Photometry of Phoebe

ICARUS 68, 167--175 (1986)

Photometry of Phoebe S. K R U S E , J. J. KLAVETTER, AND E. W. DUNHAM Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received March 17, 1986; revised May 28, 1986 Observatios of Phoebe ($9) in the V filter at small solar phase angles (0.2 ° to 1.2°) with the MIT SNAPSHOT CCD are presented. The value of Phoebe's sidereal rotational period is refined to 9.282 -+ 0.015 hr. Assuming the Voyager-derived 110 km radius, Phoebe's observed mean opposition V magnitude of 16.176 -+ 0.033 (extrapolated from small angles) corresponds to a geometric albedo of 0.084 -+ 0.003. A strong opposition effect is indicated by the 0.180 -+ 0.035 mag/deg solar phase coefficient observed at these small phase angles. The data are shown to be compatible with a phase function for C-type asteroids (K. Lumme and E. Bowell, 1981, Astron. J. 86, 1705-1721; K. Lumme, E. Bowell, and A. W. Harris, 1984, Bull. Amer. Astron. Soc. 16, 684), but give a poorer fit to the average asteroid phase relation of T. Gehrels and E. F. Tedesco (1979, Astron. J. 84, 10791087). Phoebe's rotational lightcurve in the V filter is roughly sinusoidal, with a 0.230-mag peak-topeak amplitude and weaker higher order harmonics indicating primarily bimodal surface feature contrasts. In addition to these photometric results, precise positions on 3 nights are given. © 1986 AcademicPress, Inc.

those due to solar phase angles. We examine its solar phase function at small phase angles (less than 1.2°) where the opposition effect produces a steep phase curve. To compare Phoebe's surface with asteroid surfaces, the data are fit to a linear phase function and plotted with the phase relation of Lumme and co-workers (E. Bowell, personal communication, 1985; Lumme and Bowell, 198l; Lumme et al., 1984) for Ctype asteroids. The data used for this work were obtained on 13 nights in May 1985 with the MIT SNAPSHOT CCD on telescopes at Lowell Observatory in Flagstaff, Arizona.

INTRODUCTION

Phoebe, a small dark satellite in retrograde orbit around Saturn, is an unusual body even among the diverse Saturnian satellites. Its size (220 km diameter), low albedo, neutral color, and retrograde orbit (at 215 Saturnian radii) are all indicative of a history as a captured asteroid (Degewij et al., 1980a, 1980b; Smith et al., 1982; Tholen and Zellner, 1983; Thomas et al., 1983; Cruikshank et al., 1984). Most information about Phoebe has been derived from Voyager 2 observations taken at a range of two million kilometers in November 1981. These showed an inhomogeneous surface with brighter features whose motion could be tracked, giving a prograde rotational period of about 9.4 hr (Thomas et al., 1983). In this paper we refine the Voyager estimate of Phoebe's nonsynchronous rotational period and more precisely define its lightcurve. With improved resolution of the lightcurve, we can determine the rotational phase of our observations and separate the brightness variations due to rotation from

RECENT OBSERVATIONS The best determination of Phoebe's rotational period was that made by Thomas et al. (1983) using Voyager 2 images. These images show a nearly spherical body (less than 10% flattening), and surface features with contrasts as large as 50% which could be identified in consecutive images (Smith et al., 1982). A sidereal period of 9.4 -+ 0.2 hr was calculated by following several high-

167 0019-1035/86 $3.00 Copyright© 1986by AcademicPress, Inc. All rightsof reproductionin any formreserved.

