Rings and Satellites of Uranus: Colorful and Not So Dark

ICARUS

125, 348–363 (1997) IS965631

ARTICLE NO.

Rings and Satellites of Uranus: Colorful and Not So Dark1 ERICH KARKOSCHKA Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721-0092 E-mail: [email protected] Received February 29, 1996; revised October 4, 1996

cles is limited by the spectral range of the Voyager 2 cameras (340–580 nm) and the Voyager photopolarimeter (250 and 750 nm). The uranian rings have not been detected from groundbased telescopes at visible wavelengths, where they are some 2000 times fainter than Uranus. On the other hand, in some infrared methane bands, the rings outshine the planet. Infrared photometry of the five major satellites and of the unresolved ring system has been successful from ground-based observations (Brown and Cruikshank 1983, Herbst et al. 1987, Baines et al. 1995); however, it has been difficult to tie Voyager visible data and ground-based infrared data together because of different phase angles and unknown phase laws. Uranus is observable from Earth at phase angles 0–38, whereas most Voyager observations were at phase angles above 158. In fact, Ockert et al. (1987) determined the phase law by assuming that the ring albedo is constant with wavelength. The Hubble Space Telescope is well suited to provide the missing link between Voyager and ground-based data, because its wavelength range includes that of the Voyager cameras and overlaps that of infrared ground-based observations. Additionally, it can observe minor satellites that have not been detected from the ground. It also achieves partial resolution of the ring system. Uranus was first imaged by the Hubble Space Telescope in 1994. These observations provided the first color determinations of the minor satellites Puck and Portia (Pascu et al. 1995). New Hubble Space Telescope data presented here extend the wavelength range of these earlier observations significantly. This study focuses on the presentation and discussion of the new data, while physical interpretations are left mostly for further studies. The next section describes the observations and their calibration. The following four sections discuss photometric properties of major satellites, the « ring, minor satellites, and inner rings. This order reflects the increasing difficulty and decreasing accuracy of measurements, from the major satellites with a signal 100–1000 times higher than the background level, to the inner rings with a signal 10 times

Photometric properties of nine uranian satellites and four rings, based on six Hubble Space Telescope images taken in 1995, are presented. Derived albedos are consistent with previous data taken at the same phase angle of 18, but inconsistent with most Voyager-based estimates extrapolated from observations at phase angles above 158. The shape of phase functions in the range 1–908 is similar to that of asteroids. Darker surfaces have steeper phase functions than brighter ones, except for the four brightest satellites, which have the same phase function. Puck’s geometric albedo in the visible is 0.11 6 0.015, much larger than the Voyager-based value of 0.074 6 0.008. The satellites smaller than Puck may be 10% larger than Voyagerbased estimates. Ring particles have a geometric albedo of 0.061 6 0.006, much larger than the Voyager-based value of 0.032 6 0.003. The longitudinal variation of brightness of the « ring indicates that the mean separation of particles in the ring is four to five times their diameter. While the uranian rings and satellites seemed to be all gray heretofore, the wide wavelength range of this study, 340–910 nm, detected their subtle, distinct colors. Rings and the minor satellites are brown, Miranda is blue, Umbriel is red, and Ariel, Titania, and Oberon are yellow. Rings and minor satellites belong spectrally to Mtype asteroids.  1997 Academic Press

I. INTRODUCTION

Before the Uranus flyby of Voyager 2 in 1986, our knowledge of the uranian system of rings and satellites was quite sparse. Voyager 2 revealed that in photometric and thus surface properties, the uranian system is quite different from the well-studied systems around Jupiter and Saturn. Our post-Voyager knowledge of the photometric properties was summarized by Veverka et al. (1991) for the uranian satellites and by French et al. (1991) for the rings. Understanding of the surfaces of satellites and ring parti1

Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by Association of Universities for Research in Astronomy, Incorporated, under NASA Contract NAS5–26555. 348 0019-1035/97 $25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved.

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TABLE I Log of Exposures

Filter name

Mean wavelength (nm)

F467M FQCH4-C F336W FQCH4-B F673N F850LP

470 730 340 620 670 910

Geometric albedo of Uranus

CCD No.

Mid-UT on 1995–07–03 hr:min:sec

Exposure time (sec)

STScI

ESO

WF4 WF4 PC1 PC1 PC1 PC1

09:55:21 09:59:36 10:06:06 10:11:36 10:16:07 10:20:07

8 160 100 160 100 100

0.594 0.046 0.517 0.139 0.310 0.055

0.593 0.046 0.511 0.139 0.318 0.054

lower than the background level. A conclusion summarizes the main results.

The Hubble Space Telescope recorded six images centered on Uranus on July 3, 1995. The phase angle of Uranus was 18. The line of sight was 488 below the equatorial plane of Uranus. The Wide Field Camera took two exposures at a scale of 1350 km/pixel. The Planetary Camera took the other four exposures at 620 km/pixel. Filter names, approximate mean wavelengths, and observation and exposure times are listed in Table I. Each frame yielded a maximum exposure level of about 30,000 electrons/pixel, well below the saturation level of 57,000 electrons/pixel for the chosen gain setting of 14 electrons/count. No pixel on Uranus or on the satellites was saturated. Pixels contaminated by cosmic ray hits were replaced by interpolation using an automated routine with manual intervention in questionable cases. The first two exposures contained the whole uranian system on the WF4 chip; however, Titania was at a position where the filter FQCH4-C is slightly vignetting. Thus, Titania was not measured with this filter. The last four exposures imaged the whole uranian system on the PC1 chip with the exception of Oberon.

etry since it does not necessarily preserve the flux. The Wiener method, a Fourier transform technique, does preserve the flux. It allows specification of the point-spread function of the deconvolved image. One could specify a narrow point-spread function yielding sharp images, but this would strongly boost the noise. For this investigation, the specified point-spread function was similar to the original point-spread function over a 3 3 3-pixel area, but without the extended wings outside this area. This caused only a slight increase of noise and allowed photometry with spatial resolution close to the limit of 0.10. The deconvolution method used theoretical pointspread functions generated for each filter by the Tiny Tim software of the Space Telescope Science Institute (Krist 1994). It simplified the photometry of the faint, inner satellites. In the raw images, Uranus has diffraction spikes from the spider of the telescope with radial and azimuthal structure. Some of the inner satellites are within or close to this diffraction pattern of similar data number levels. Photometry of faint objects on top of such a background would be a challenge; however, in deconvolved images, the diffraction pattern is subtracted, and the satellites can be measured on top of an almost black, flat background. The central part of the deconvolved 910-nm image is displayed in Fig. 1. Visible are the brightest rings around Uranus and five satellites.

