degrees of opposition. Observations made at extremely small phase angles (~ = 0.°06) in both V and near-infrared wavelengths show both satellites to be - 0 . 2 mag brighter than the linear extrapolation of the phase coefficient found from all the data. None of these satellites shows orbital variation greater than 0. I mag. Where measurements were made at similar phase angles, the photometry reported here is in good agreement with photometry from Voyager 2. Triton's phase variation is distinctly different from Titania's and Oberon's. Triton's small phase coefficient is consistent with a high-albedo regolith or an optically thick nonparticulate scattering layer, such as an atmosphere or ocean, but a low-albedo regolith cannot be ruled out. Orbital brightness variation is <0.1 mag.
ACKNOWLEDGMENTS Part of this work was done while Jay Goguen held a National Research Council Research Associateship at JPL. The Jet Propulsion Laboratory, California Institute of Technology, is under contract to the National Aeronautics and Space Administration. We thank S. Peale for helpful discussions, and C. Blanco and B. J. Buratti for careful reviews of this
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manuscript. This work was supported in part by NASA Grant NGL 12-001-057.
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