168

KRUSE, KLAVETTER, AND DUNHAM TABLE I OBSERVATIONS a

UT date (1985)

07 May 08 May 10 May 1! May 13 May 14 May a 15 May a 18 May 20 May 21 May 25 May 26 May 27 May

Observers b

Telescope'

N u m b e r of Phoebe observations

Solar phase angle (deg)

79 79 79 79 79 79 79 79 79 79 1.8 1.8 1.8

4 8 6 9 4 3 4 3 2 11 3 7 2

0.86 0.76 0.57 0.48 0.31 0.26 0.24 0.41 0.59 0.68 1.08 1.18 1.27

ED ED ED ED ED, J K JK JK JK JK JK JK, SK JK, SK JK, SK

Extinction coefficient

0.168 0.192 0.247 0.239 0.178 0.169 0.138 0.141 0.137 0.187 0.082 0.143 0.142

+_ 0.009 _+ 0.025 _+ 0.019 _+ 0.033 +_ 0.006 _+ 0.003 _+ 0.009 +_ 0.006 _+ 0.012 _+ 0.007 _+ 0.009 _+ 0.005 _+ 0.085

a Titan was used as a standard on all nights. b ED - E.W. Dunham; JK - J.J. Klavetter; SK - S.E. Kruse. ' 79--79-cm telescope on Anderson Mesa, Lowell Observatory; 1.8--1.8-m telescope on Anderson Mesa, Lowell Observatory. d On these nights the Landolt standard stars listed in Table II were used as primary standards.

contrast spots (Thomas et al., 1983). Diskintegrated brightness variations of the Phoebe images yielded a consistent result. The observed lightcurve amplitude of 0.36 mag (peak-to-peak) was measured at approximately 25° solar phase. Extrapolating their data to zero degrees using linear phase coefficients for the brighter and darker regions, Thomas et al. (1983) report a predicted amplitude of 0.29 mag at zero degrees. Phoebe's nearly spherical shape and the use of individual features in determining rotational motion removed the possibility of a period with two maxima and two minima as is commonly seen aspherical asteroids. The most recent reported observations of Phoebe are those of Tholen and Zellner in March 1982. They observed Phoebe on 4 nights in eight colors (Tholen and Zellner, 1983) in order to investigate its spectrum. PRESENT OBSERVATIONS

We present observations of Phoebe obtained on 13 nights over a period of 21

nights in May 1985, summarized in Table I. The MIT SNAPSHOT CCD camera (Dunham et al., 1985) was used with a V filter on the 79-cm and 1.8-m telescopes at Lowell Observatory in Flagstaff, Arizona. Approximately 4 hours were available for observing each night, so a complete 9-hr period could not be seen in one night. The nearby Saturnian satellite Titan was used as a secondary standard for relative photometry of Phoebe. Titan exhibits no brightness variations due to rotation, and although very-long-period variations are reported, Titan maintains a constant magnitude over an observational period of one month (Andersson, 1977). Additionally, five primary standards from Landolt's list (Landolt, 1983) were observed in V and B filters on May 14 and 15 on the 79-cm telescope (see Table II). These filters do not correspond exactly to Johnson B and V bandpasses. From the standards we determined color transformation coefficients which are consistent with color coefficients derived from less extensive standard star

PHOTOMETRY OF PHOEBE T A B L E II

Standard Stars Star ~

V

B-V

106 834 106 700 106 485 149382 108 1332

9.088 9.787 9.484 8.944 9.199

+0.701 + 1.361 +0.380 -0.281 +0.384

Filters Band

Center wavelength(A)

Bandpass b (~)

B V

4300 5500

980 1100

gion of the chip, so as to minimize errors between images due to sensitivity variations among pixeis. P h o e b e ' s true position deviated on some nights more than an arcminute from that predicted by the 1985 Astronomical Almanac. The Almanc uses Ross' (1905) orbit; more recent orbits by Zadunaisky (1954) and Rose (1979) seem preferable. Phoebe's topocentric position was determined to within an arcsecond on three occasions using field stars in the CCD image. The field star coordinates were derived from plate solutions of Palomar sky survey prints based on SAO star positions. The Phoebe positions are listed in Table III. DATA REDUCTION

a F r o m L a n d o l t (1983). b F u l l - w i d t h at h a l f - m a x i m u m .