Deconvolution

Intensity Calibration

While the Planetary Camera has a resolution of 0.10, its point-spread function is wide enough that photometry of point sources requires summation of the received signal over an aperture of diameter 1–20 (Whitmore 1995). For the photometry of extended sources, such as Uranus and its rings, images need to be deconvolved unless one is willing to give up a factor of 10–20 in resolution. There are two main deconvolution algorithms, the Lucy and Wiener methods. The Lucy method is the preferred method for feature recognition, but it is not recommended for photom-

The determination of the conversion factor between data numbers and albedo used two completely independent methods. The first method used filter and system response data by the Space Telescope Science Institute as of August 1995. These data provide the intensity I for a count rate of 1 data number/sec. The solar flux was taken from Neckel and Labs (1984) and adjusted to the heliocentric distance of Uranus. The appropriate flux for each filter is efF(l)S(l) dl /eS(l) dl, where fF(l) is the solar flux, S(l) the filter 1 system response, and l the wavelength.

II. CALIBRATION

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FIG. 1. Central part of the deconvolved 910-nm image displaying Uranus, the ring system, and five satellites. The intensity of Uranus was suppressed by a factor of 50 to avoid saturation in the display.

The derived albedo for each pixel is I/F. Derived geometric albedos of Uranus are listed in column ‘‘STScI’’ of Table I. The second method yields albedos I/F for each pixel by using the total data numbers of Uranus and the geometric albedos of Uranus by my spectroscopic observations during the same first week of July 1995 (yet unpublished). These geometric albedos of Uranus are 0–7% lower than those by Karkoschka (1994), taken with the same instrument at the European Southern Observatory. At wavelengths where the disk of Uranus displays no contrasts, the decrease is 0–1%. At wavelengths with the highest-intensity contrast between equator and pole, the decrease is 5–7%. A decrease of 4% would be expected from the fact that the bright polar region takes a smaller and smaller fraction of the disk of Uranus due to the changing viewing angle with the seasons of Uranus. The additional decrease by 1–3% may indicate a change or may be due to calibration uncertainty stated as 4% in Karkoschka (1994). The appropriate geometric albedo for each filter is ep(l)F(l)S(l) dl /eF(l)S(l) dl and listed in column ‘‘ESO’’ of Table I [p(l) is the geometric albedo of Uranus]. For all six filters, both calibration methods agree to 3% or better. The adopted calibration was the mean of both methods. The accuracy of the intensity calibration is estimated at 3%. Aperture Photometry A full-disk albedo is derived by the summation of I/F over the area with significant data numbers and by dividing by the area of the object. The area of the satellites was calculated from radii by Davies et al. (1992), listed in Table II, and from known scales for both cameras. It was taken into account that the scale varies slightly across each chip (Trauger et al. 1995). If a satellite would be a point source and would fall on the

center of a pixel, one would expect from the deconvolution method that 100% of its signal is contained in a 3 3 3pixel area. The pixel size is 0.10 (WF4) and 0.0460 (PC1). Measurements of the five brighter satellites indicate that increasing the aperture to 0.60 diameter still increases the total signal. Increasing the aperture beyond 0.60 gives constant signals within 0.5%. Thus, a 0.60 aperture was used for the brighter satellites. The background was based on an annulus of 0.80 inner diameter and 1.10 outer diameter. Background subtraction caused a correction of less than 1%. The larger-than-expected aperture size to contain 100% of the signal may be due to imperfect theoretical point-spread functions or to the variation of the pointspread functions across the field of views, which was ignored in the deconvolution. The latter possibility is supported by the observation that satellites close to Uranus gave an essentially constant signal for all apertures larger than 0.40 diameter, while satellites near the edge of the field of view displayed this feature only for apertures larger than 0.60. Photometry of the fainter satellites used a 0.20-diameter aperture, since a larger aperture would have caused too much noise. The annulus for the sky background was 0.30 inner and 0.40 outer diameter. These numbers apply for the PC1 chip; they were increased by 0.10 for the WF4 chip. These smaller apertures do not contain 100% of the signal. Thus, the total signals were corrected according to the fractions of signal seen in the same aperture for Miranda in each filter. Error estimates for the fainter satellites are accordingly higher than for the brighter satellites. Three small corrections were applied, although they turned out much smaller than other errors and thus almost negligible. First, the total signal in small apertures is slightly dependent on the position of the source, if it is centered on a pixel or near the corner of a pixel. This effect was modeled by shifting Miranda’s image by fractional pixels with bicubic interpolation. Second, the finite size of Miranda and the smear due to the finite exposure times, both about 1 pixel or less, decrease the signal in a small aperture. This effect was modeled by smearing point-spread functions. Third, every 34th row of the chips has 3% smaller pixels due to a manufacturing error (Biretta 1995). In two cases a satellite was close to such a row. Its signal was corrected by 1%. The signal of uranian rings was initially summed over bands 3–5 pixels wide. These values had to be slightly adjusted by the following method because the spacing of the rings is similar as the width of the point-spread function. Line-spread functions were inferred from profiles across the « ring near both ansae. Synthetic images of the ring system were then convolved by these line-spread functions and compared with the data. Small adjustments to the total signal for each ring yielded the least-squares fit. In the error estimation it was considered that different assumptions of

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TABLE II Full-Disk Albedos at 18 Phase Angle Ring (-group), satellite

Wavelength (nm) 340

470

550

620

670

730

910

Error

6, 5, 4 a, b h, c, d « ring Juliet Portia Belinda Puck Miranda Ariel Umbriel Titania Oberon

— — — 44 — — — — 320 342 196 219 —

— — — 52 — — — — 315 350 185 239 201

— 56 63 53 — 98 — 91 307 350 189 232 205

— 56 63 55 — 107 — 95 310 374 185 234 —

— — — 54 — 104 — 91 298 343 190 235 —

— — — 58 — 105 — 97 294 354 196 — 218

52 56 64 58 130 123 132 101 301 371 203 265 —

612 6 7 6 7 6 4 614 610 616 6 6 612 614 6 8 610 6 9

EW, radius (km) 2.2 5.1 6.1 27.5 42 54 33 77 236 579 585 789 761

6 6 6 6 6 6 6 6 6 6 6 6 6

0.1 0.2 0.6 1.0 5 6 4 5 1 1 3 2 3

Note: All albedos are given in units of 1023. The albedo at 550-nm wavelength corresponds to the fitted curve; all other data are individual measurements. EW is the equivalent width for rings only. Error estimates for albedos do not include uncertainties in the equivalent width or satellite radius.

the line-spread function influenced the best-fitting values by some 2%. Linearity The used CCDs are highly linear between data numbers and photon flux. The exponent of the power law between both variables is 1.0004 6 0.0001 for the PC1 chip and 1.0018 6 0.0012 for the WF4 chip (Biretta et al. 1996). The nonlinearity was ignored since it causes a maximum error of 0.2% between the faintest and brightest objects for the PC1 and p1% for the WF4. The observations were performed within 1 week of a decontamination cycle. Thus, contamination effects in the used filters were well below 1% and thus ignored.

In the raw frames for both methane-band filters, Uranus and Ariel were measured with apertures of 50 diameter. The ratios of the total signal between Ariel and Uranus matched the ratios determined from the deconvolved images to better than 1%. In the raw frames for all filters, Miranda, Ariel, and Umbriel were measured with apertures of 10 diameter. Most of the ratios between two satellites match those determined from deconvolved images to 1%. In a few cases, there was a mismatch of about 3%. These checks show that photometry on the brighter satellites gives the same results by using raw or convolved images within stated error margins. For reasons of consistency, all further data are based on the deconvolved images.