observations on the 1.8-m telescope. The color coefficients from the observations with the 79-cm telescope were subsequently used in reducing all data points. The CCD chip in the direct beam of the S N A P S H O T was used with a plate scale of 0.7 arcsec per pixel on the 79-cm telescope, and approximately 0.2 arcsec per pixel on the 1.8 m. On the 79-cm telescope, a 105mm printing Nikkor lens was used to reduce the image scale. Exposure times were generally 600 sec (79 cm) and 300 sec (1.8 m) for Phoebe, and 2 and 1 sec, respectively, for Titan. Care was taken to center the images whenever possible in a fixed re-

169

AND DISCUSSION

In reducing the raw CCD images to brightness measurements whose differences theoretically reflect only Phoebe's lightcurve, we must (1) correct for variations in the CCD chip pixel responses; (2) determine the background sky level, the intensity of the images, and their uncertainties; (3) account for atmospheric effects and the color response of the detector; and (4) r e m o v e brightness variations due to changing solar phase angles and geocentric and heliocentric distances. We reduced each pixel in the raw CCD frame by subtracting a bias level and dark current, and dividing by a flat field calibration frame. Dark current and flat field calibration frames were taken at the beginning and end of each night. Flat field frames

TABLE III

TOPOCENTRIC PHOEBE COORDINATES D a t e (UT) (1985)

A p r i l 2.329 M a y 8.399 M a y 21.120

Observed"

R e l a t i v e to 1985 A A b

RA

Dec

RA

Dec

15h41m12.12 s 15h32m31.95s 15h28m47.98 ~

-17°10'16.9" -- 16°38'22.3 " - 16°25'51.1"

2.5 ~ 5.P 5.4 s

2.0" --3.7" - 14.8"

C o o r d i n a t e s to w i t h i n 1 a r c s e c . b A A - A s t r o n o m i c a l A l m a n a c ; c o o r d i n a t e s in s e n s e o b s e r v e d m i n u s predicted.

170

KRUSE, KLAVETTER, AND DUNHAM

were acquired by exposure to the evening and morning twilight skies. Bias level frames were taken throughout the night. As a result of problems in the flat field exposures, little improvement resulted in the Phoebe exposures reduced in this manner. The much shorter Titan and standard star exposures were not improved, and uncorrected frames were used. The photometric response was known to be linear at all exposure levels used, since the highest gain setting was used exclusively (Dunham et al., 1985). On each image, obviously anomalous " h o t " pixels were replaced by the average of 2 neighboring pixels in the same rOW.

In order to determine background sky level on each exposure, we defined an effective aperture on each image as a circle centered on the image. A mean background level was established by averaging pixels whose centers lay within a concentric ring surrounding the circular aperture. Phoebe was sufficiently far from Saturn, and Titan sufficiently bright that any gradient in the background was negligible. We chose an aperture radius of approximately 25 pixels (17.5 arcsec) for frames taken with the 7% cm telescope, and about 42 pixels (approximately 9 arcsec) for the 1.8-m telescope. These apertures included effectively all of the light of the image based on radial intensity profiles of standard stars. The smaller effective aperture is preferable on the 1.8-m images because of the larger number of pixels used, and because the images are generally smaller due to shorter exposure times, better telescope tracking, and better quality optics. Unless an image was very smeared due to tracking problems, we applied the same aperture size to all images taken during a night. A color transformation coefficient ev (V = v + ev (b - v); V = absolute magnitude, b, v = instrumental magnitudes corrected for extinction) was determined from primary standard observations in B and V filters on May 14 and 15. The weighted mean of the color transformation coefficients calculated separately on May 14 and

May 15, ev = 0.1043 -+ 0.0034, was used in subsequent calculations for all nights. Using the primary standards, we find a mean opposition Titan magnitude of 8.36, 0.08 mag fainter than the 8.28 mag reported in the 1985 Astronomical Almanac. We are unsure of an explanation for this discrepancy. The Landolt standards proved internally consistent on these nights; e.g., the magnitude of a standard with nearly the same color as Titan can be recovered to within 0.02 mag. We chose to use our measured Titan magnitude of 8.36 in calculations of zero point values, and hence Phoebe magnitudes. Extinction and zero point coefficients were then derived for each night from a fit to Titan measurements corrected for distance and phase angle. For Titan's phase coefficient we adopted Andersson's (1974) value of 0.004 mag/deg, and for heliocentric and geocentric distances and solar phase angle we used the 1985 Astronomical Almanac values for Saturn, which are sufficiently close to the Titan values. Phoebe magnitudes were then determined assuming 0.70 mag for the (B-V) color term. Reported (B-V) values range from 0.58 to 0.77 (Degewij et al., 1980a) and 0.59 to 0.72 mag (Tholen and Zellner, 1983). An error in this value of less than 0.1 mag would produce an error of less than 0.01 mag in all Phoebe data points, as it is multiplied by the color transformation coefficient for all observations. The calculated formal uncertainties in the data (shown as error bars in Figs. I and 4) reflect photon noise and uncertainty in background sky level (as in Conner, 1982), and uncertainties in the extinction correction, accounting for correlation between the extinction coefficient and zero point level. The primary source of uncertainty for images taken with the 79-cm telescope is uncertainty in background level; for 1.8-m images the primary source is uncertainty in the extinction correction. In order to reduce Phoebe magnitudes to mean opposition magnitudes and compute solar phase angles, Phoebe's coordinates

PHOTOMETRY OF PHOEBE

15.9 161 16.3 16.5

'°;

'o12 'oi,

'o'6 '°'8 ','9 ','2 '1,

Solar Phase Angle (degrees)

FIG. l. Phase coefficient of Phoebe. Data points are mean opposition magnitudes from which the best-fitting sine curve amplitudes (Table IV) have been subtracted. Error bars reflect CCD chip noise and uncertainty in extinction calculations. The solid line corresponds to a phase coefficient of 0.180 mag/deg. were calculated from the coordinates relative to Saturn available in the 1985 Astronomical Almanac, and from values from the same ephemeris for P h o e b e ' s radial distance from Saturn supplied by the U.S. Naval Observatory. Deviations of these coordinates from the true position as discussed above p r o v e d insignificant in our computations. To a c c o u n t for brightness variations with solar phase angle, we assumed a linear phase relation, V(~) = V(0) + aft, and fit the data to the phase coefficient/3 and the zero phase angle magnitude V(0). This was performed iteratively with a fit to the rotational lightcurve. The lightcurve resulting from the second iteration deviated from the first by much less than their respective uncertainties, so no further iterations were required. (This curve is discussed below.) The second fit p r o d u c e d a phase coefficient /3 = 0.180 -+ 0.035 mag/deg and zero phase mean opposition magnitude V(0) = 16.176 -+ 0.026 mag. (The uncertainties reflect only uncertainties in fitting for the phase coefficient.) This function V ( a ) is plotted against the solar phase angle a as the solid line in Fig. I. The Phoebe magnitude data points in Fig. 1 are the V ( a ) , which have been corrected for distance, but not for phase, and the best fitting sine curve through the data points has been subtracted in order to remove rotational brightness variations.

171

The 0.180 mag/deg phase coefficient for angles less than 1.2 ° completes a continuous trend of increasing effective phase coefficients with decreasing solar phase angles (0.15-0.10 mag/deg for 1° to 6° (Degewij et al., 1980a) and approximately 0.035 mag/deg for 8° to 34 ° (Thomas et al., 1983; see Fig. 2). We note that P h o e b e ' s observed opposition effect is stronger than those exhibited by the brighter Saturnian satellites as estimated from the slope of their phase curves at zero degrees (Franz and Millis, 1975; Noland et al., 1974), as would be expected from the low albedo of Phoebe. The dark side of Iapetus may be the most similar surface, showing a phase coefficient of 0.060 mag/deg for I ° to 6 ° phase angles which increases to perhaps 0.15 mag/deg at smaller angles (Millis, 1977). In addition, we c o m p a r e d our data to the p h a s e relation for asteroids developed by L u m m e and Bowell (1981; L u m m e e t al., 1984). Values of the parameters were sup-

16.1 t ^

16.3 ~

°

~

f

G a x . ~ []°

[]