Checks Photometry of rings and faint satellites requires background subtraction. This has been achieved by the presented deconvolution method; however, photometry of bright satellites can be done on images that have not been deconvolved. Several such measurements are described here. They provide a check that the deconvolution method adopted here preserves photometric properties. In the raw frames for each filter, the total signal of Uranus in apertures of 120 diameter was measured. In all cases, it was within 1% of the signal measured in deconvolved frames with an aperture of 40 diameter (the diameter of Uranus is 3.80). As expected, the deconvolution process concentrates the signal spread over about 120 onto the disk of Uranus. The contribution from rings and faint satellites in apertures of 120 is below 1%.

III. MAJOR SATELLITES

Photometry Before Voyager 2 approached Uranus in 1985/1986, five satellites of Uranus were known. Full-disk albedos of these major satellites are listed in the bottom rows of Table II and displayed in Fig. 2 (open and filled symbols). Albedos of this work are compared with Voyager-based albedos at the same phase angle. Titania was the only satellite Voyager 2 observed at a phase angle of 18. Veverka et al. (1987) give Voyager imaging (IIS) data of Titania in three filters, marked ‘‘V’’ in Fig. 2. Their original albedos were increased by 4% since they refer to a 2% larger size of Titania than adopted here (cf. last column in Table II). Albedo ratios between five IIS filters by Buratti et al. (1990)

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spectral curvature, about twice as much as expected from statistical variations. Thus, the curvature may well be real; however, a variation of curvature between satellites or as function of wavelength is not statistically significant. Therefore, data points are fitted by least-square curves with a constant spectral curvature as displayed in Fig. 2. The standard deviation between all data points for the major satellites and their fitted curves at the same wavelength is 2%. Since 11 parameters were estimated from these 25 data points, the value of 2% multiplied by Ï25/14 yields an estimate of the precision, which is 3%. Since the independent calibration uncertainty was also estimated at 3%, the accuracy is Ï32 1 32 p 4%. Error bars of 4% are listed in Table II and plotted in Fig. 2. Color

FIG. 2. All albedo measurements of this work as a function of wavelength (open and filled symbols). Fitted spectra are also shown. Error bars apply for all wavelengths. The bars at the bottom indicate the widths of the filters. For comparison, published observations at 18 phase angle are plotted as capital letters (see text).

yielded albedos for the two filters not listed by Veverka et al. (1987). They are marked ‘‘B’’ in Fig. 2. Nelson et al. (1987) give Voyager photopolarimeter (PPS) data, marked ‘‘N.’’ Compared with the data of this work, the IIS data points are 6–8% too high, while the PPS point is 7% too low. Buratti et al. (1990) saw a similar discrepancy between both data sets for all major satellites and concluded that there is an offset between the IIS and PPS calibration. This offset is consistent with given error bars of 7–10% for data of both instruments. If the albedo by Nelson (1987) was also calculated with a size 2% too large, their data come in better agreement with the data presented here. They do not say which size they used. Figure 2 displays ground-based measurements of Titania and Oberon at 18 phase angle by Goguen et al. (1989), marked ‘‘G.’’ There is agreement (to 4%) with those data. Albedos calculated from V(1,0) data by Brown (1982) also agree with albedos of this work within his error bars of 20%. The precision of the data presented here can be estimated by statistical means. Statistical tests based on the 25 data points of the major satellites show that the albedo spectra are not constant with a high level of confidence. There are significant spectral slopes. This may be evident by looking at the data points of Fig. 2 without the need of statistical calculation. The four major satellites with more than two data points all indicate a small positive

The major uranian satellites display simple spectral shapes in the considered wavelength region, which can be described by only two parameters, slope and curvature. A normalized slope parameter is the spectrophotometric gradient, which is proportional to the spectral slope. It is defined by the logarithmic derivative d ln p(l)/d ln l ( p 5 albedo, l 5 wavelength). A spectrophotometric gradient of zero corresponds to constant albedo and thus a solar color index B 2 V 5 0.66. A spectrophotometric gradient of unity corresponds to albedos proportional to wavelength and a B 2 V 5 0.90, which is close to the case of the lunar visible spectrum (Lane and Irvine 1973). The spectrophotometric gradient is evaluated in this work at 550-nm wavelength. Spectrophotometric gradients corresponding to the curves of Fig. 2 are shown in Fig. 3 (filled circles). The

FIG. 3. Spectral slopes in the uranian system measured by the spectrophotometric gradient at 550-nm wavelength. Results of this work are compared with four previous investigations, three by Voyager 2 and one by Hubble Space Telescope data. All data are consistent with each other. This work has the smallest error bars.

URANIAN RING AND SATELLITE PHOTOMETRY

error bars are based on error bars listed in Table II and assume independent statistics. The same method was applied to Voyager-based geometric albedos by Nelson et al. (1987) and Buratti et al. (1990), shown as triangles and open circles in Fig. 3. Since Voyager-based data do not indicate a curvature, their spectrophotometric gradients correspond to least-squares linear fits. Both investigations concluded that all major satellites are gray with a possible exception for Titania. The wide spectral range of this work allows more accurate measurements of spectral slopes of the satellites than previous investigations. Pascu et al. (1995) gave B 2 V color indices for Miranda and Ariel, using the Hubble Space Telescope, corresponding to spectrophotometric gradients of 20.4 (Miranda) and 20.1 (Ariel). While there is agreement in the relative values between both satellites, there seems to be a calibration offset between Pascu et al. (1995) and this work. They calibrated their data with Titania’s color index by Anderson (1974) and used their relative, ground-based observation between Titania and Ariel (private communication). The given error bar for the color index of Anderson (1974) corresponds to an uncertainty of 0.5 in the spectrophotometric gradient. Thus, the observed difference of 0.2–0.3 in the calibration between Pascu et al. (1995) and this work is completely consistent with expected uncertainties in their calibration. The spectral slope of the outermost satellite, Oberon, was established to comparable accuracy 22 years ago. Anderson (1974) gives B-V and U-B color indices which correspond to a spectrophotometric gradient of 0.1 6 0.2, consistent with newer data shown in Fig. 3. A comparison with spectra of other Solar System objects needs to include the spectral curvature. A normalized spectral curvature is the spectrophotometric curvature, the derivative of the spectrophotometric gradient, d 2ln p(l)/(d ln l)2. The spectrophotometric curvature is evaluated in this work at 550-nm wavelength by the fitted curves shown in Fig. 2. For example, a spectrophotometric curvature of unity indicates that the spectrophotometric gradient increases by 0.1 for each 10% increase in wavelength. The locations of the major uranian satellites in the twoparameter space of the spectrophotometric gradient and curvature are shown in Fig. 4. Numbers for the satellites are listed at the bottom left. The size of the open circles displays the geometric albedo at 550-nm wavelength according to the scale shown at the top right. The spectral shapes of the major uranian satellites follow a regular trend. Miranda, the smallest and innermost of the group, has a negative slope of the albedo spectrum (far left in Fig. 4). Titania and Oberon, the two largest and outermost of the group, have a positive slope (to the right of the origin in Fig. 4). The two satellites inbetween, Ariel and Umbriel, are in size about halfway from Miranda to Titania, and they also plot about halfway between Miranda