~'~ 16.5

~

~

o

16.7

16.9 L 0

I

I

I

I

1

2

3

4

5

Solar Phase Angle (degrees)

FIG. 2. Phase coefficient of Phoebe. Short solid line at small phase angles shows the best-fitting 0.180 mag/ deg phase coefficient. Solid curve indicates phase function of Gehrels and Tedesco (1979); dashed curve is phase function of Lumme et al., (1984) for C-type asteroids (E, Bowell, personal communication, 1985). Data are mean opposition magnitudes measured during apparitions in 1970-1971 (squares), 1972-1973 (crosses), and 1977-1978 (triangles) by Degewij et al. (1980a), in 1982 (Xs) by Tholen and Zellner (1983). Circles show our nightly averages. No corrections have been made for brightness variations due to rotation.

172

KRUSE, KLAVETTER, AND DUNHAM

o.9-

rr

08 /

/ /

"\ / /

07

O6

'

03

/

\/ 04

~ 90

_ 91

92

/ i

i

I

]

93

94

95

96

Period (hours)

F]o. 3. Goodness of period fit. Crosses show the adopted _+0.015-hr uncertainty in the 9.282-hr period.

plied by E. Bowell (personal communication, 1985). In particular, G, a measure of the slope of the phase curve, is set to 0.15, appropriate for C-type asteroids. This phase function is only slightly flatter than our best-fit linear function, and lies within the uncertainties of the linear function (see Fig, 2). The rough a g r e e m e n t between the shape of this phase function and the trend of Phoebe magnitudes versus phase angle confirms that P h o e b e ' s phase function is similar to that of C-type asteroids at small phase angles where the opposition effect is important. At larger angles similarity to asteroid phase relations has previously been shown (Degewij et al., 1980a). The large (0.180 mag/deg) phase coefficient we derived also indicates that at small angles P h o e b e ' s phase curve matches model curves for C-type asteroids more closely than the flatter phase curves for M- and Stype asteroids (Bowell and L u m m e , 1979, Table IV). After all Phoebe m e a s u r e m e n t s were referred to zero phase angle via the linear phase function, the data were fit to a sine curve. Although albedo contrasts in surface features should not necessarily produce sinusoidal brightness variations, it is the most obvious function to fit in order to quantify a period within the variations, and the V o y a g e r 2 observations suggest a lightcurve similar to a sinusoidal curve. The program p e r f o r m e d a nonlinear least-

squares unweighted fit for lightcurve amplitude, phase, and mean level given a fixed period. An unweighted fit was chosen because the formal uncertainties do not reflect the true uncertainties in the m e a s u r e m e n t s , which are discussed below. A 9.282-hr period minimized the sum of squared residuals (see Fig. 3). The sidereal period differs negligibly f r o m this synodic period (by less than 0.001 hr). The data folded back onto this period are plotted in Fig. 4, and the p a r a m e t e r s of the best-fitting lightcurve are shown in Table IV. The data scatter about the best-fit curve is larger than the formal uncertainties (shown with error bars) allow. S o m e of this scatter appears to be due to inconsistencies in zero point level from night to night, as data from some nights appear consistently bright or faint. Other possible sources of noise include problems with the C C D chip and weather variations on time scales shorter than consecutive Titan observation times. S o m e residuals certainly arise f r o m the implicit assumption that the lightcurve amplitude is independent of solar phase angle, and from deviations of P h o e b e ' s lightcurve from a true sinusoidai function. Despite the relatively large residuals of individual data points, the best-fit lightcurve p a r a m e t e r s c o m p a r e favorably with previous observations, indicating that the data set as a whole is robust. The 9.282-hr pe156--

i

t ~

16.0 c 162

90 Rotational

180 Phase

270

360

(degrees)

FIG. 4. Phoebe magnitudes, corrected for distance and phase angle, folded back onto one 9.282-hr period. Zero time is chosen arbitrarily at 1985 May 7.375 UT. The solid curve is the best-fitting sine curve with parameters listed in Table IV.