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FIG. 4. Comparison of spectral shapes and, thus, colors of a variety of Solar System objects. Sizes of the circles correspond to geometric albedos according to the circles shown at the upper right. Albedo, gradient, and curvature are evaluated at 550-nm wavelength. Numbers for the uranian satellites are listed at bottom left. Large satellites of Jupiter, Saturn, and Neptune are labeled similarly. ‘‘«’’ is the « ring. Single letters correspond to mean location of asteroid types. Dashed lines separate primary colors.

and Titania in Fig. 4. The uncertainty for the locations of the major uranian satellites in Fig. 4 is slightly larger than the size of their symbols (circles). One of the most complete investigations of spectral shapes was performed by Tholen (1984). He used eightcolor photometry of some 400 asteroids to classify them into 14 types according to their spectral shapes. He found that almost all information in the spectral shapes is contained in only two parameters if chosen wisely. His first parameter (first principal component) corresponds to almost linear spectra of different slopes. His second parameter corresponds to different spectral curvatures. Thus, his two-parameter plot of asteroid classification has a similar layout as Fig. 4, except that the axes are labeled differently. The mean of each asteroid type is displayed in Fig. 4. The coordinates for plotting were derived by fitting seven-color data of Tholen (1984) to a curve of constant curvature. His eighth color at 1040-nm wavelength was not used to be consistent with the spectral range of this work. Many asteroid spectra do not display a constant spectral curvature. Thus, the derived parameters depend on the spectral range used. They should be considered as average values over the spectral range (340–950 nm) and not as the actual values for a narrow interval around 550-nm wavelength. The major uranian satellites plot in the area of F-type asteroids, but they are much brighter than the brightest Ftype asteroid.

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Planets and major satellites without a significant atmosphere are also plotted in Fig. 4. The parameters were calculated in the same way from published spectra: Vilas (1988) for Mercury, Lane and Irvine (1973) for the Moon, Morrison and Burns (1976) for the Galilean satellites, Cruikshank et al. (1984) for the saturnian satellites, and Grundy (1995) for Triton and Pluto. It is clear that a collection of publications by several different authors does not yield data as consistent as those for the uranian satellites of this work or for asteroids by Tholen (1984). Nevertheless, Fig. 4 gives an idea how the spectral shapes of Solar System objects compare. Mercury and the Moon have an almost constant spectral slope in the wavelength range considered. The Galilean satellites JII–IV plot further down, corresponding to a negative curvature. Their spectra are very steep in the near ultraviolet, but almost flat toward the near infrared. Io would plot well outside the area of Fig. 4, to the lower right. The saturnian satellites Tethys (SIII) and Rhea (SV) are more neutral than the Galilean satellites. The major uranian satellites plot further upper left, still. Triton (NI) and Pluto are closing in on Mercury in spectral shape. Asteroids follow roughly the region of Galilean and saturnian satellites. That reality is a lot more complex than this simple scheme is indicated by the spectral shape of the dark side of Iapetus (SVIII). The three parameters of albedo, spectral gradient, and curvature displayed in Fig. 4 correspond uniquely to the three-parameter color vision of the human eye. Approximate limits between different primary colors are indicated by the dashed lines. Note that yellow and brown are not distinguished by the spectral shape, but only by albedo. The vast majority of Solar System objects are yellow/ brown. The yellow-orange color of Ariel, the red color of Umbriel, and the blue color of Miranda are almost unique. These are very subtle colors, just barely distinguishable from gray for the human eye. Phase Functions Voyager 2 observed Titania at phase angles down to 0.88, whereas the other satellites were only observed at phase angles of about 158 and larger. The data points at 18 phase angle of this work allow an improved evaluation of phase curves for satellites other than Titania. Since Voyager’s clear-filter data are by far the most complete, the comparison was performed at that wavelength (480 nm) with data listed by Veverka et al. (1987). The curves of Fig. 2 were evaluated at the same wavelength. Taking the data points at 470 nm instead would have yielded almost the same results. Figure 5 shows the phase curves of the major satellites. Data are corrected for different assumed radii and for a 6% calibration offset between Voyager’s and this work’s data estimated from Fig. 2. Multiple data at the same or

FIG. 5. Phase dependence of the seven largest satellites and particles of the « ring fitted to phase functions of the IAU system. Phase integrals of best fits are indicated. Arrowed data are from this work; all other data are from Voyager 2 (see text). Note that for most objects, geometric albedos necessary to plot normalized phase function data have not been well established before this work. The new data points allow correct scaling of Voyager data and, thus, calculation of phase integrals.

similar phase angle have been averaged and are shown as one data point only. The horizontal scale is linear in the square root of phase angle to avoid cluttering of data near 08. This transforms the strongly curved phase functions into almost straight lines. All data points are fitted to normalized phase functions of the IAU magnitude system for asteroids (Bowell et al. 1989). This is a simple set of phase functions. It is based on two standard phase functions: one strongly back-scattering phase function (phase integral q 5 0.29) typical for dark surfaces, and one weakly back-scattering phase function (q 5 0.94) typical for bright surfaces. The IAU system assumes that phase curves are a linear combination of both standard phase curves. Thus, there is one normalized phase curve for each value of q. At each phase angle, the value of the phase function is linear in q. All data shown in Fig. 5 can be fitted to phase curves of the IAU system to p2% which is remarkably well. Umbriel, the darkest major satellite, has the steepest phase curve as expected. Phase curves of the other major satellites are very similar to each other over the observed range of phase angles. Ariel is 70% brighter than Oberon. Thus, one may have expected it to have a shallower phase curve though this is not the case. Phase integrals listed in Fig. 5 are consistent with values derived by Helfenstein et al. (1988). A constant phase integral for all satellites was also well within their error bars, which can be excluded now based on the new data. This

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new information allows a more accurate evaluation of surface properties which is beyond the scope of this work. Ground-based data by Goguen et al. (1989) of Titania and Oberon agree within a few percent with the curve shown in Fig. 5 in the range of phase angles 0.5–38; however, their data point at 0.068 phase angle is about 30% above the curve, for both Titania and Oberon. Both data points were taken under bad atmospheric conditions. Nevertheless, Brown and Cruikshank (1983) saw a similar behavior in the infrared for Ariel, Titania, and Oberon. Thus, below 0.58 phase angle, real phase curves may be quite different from the phase functions of the IAU system shown in Fig. 5. This opposition spike (if real) is not to be confused with the normal, and much wider, opposition surge in the range of phase angles 0–108. The IAU phase curves account for the normal opposition surge, but not for an usual opposition spike. Such an opposition spike would change the phase integral completely due to the necessary renormalization, although albedos in the range 0.5–1808 are unchanged. Albedos extrapolated to 08 based on data in the range 0.5–908 are called pseudo geometric albedos to distinguish them from real albedos at 08 phase angle. Pseudo-geometric albedos of the major satellites from six investigations are listed in Table III. The wavelength for the data is 550 nm whenever data were listed for that wavelength. For the investigation by Nelson et al. (1987), data were linearly interpolated to 550 nm. Veverka et al. (1991) noted large discrepancies between geometric albedos of different investigations. This is evident in Table III. Disagreement is not just due to different absolute calibration; ratios between satellites are not consistent either. The three investigations based on the same IIS Voyager data set also disagree with each other. For example, for the green filter, Veverka et al. (1987) found a geometric albedo for Ariel 35% larger than that found by Buratti et al. (1990), while they agree on Umbriel’s geometric albedo. These discrepancies are not anywhere close to the accuracy of relative geometric albedos of p3% claimed by Buratti et al. (1990).

Ground-based photometry, summarized by Veverka et al. (1991), is uncertain since observations of different investigations do not agree with each other. Ground-based photometry of Ariel and Umbriel is clearly difficult, and Miranda, very close to Uranus, is 15,000 times fainter than Uranus in the visible. Among the five listed investigations previous to this work, there is not a single pair of investigations where all albedo ratios between satellites agree to 20%; however, there is good agreement between this work and Helfenstein et al. (1988). If the 6% calibration offset between both data sets is considered, then there is a 3% standard deviation between both data sets, almost perfect agreement. Helfenstein et al. (1988) modeled observed phase curves by Hapke’s theory to derive geometric albedos. On the other hand, Nelson et al. (1987) and Buratti et al. (1990) simply extrapolated phase curves on the basis of Titania’s phase curve from 208 phase angle or 10–148 phase angle, respectively. Veverka et al. (1987) also included a correction factor due to different phase coefficients. Now there is at least one pair of investigations agreeing on pseudo-geometric albedos. Extrapolation to lower phase angles by other investigations may have been too simple. Note that the discrepancies apply only for groundbased data of satellites inside of Titania’s orbit and for Voyager’s data extrapolated over a large range of phase angles. As noted above and shown in Fig. 2, there is acceptable agreement for albedos of observations taken at 18 phase angle from ground-based, Voyager, and Hubble Space Telescope observations. IV. « RING

Longitudinal Variation Figure 1 displays the « ring. Its obvious variation of brightness with longitude is due to its variation in width. Its faintest section was measured at the center of the upper right quadrant, 135 6 68 past superior conjunction (counterclockwise from bottom). The ring is eccentric with respect to Uranus with its periapse at 142 6 68 past superior conjunction. Both numbers agree with the accurately

TABLE III Pseudo-Geometric Albedos of Major Satellites

Satellite

Nelson et al., 1987 (PPS)

Veverka et al., 1987 (IIS)

Helfenstein et al., 1988 (IIS)

Buratti et al., 1990 (IIS)

Veverka et al., 1991 (ground)

This work (HST)

Miranda Ariel Umbriel Titania Oberon

0.32 0.31 0.18 0.23 0.18

0.43 0.42 0.21 0.32 0.28

0.35 0.39 0.22 0.28 0.24

0.34 0.31 0.21 0.29 0.24

0.32 0.40 0.17 0.28 0.24

0.33 0.38 0.21 0.25 0.22

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known value of 1388, calculated from data by French et al. (1988). This location was adopted as the zero point for measuring true anomaly. The offset between the centers of the « ring and Uranus (0.024 6 0.0040) is also consistent with the calculated value (0.0260). The amplitude of the brightness variation with longitude provides valuable constraints on ring properties. Figure 6 displays data numbers summed radially across the ring and longitudinally over each 108-long section. Data are normalized to unity at periapse. All images display a similar variation, and the data points shown are derived from a weighted average of all images. Errors are estimated at 3% near the ansae (filled circles) and at 5% near Uranus (open circles). The observed variation by a factor of 2.5 between apoapse and periapse is compared with the following model. The width of the « ring (20–96 km) and its equivalent depth (radially integrated optical depth, 42 km) have been well constrained by observations of stellar occultations (French et al. 1986). Optical depths quoted here correspond to the geometric particle cross section without diffraction (cf. Cuzzi 1985). The optical depth was assumed to be twice as large across one-third of the ring width compared with the other two-thirds of the width. This profile is closer to observed profiles (Holberg et al. 1987) than a constant profile. Both approaches give results differing by somewhat less than observational errors. To keep the model simple, it was assumed that all ring particles are spheres of equal size and that the filling factor is radially and vertically constant across the width and thickness of the ring. The filling factor is the fractional volume taken by ring particles. The thickness of the ring was assumed constant with longitude, which makes the product of ring width and filling factor constant along the ring. The calculation of the fractional illuminated area was

FIG. 6. Longitudinal variation of the brightness of the « ring compared with three models. A filling factor D 5 0.008 gives the best fit. Error bars are smaller near the ansae (filled circles) than near Uranus (open circles).

presented by Irvine (1966). The filling factor is the only free parameter in this model. This calculation is equivalent to a radiative transfer calculation neglecting multiple scattered light. At small phase angles, this is a very good approximation because the rings are dark and backscattering. Ockert et al. (1987) found that this approximation still holds at much larger phase angles. There are two extreme cases where the normally required numerical integration can be solved analytically, leading to a simple function. The first case is for a phase angle of zero where all shadows are hidden. The illuminated area is the same as the particle area, and the method used for occultation data applies (cf. French et al. 1991). This case is shown in Fig. 6, bottom curve. The other extreme is the case of both phase angle and separation of ring particles large enough so that ring particles do not hide their own shadows. This case is described by Hapke (1981). It has been used in many investigations of rings and surfaces. At apoapse, the « ring is optically thin, so that shadowing is a minor effect. At periapse, the ring is optically thick, so that shadows significantly reduce the illuminated area. Thus, shadowing increases the amplitude of ring brightness as shown in Fig. 6, top curve. The observed brightness variation at a phase angle of 18 follows neither extreme but lies inbetween. This fact can be used to determine the filling factor. The best fit to the observations occurs for a filling factor of 0.008 at quadrature (908 from periapse), also shown in Fig. 6, central curve. Filling factors between 0.005 and 0.015 are consistent with the observations, corresponding to a mean ring thickness of 60 6 30 times the particle diameter. The mean separation of ring particles is 4.5 6 0.8 times the particle diameter. French et al. (1991) gave several arguments that the filling factor of the uranian rings is quite low. One of the best constraints comes from the Voyager radio occultations requiring the filling factor to be no greater than 0.01 (Tyler et al. 1986, Gresh et al. 1988), consistent with the presented result. On the other hand, Herbst et al. (1987) give a lower bound of p0.0005 for the filling factor, 10 times lower than the new lower limit. The azimuthal brightness variation of the « ring was measured in Voyager images by Svitek and Danielson (1987). They assumed the limiting case of the filling factor approaching zero, but adjusted the equivalent depth to fit their observations. They found an equivalent depth of 38 6 5 km, somewhat smaller than the occultation-derived value of 42 6 1 km. They suggested that this difference could be due to an unresolved ‘‘zebra’’ pattern of lower and higher optical depths; however, at the phase angles of their images (16–228), the negligence of a finite filling factor of 0.008 results in an underestimation of the equivalent depth by 3 km. With this adjustment, optical depths agree very well without a ‘‘zebra’’ pattern.