PHOTOMETRY OF PHOEBE T A B L E IV ADOPTED SINUSOIDAL LIGHTCURVE PARAMETERS Period Amplitude b M e a n opposition magnitude e T i m e of m a x i m u m brightness

9.282 hr 0.230 m a g

-+0.015 hr" -+0.030 m a g c

16.176

-+0.033 m a g d

JD 2446193.183

-+0.305 hr f

a See text for discussion. b Peak-to-peak amplitude. ' Uncertainty resulting from a three-parameter fit for a fixed 9.282-hr period. d Reflects uncertainties in the p h a s e coefficient and m e a s u r e d m a g n i t u d e of Titan. ' A s s u m i n g 9.54 A U S u n - P h o e b e distance, 8.54 A U E a r t h - P h o e b e distance. See text for discussion of p h a s e function. I F r o m best-fitting values of u p p e r and lower limit periods.

riod falls well within the 9.4 - 0.2-hr sidereal period derived from the Voyager 2 observations (Thomas et al., 1983). The amplitude, 0.230 mag, appears slightly smaller than the brightness variations of Andersson's (1974) observations, and is smaller than the 0.29-mag zero phase amplitude predicted by Thomas et al., (1983). This latter discrepancy is probably due to uncertainities in extrapolating Voyager measurements at 25 ° solar phase to 0°, as the phase functions of the albedo features on Phoebe are not well known. The mean opposition magnitude, V(0) = 16.176, corresponding to H = 6.621 mag at unit geocentric and heliocentric distances, is our estimate of Phoebe's true zero phase magnitude, not the traditional V(1, 0) derived by extrapolation of the linear phase function at large angles which removes the opposition effect. For comparison we applied the average asteroid phase relation of Gehrels and Tedesco (1979) used by previous observers (Degewij et al., 1980a; Tholen and Zellner, 1983). Although this phase relation shows good agreement with Phoebe measurements at 1° to 6° phase angles (Degewij et al., 1980a), at angles less than I ° it predicts phase coefficients which

173

are clearly smaller than our observed value (eg., 0.135 mag/deg at 0.3°). So in computing V(1,0) with this relation, we inserted our predicted mean magnitude at one degree solar phase, the angle at which the apparent regions of validity of our calculated phase coefficient and of the phase function of Gehrels and Tedesco (1979) overlap. For the large-angle linear phase coefficient, we used 0.035 mag/deg (the average of Voyager-derived coefficients for bright and dark surface regions). The computed V(1,0) 6.960, is consistent with Andersson's (1974) mean value which reduces with the same large-angle phase coefficient to 6.92 +- 0.06 mag. The observations of Tholen and Zellner (1983) and Degewij et al. (1980a) in 1977 and 1978 (neglecting two apparently too faint points) reduced in a similar fashion fall within the 6.84 to 7.08 mag limits of our lightcurve. Similar comparison of data using the phase function of Lumme and Bowell (Lumme et al., 1984; E. Bowell, personal communication, 1985) also gives consistent zero phase magnitudes for all data sets. The uncertainty in the best-fit period was estimated by subdividing the data set into six subsets of 11 points each, where each subset spanned as much of the observing run as possible. Each subset was fit independently to a sine curve. The uncertainty in the period is defined as the uncertainty in the mean of the best-fitting periods of each subset. This method produced an uncertainty of 0.015 hr (see Table IV). The mean opposition magnitude uncertainty, 0.033 mag, is derived from the uncertainties in the phase function and the 0.02-mag uncertainty in the measurement of the magnitude of Titan. The uncertainty in the mean magnitude from the sine curve fit is negligible. The 0.030-mag uncertainty in the sine curve amplitude results from the three-parameter fit for the 9.282-hr period. The relatively large uncertainty limits in the time of maximum brightness are derived from the best-fitting values of the upper and lower limit periods, which shifted as the

174

KRUSE, KLAVETTER, AND DUNHAM

to

er

0

90

180

270

360

Rotational Phase (degrees)