URANIAN RING AND SATELLITE PHOTOMETRY

Photometry The described model provides not only the relative longitudinal variation of illuminated area, but also the total illuminated area. For the geometry in 1995, the fractional illuminated area is 56% at 08 phase angle and 47% at 18 phase angle. The rest of the area is filled by holes in the ring or by shadows cast from ring particles near the front of the ring. Thus, the 58-km-wide « ring was only as bright as a ring of 0.47 3 58 5 27 km width which does not have holes or shadows. This number is listed as equivalent width in Table II. It provides the conversion from observed flux into a full-disk particle albedo at 18 phase angle. The derived albedos for particles of the « ring are listed in Table II and displayed in Fig. 2. The albedo in the visible is 0.053. Note that ring albedos listed in some publications (in contrast to ring particle albedos) are accordingly lower since they are calculated with the full ring width. Color Porco et al. (1987) determined the spectral slope of the « ring by ratioing albedos between 410- and 550-nm wavelengths. Their data point and error bar is shown in Fig. 3. They noted that their data likely need a calibration offset, indicated by the arrow pointing down. They concluded that the « ring is gray. The Voyager-derived spectrophotometric gradient of about 0–1 is consistent with the gradient of most Solar System objects (cf. Fig. 4). Porco et al. (1987) also noted that their ring albedos for the clear filter (480 nm) would indicate a strong spectral curvature of the ring spectrum. They did not consider this to be real, but attributed it to a nonlinearity problem of the camera at low data numbers. The much wider spectral range of this work allows a five times more accurate determination of the spectral slope of the « ring, shown in Fig. 3. The « ring has a significant positive spectral slope, larger than that of all major uranian satellites. The ring spectrum is close to linear over the whole observed wavelength range. A slight negative spectral curvature is hardly significant. The « ring is not gray, but brown. The « ring, marked ‘‘«’’ in Fig. 4, is within the region of EMP-type asteroids of Tholen’s asteroid taxonomy (1984). These three types are distinguished only by albedo, not by spectral shape. The albedo of the ring particles locates them between the M and P types. Phase Function Voyager data shown by Ockert et al. (1987) at phase angles 158, 218, and 888 were converted here to particle albedos by the same ring model as described above. These three Voyager data points fit perfectly to a phase function of the IAU system described in Section III. The fit is still very good if the data point of this work is included (Fig.

357

5). The phase function of ring particles is much steeper than that of the major satellites, consistent with the expected variation for a darker surface. Ring particles have a steeper phase function (phase integral 0.30) than the majority of asteroids, but not the steepest one. Data listed by Tedesco (1989) indicate that some asteroids have phase integrals as low as about 0.25. The phase integral of ring particles was not known so far. Voyager data analysis did not provide a reliable result. Ockert et al. (1987) give a phase function with a phase integral of 0.28, but their Bond albedo and normal reflectance yield a phase integral of 0.47. Ockert et al. (1987) found an enhanced phase dependence between 158 and 218 compared with that between 218 and 888 phase angle. Their comparison was based on phase functions of the Moon and Callisto which are not similar to the ring’s phase function but closer to Titania’s phase function. If the comparison is made with phase functions as steep as the ring’s phase function, the peculiarity disappears. Note that the phase function displayed in Fig. 5 applies for the phase function of ring particles. It is not the phase function of the « ring, which is steeper due to shadowing between ring particles. Because the shadowing is dependent on the angle between the ring plane and the line of sight, and dependent on the true anomaly, there is no such thing as ‘‘the’’ phase function of the « ring. Plots of phase functions where different data points correspond to different geometries and different true anomalies, such as Fig. 6 by Ockert et al. (1987), give a distorted view, since albedos vary with geometry and true anomaly. The phase function of ring particles shown in Fig. 5 is independent of geometry and true anomaly, as long as the model accounted for the correct fractional illuminated area. Herbst et al. (1987) measured the infrared opposition surge of the rings at 0–2.58 phase angle. If a filling factor of 0.008 is applied to their observing geometry, interparticle shadowing can almost completely explain their observations at 1–38 phase angle, but only about half of the observed surge at 0–18. This is consistent with their interpretation that the phase angle dependence cannot be exclusively due to interparticle shadowing. The extra 10– 15% of variation between 08 and 18 must be provided by the phase dependence of ring particles. Such a variation is normal for dark surfaces. If this variation is similar at visible wavelengths, then the geometric albedo of ring particles in the visible is 10–15% larger than the observed value at 18 (0.053) and thus 0.060. The phase function of the IAU system fitted to the three Voyager data points and the data point of this work shown in Fig. 5 has a geometric albedo of 0.062. This number corresponds to the visible (550 nm) and contains a small correction (4%) from the data at 480-nm wavelength according to the measured spectral slope. Considering the

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ERICH KARKOSCHKA

value of 0.060 above, the geometric albedo of ring particles in the visible is estimated here at 0.061 6 0.006. This estimate is in serious disagreement with the normal reflectance derived by Ockert et al. (1987) of 0.032 6 0.003, corresponding to a geometric albedo of 0.032 with their assumed Lommel–Seeliger scattering law. Any (unlikely) limb darkening would make the geometric albedo lower still. While their ring model is slightly different from that adopted here, some differences cause a small increase, some a small decrease in derived albedos. Thus, their geometric albedo should have been very similar to that derived here. The discrepancy is 10 times their error bar, a 10s event, which has a probability of occurring once every 1023 events. There seems to be an error in their calculation. They give a phase function for the « ring, their Eq. (6) with n 5 6.5, which has a phase integral of 0.281. They list its single scattering albedo as 0.0179. Both numbers yield a geometric albedo of 0.0179/0.281 5 0.064. This is close to the value derived here, but twice as much as their value of 0.032. Since the rings have not been observed at visible wavelengths from ground-based observatories, the Voyagerderived geometric albedo played an important role in our understanding of the rings. A factor of 2 in geometric albedo makes a difference in our view of the ring among known geometric albedos of Solar System objects, mainly of more than 1000 asteroids (Tedesco 1989) and some 50 satellites listed in The Astronomical Almanac 1996. Our view so far was that the uranian rings are about as dark as the darkest objects in the Solar System, darker than at least 96% of the satellites, and darker than about 90% of the asteroids. With the new value of 0.061, the ring particles are not especially dark. They are brighter than several satellites and brighter than more than half of the asteroids! V. MINOR SATELLITES

Photometry Figure 1 displays the 4 brightest of the 10 known minor satellites discovered by Voyager 2. Their albedo measurements are presented in Table II and Fig. 2. In the 340- and 470-nm filters, fewer than 200 photons were detected, not enough for a useful measurement. Juliet and Belinda were well exposed only in the 910-nm filter. Pascu et al. (1995) give V(1,0) magnitudes for Juliet, Portia, and Puck, listed in Table IV. Corresponding albedos are also listed. Because of their considerable calibration uncertainty, their data have been re-calibrated here by albedos of Miranda and Ariel of this work. Recalibrated albedos are listed in the last column of Table IV and plotted in Fig. 2, marked ‘‘P.’’ These data are consistent with linear fits shown in Fig. 2. Linear fits are derived from data of this work alone. Thus, there is no indication that Puck’s and Portia’s spectra are curved.

Color Voyager 2 could not provide any colors for the minor satellites (Thomas et al. 1989). Pascu et al. (1995) found Puck and Portia to be gray. Their color measurements are displayed in Fig. 3. Error bars are based on their uncertainty of 0.1 in B 2 V. Arrows on top of their error bars indicate the shift of their data due to the recalibration described above. The wider spectral range of this work establishes that Puck and Portia are not gray, but brown. Note that error bars allow a constant color throughout the inner uranian system. The average spectrophotometric gradient of wellstudied asteroids is 0.3–0.4 according to color indices given by Tholen (1984). In this sense, Puck and Portia have average colors. Puck’s location in spectral shape lies close to the mean location of M-type asteroids, marked ‘‘UXV’’ and ‘‘M’’ in Fig. 4. The curvature of Puck’s spectrum is not well constrained due to the reduced wavelength range. Thus, its location in Fig. 4 would be also consistent with that of C-type asteroids; however, Puck’s surface is not similar to that of C-type asteroids, since Puck is much brighter than the brightest C-type asteroid. The spectral range can be enhanced by combining both data sets from the Hubble Space Telescope. One can conclude that Juliet has about the same color as Portia. The error bars on Puck’s and Portia’s spectrophotometric gradient become slightly less than with the data of this work alone. They still overlap considerably. Portia may be of the same color as Puck. Phase Function Figure 5 displays the phase function of Puck and Portia derived from the albedo at 18 phase angle from this work and from data at 15–338 phase angle by Thomas et al. (1989). Data points fit well to a phase function of the IAU system. Puck’s and Portia’s albedo and phase function lie between those of Umbriel and the « ring, following the regular trend in the uranian system. A phase integral near 0.35 is quite typical for surfaces about as bright as Puck and Portia. The average phase integral for M-type asteroids is about 0.4. These numbers assume that the phase curves follow those of the IAU system at higher phase angles which is not known and will not be known for many years. The IAU phase function corresponding to Puck’s data has a Bond albedo of 0.04 and a geometric albedo of 0.107 at 550-nm wavelength. Puck’s geometric albedo, possibly larger than this extrapolation due to an additional opposition surge, is estimated here at 0.11 6 0.01 based on a radius of 77 km. Considering the uncertainty in its radius, one has to increase the error bar to 0.015. A geometric albedo of 0.11 is far outside the range of 0.074 6 0.008 by Thomas et al. (1989). A similar discrepancy was found

359

URANIAN RING AND SATELLITE PHOTOMETRY

TABLE IV Albedos from Pascu et al. (1995) Original data

Corresponding albedo

Recalibrated albedo

Satellite

V(1, 0)

B2V

440 nm

550 nm

440 nm

550 nm

Juliet Portia Puck Miranda Ariel

21.2 20.68 19.95 16.21 14.06

— 0.63 0.69 0.56 0.63

— 0.103 0.094 0.353 0.400

0.10 0.100 0.097 0.322 0.389

— 0.090 0.082 0.308 0.349

0.09 0.092 0.089 0.296 0.357

Note. Original data were calibrated by a ground-based V(1, 0) and B 2 V for Ariel. Corresponding albedos are calculated with a solar V 5 226.74 and B 2 V 5 0.66. Recalibrated albedos use albedos of Miranda and Ariel of this work.

by Pascu et al. (1995). Thomas et al. (1989) extrapolated Voyager data by assuming a constant phase coefficient, very different from phase curves of the IAU system. This caused a large underestimation of its geometric albedo. This is another case where extrapolation of Voyager data to 08 phase angle was inaccurate. Voyager data were not sufficient to constrain Puck’s geometric albedo to 10% accuracy as claimed by Thomas et al. (1989). Flux Ratios Thomas et al. (1989) noticed that images with low data numbers seemed to give too low intensities by some 10– 30%. They could not correct for this problem because the camera was not calibrated well at low data numbers. Such a linearity failure produces too low disk-integrated fluxes for small satellites. One can derive fluxes from Voyager data that are less affected by linearity failure by ignoring images with the worst image scale (p160 km/pixel). This works for all minor satellites except for Belinda which does not have a closeup image. These data were processed in the same way as by Thomas et al. (1989). The resulting eight ratios of fluxes relative to Puck’s flux are all larger than flux ratios by Thomas et al. (1989). This strongly indicates the presence of a systematic error. Flux ratios derived from selected (better) images are inconsistent with flux ratios based on the whole image set (cf. Table V). Note that statistical error

bars for the selected images come out larger because of the smaller number of images. Nevertheless, fluxes based on selected images are probably more accurate since they are less affected by the systematic nonlinearity. Flux ratios based on selected images are in general agreement with flux ratios from this work (third column of Table V) at longer wavelengths and smaller phase angle (18 versus about 208 for Voyager data). There is no significant indication of differences in phase dependence or color among the observed minor satellites. Sizes This result may suggest that the surfaces of the minor satellites are similar, and thus their albedos are similar too. This supports the method of Thomas et al. (1989), who calculated sizes of minor satellites other than Puck by assuming that all minor satellites share the same albedo. Voyager 2 only provided an accurate size of Puck and a rough size of Cordelia by resolved imaging. With the assumption of constant albedo, averaged flux ratios of Voyager (selected images) and this work yield radii listed in the last column of Table V, based on Puck’s radius of 77 6 5 km by Davies et al. (1992). These radii are some 10% larger than current values (cf. Table II). One should increase the error bars on sizes in Table V according to a possible variation of albedos among the

TABLE V Minor-Satellite Flux Relative to Puck Satellite

Thomas et al. (1989)

Voyager 2, selected data

Hubble Space Telescope, this work

Guessed radius (km)

Juliet Portia Belinda

0.298 6 0.016 0.503 6 0.012 0.200 6 0.019

0.345 6 0.028 0.556 6 0.037 —

0.383 6 0.047 0.561 6 0.032 0.240 6 0.032

48 6 4 58 6 4 38 6 4

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minor satellites. Thomas et al. (1989) considered 25% a reasonable guess, corresponding to 12% in radius. There is a consistent brightening trend from the ring system via Puck, and Miranda to Ariel. Since Puck is the outermost minor satellite, one may guess that albedos of the other minor satellites lie between those of Puck and the rings. This assumption would change the radii of Table V to lower limits, and upper limits would be 40% larger. This interpretation is supported by Cordelia’s data. Its current radius of 13 km, based on the indirect guess of constant albedos, is close to the lower limit of its real measurement of 15.5 6 3.1 km. A 40% larger value is close to the measured upper limit. There is indirect evidence that current estimates of the sizes of minor satellites other than Puck are too small by some 10%, possibly more. A 10% increase in size would decrease the albedos for Juliet, Portia, and Belinda of this work to those of Puck, with deviations well below given error bars at all wavelengths. Note that error bars in Table II and Fig. 2 correspond to the measured fluxes only. They do not include uncertainties of sizes. Uncertain sizes introduce uncertainties in calculated albedos, but the comparison between data points at different wavelengths or different phase angles is not influenced by an uncertain size. VI. INNER RINGS