F1o. 5. Difference between data points and best-fit sine curve folded back onto one period as in Fig. 4. Note that no evidence for large systematic deviations from a sinusoidal lightcurve is seen.

data were forced to fit to different periods. More important for observations made before or since May 1985 is the 0.015-hr uncertainty in the period. An uncertainty of one period in the rotational phase develops after 619 rotations, or 8 months. Our lightcurve, therefore, cannot be extrapolated to the four observations of Phoebe reported by Tholen and Zellner (1983). The residuals of the best-fit 9.282-hr period are scattered fairly evenly over all phases of the sine curve (Fig. 5). No large higher order harmonics in the lightcurve appear in the residuals. Evidence for diminished second-, third-, and fourth-order harmonics is seen on a plot of the sum of the

squared residuals for fixed periods (Fig. 6), and when the same residuals are plotted against lightcurve frequency (Fig. 7). From the frequency plot it is clear that the very deep minima occur at even 1/24 (0.0417) hr -J spacings off the 1/9.282 (0.1077) hr -~ base frequency, a result of our 24-hr sampling bias. Other 1/24 spaced minima can be identified with 3/9.282, and a sum of 2/9.282 and 4/9.282 hr -1 base frequencies (second-, third-, and fourth-order harmonics), and probably a sum of fifth- and seventh-order harmonics. We conclude that Phoebe's lightcurve is primarily bimodai with smaller contrasting surface features providing secondary brightness variations, in rough agreement with a sketch map of Phoebe's surface drawn from Voyager data (Thomas et al., 1983, Fig. 4). CONCLUSIONS

Phoebe's sidereal rotational period is determined to be 9.282 -+ 0.015 hr. Its roughly sinusoidal lightcurve in the V filter exhibits 20% brightness variations with weaker higher order harmonics. The effective solar phase coefficient at angles less than 1.2° is found to be very large, 0.180 _+ 0.035 mag/ deg, indicating the strong opposition effect typical of dark surfaces. The data are corn-

E

004

01

0 16

0.22

028

034

Frequency ( h o u r s -1)

3

5

7

9

11

13

15

17

19

Period (hours)

FIG, 6. Goodness of period fit, plotted for a wider range of periods. The true period occurs at 9.282 hr, shown with the arrow. Other minima marked with tick marks are due to our 24-hr sampling bias. See the text for explanation.

FIG. 7. Sum of squared residuals as in Fig. 6 plotted against the inverse of the period. The effect of 24-hr sampling intervals is seen in equal 1/24 hr t spacing of minima. The longest tick marks indicate minima corresponding to a 1/9.282 hr t base frequency, intermediate length to 3/9.282 hr ~ and the shortest to a sum of 2/9.282 and 4/9.282 hr -t base frequencies. The arrow lies at 1/9.282 hr t.

PHOTOMETRY OF PHOEBE

patible with a phase function for C-type asteroids (Lumme and Bowell, 1981; Lumme et al., 1984) at these small phase angles, giving further credence to spectral evidence that Phoebe may be a captured asteroid. For a 110 km radius (Thomas et al., 1983) and a solar V magnitude of -26.74, Phoebe's observed mean opposition V magnitude of 16.176 --- 0.033 (extrapolated from small angles) corresponds to a geometric albedo of 0.084 -+ 0.003. Further refinement of the rotational period is necessary to determine the rotational phase of previous and future observations. ACKNOWLEDGMENTS We are grateful to A. S. Bosh for computer work and to the staff at Lowell Observatory for assistance and encouragement. This work was supported in part by NASA Grants NAG2-257 and NSG 2342. REFERENCES ANDERSSON, L. E. (1974). A Photometric Study of Pluto and Satellites o f the Outer Planets. Ph.D thesis, Indiana University. ANDERSSON, L. E. (1977). Variability of Titan: 18961974. In Planetary Satellites (J. A. Burns, Ed.), pp. 451-459. Univ. of Arizona Press, Tucson. BOWELL, E., AND K. LUMME (1979). Colorimetry and magnitudes of asteroids. In Asteroids (T. Gehrels, Ed.), pp. 132-169. Univ. of Arizona Press, Tucson. CONNER, S. R. (1982). Photometry o f Hyperion. M.S. thesis, Massachusetts Institute of Technology. CRUIKSHANK, D. P., J. VERVERKA, AND t . A. LEeOSFKV (1984). Satellites of Saturn: Optical properties. In Saturn (T. Gehrels and M. S. Matthews, Eds.), pp. 640-667. Univ. of Arizona Press, Tucson. DEGEWIJ, J., L. E. ANDERSSON, AND B. ZELLNER (1980a). Photometric properties of outer planetary satellites. Icarus 44, 520-540. DEGEWIJ, J., D. P. CRUIKSHANK, AND W. K. HARTMANN (1980b). Near-infrared colorimetry of J6 Himalia and $9 Phoebe: A summary of 0.3-2.2/zm reflectances. Icarus 44, 541-547. DUNHAM, E. W., R. L. BARON, J. t . ELLIOT, J. V. VALLERGA, J. P. DOTY, AND G. R. RICKER(1985). A

175

high speed dual-CCD imaging photometer. PASP 97, 1196-1204. FRANZ, O. G., AND R. L. MILLIS (1975). Photometry of Dione, Tethys, and Enceladus on the UBV system. Icarus 24, 433-442. GEHRELS, T., AND E. F. TEDESCO (1979). Minor planets and related objects. XXVIII. Asteroid magnitudes and phase relations. Astron. J. 84, 1079-1087. LANDOLT, A. U. (1983). UBVR1 photometric standard stars around the celestial equator. Astron. J. 88, 439-460. LUMME, K., AND E. BOWELL (1981). Radiative transfer in the surfaces of atmosphereless bodies. II. Interpretation of phase curves. Astron. J. 86, 17051721. LUMME, K., E. BOWELL, AND A. W. HARRIS (1984). An empirical phase relation for atmosphereless bodies. Bull. Amer. Astron. Soc. 16, 684. MILLIS, R. L. (1977). UBV photometry of Iapetus: Results from five apparitions. Icarus 31, 81-88. NOLAND, M., J. VEVERKA, D. MORRISON, D. P. CRUIKSHANK, A. R. LAZAREWICZ, N. D. MORRISON, J. L. ELLIOT, J. GOGUEN, AND J. A. BURNS. (1974). Six-color photometry of Iapetus, Titan, Rhea, Dione and Tethys. Icarus 23, 334-354. ROSE, L. E. (1979). Motion of Phoebe (Saturn IX) 1904-1969 and a determination of Saturn's mass. Astron. J. 84~ 1067-1071. Ross, F. E. (1905). Investigations on the orbit of Phoebe. Ann. Harvard College Obs. 53, 101-142. SMITH, B. A., L. SODERBLOM, R. BATSON, P. BRIDGES, J. INGE, H. MASURSKY,E. SHOEMAKER, R. BEEBE, J. BOYCE, G. BRIGGS, A. BUNKER, S. A. COLLINS, C. J. HANSEN, T. V. JOHNSON, J. L. MITCHELL, R. J. TERRILE, A. F. COOK II, J. CUZZl, J. B. POLLACK, G. E. DANIELSON, A. P. INGERSOLL, M. E. DAVIES,G. E. HUNT, D. MORRISON, T. OWEN, C. SAGAN, J. VERVEKA, R. STROM, AND V. SUOM! (1982). A new look at the Saturn system: The Voyager 2 images. Science 215, 504-537. THOLEN, D. J., AND B. ZELLNER (1983). Eight-color photometry of Hyperion, Iapetus, and Phoebe. Icarus 53, 341-347. THOMAS, P., J. VEVERKA,D. MORRISON, M., DAVIES, AND T. V. JOHNSON (1983). Phoebe: Voyager 2 observations. J. Geophys. Res. 88, 8736-8742. ZADUNAISKY, P. E. (1954). A determination of new elements of the orbit of Phoebe, ninth satellite of Saturn. Astron. J. 59, I-6.