The « ring, the outermost ring, emits about 70% of the light coming from the ring system. The other nine rings share the rest of the light. The only photometric data on these rings so far came from Voyager 2 with exposure levels below one data number. Figure 7 displays radial ring profiles at 910-nm wave-

FIG. 7. Radial intensity profiles for two opposite sections of the ring system. The given angles refer to the mean anomaly of the « ring. The circles mark measurements at 910-nm wavelength. Vertical bars indicate calculated ring positions. The curves are synthetic profiles based on an albedo of 0.058 for all ring particles. The scale for the upper curve is on the right-hand side. One data number corresponds to 14 electrons/pixel, or 1000 electrons total along the 458-long averaged arcs.

TABLE VI Relative Ring-Particle Albedos (« Ring 5 100%) Ring

Ockert et al. (1987)

This work

6, 5, 4 a, b h, c, d

67, 53, 74 (mean: 65) 89, 79 (mean: 84) 89, 73, 98 (mean: 87)

92 6 22 99 6 10 112 6 10

length. The open and filled circles correspond to opposite ring sections, near periapse and near apoapse of the « ring. The Hubble Space Telescope resolves the rings inside the « ring into three groups, from inside to outside: rings 6, 5, 4; rings a, b; and rings h, c, d. The tenth ring, the l ring, does not make a significant contribution (Esposito et al. 1991). The locations of theoretical radii of all rings are indicated by the vertical bars in Fig. 7. Photometry The observed fluxes were converted into particle albedos by a model similar to the model for the « ring described above. Widths and optical depths for the inner rings were taken from French et al. (1986) for the narrow rings and from Gresh et al. (1989) for the extended parts of the d and h rings (average of ingress and egress data). Calculation of the equivalent widths followed the same method as for the « ring. A determination of filling factor for the inner rings was not feasible. Thus, it was assumed that these rings have the same filling factor as the « ring. A factor of 2 in the filling factor changes the equivalent widths by 2–4%. Results and derived particle albedos are listed in Table II and shown in Fig. 2. Only the one or two filters with the highest exposure levels allowed a sensible measurement. Particle albedos for the inner rings relative to that of the « ring are listed in Table VI. The Voyager-based data refer to single-scattering albedos given by Ockert et al. (1987), whereas data of this work refer to albedos at 18 phase angle. The Voyager-based data show much larger albedo variations among the different rings than this work. Nevertheless, Ockert et al. (1987) concluded that all rings share the same albedo. Voyager images of the rings show only ring sections, and Ockert et al. (1987) suspected that azimuthal variations could cause larger variations than seen in their albedo data. This is not a problem for Hubble Space Telescope images which display the whole ring system. In the Voyager data, there is a strong correlation between albedo and equivalent width. The « ring yielded the largest albedo, and the most tenuous rings (6,5,4) yielded the smallest albedos. This is another indication of linearity failure of the Voyager camera since there is no such correlation in the data presented here. If all ring particles share the same albedo of 0.058 at 910-nm wavelength, the calculated equivalent widths can be used to derive a synthetic ring profile by smearing the

URANIAN RING AND SATELLITE PHOTOMETRY

essentially sharp rings with a point-spread function of 0.10 full width half-maximum. The peak of each synthetic profile is indicated by the lengths of vertical bars in Fig. 7 which are proportional to equivalent widths. A ring with an equivalent width of 1 km gives a peak data number slightly less than unity. The superposition of the synthetic profiles of all rings is shown by the solid and dashed curves. The agreement with the measured data points is good. Note that before deconvolution of the image, the sloping background level due to scattered light from Uranus was about 10 data numbers, and the amplitude of features was only about half as large. Equivalent depths of the two innermost ring groups and of the « ring are well known, so that their equivalent widths are better known than measured fluxes. On the other hand, occultation data for the h, c, and d rings show inconsistencies, so that the published error bars for their equivalent depths cause an uncertainty of their total equivalent width of 10%. This uncertainty is not included in the error bar of Table VI (112 6 10%). If the true equivalent depths are close to the published lower limits, this group of rings has lower surface area than assumed, causing their albedos to increase. In this case, these rings have definitely brighter particles than the other rings. If the equivalent depths are somewhat above the nominal values, all rings have particles with the same or similar albedo. This case seems more likely. Color Albedo ratios between Voyager’s violet and green filters have been published by Porco et al. (1987) for five inner rings. To decrease the rather large error bars, these data were averaged here according to the ring groups and converted into spectrophotometric gradients. The data, shown in Fig. 3, are consistent with spectral slopes seen for almost all other Solar System objects. The smaller error bars of this work constrain the type of surface material to some extent. The inner rings may be similar in color to the « ring. Phase Functions Data points for the inner rings would indicate a more backscattering phase function than for the « ring. This is probably not real, but due to the nonlinearity of Voyager data. Ockert et al. (1987) found large variations in the phase dependence among different rings. They did not consider them to be real. Phase functions of inner-ring particles are not well constrained. VII. SUMMARY

There is limited information on photometry of the uranian rings and satellites at phase angles of 0–38, accessible from Earth. Most ground-based observations were restricted to the outermost satellites. Voyager observed only

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Titania at phase angles below 108. This work provides accurate photometric data for nine satellites and four rings at 18 phase angle. There is agreement (p6%) with other measurements at 18 phase angle. Voyager data together with the new data provide phase functions over large ranges of phase angles. Phase functions fit well to those of the IAU system (Bowell et al. 1989) in the range 1–908. Phase functions for darker surfaces are steeper than for those for moderately bright ones. This regular pattern has been previously observed in the asteroid belt (Bowell et al. 1989) and in the jovian satellite system (Morrison and Morrison 1977). This trend does not continue for the four brightest surfaces, which all have similar phase curves (Miranda, Ariel, Titania, and Oberon). There were significant discrepancies in pseudo-geometric albedos of the major satellites between different investigations based on the same Voyager images. Ground-based photometry summarized by Veverka et al. (1991) is not consistent with any Voyager-based investigation. The data presented here agree with one Voyager-based data set, the set by Helfenstein et al. (1988), who modeled phase curves instead of using simple extrapolations from phase angle near 208 to 08. The data presented here indicate that Voyager data of faint rings and satellites were systematically affected by the linearity failure of the camera at low data numbers. This was suspected by Porco et al. (1987) and Thomas et al. (1989). Puck’s geometric albedo is 0.11 6 0.015 in the visible, much larger than the Voyager-based estimate of 0.074 6 0.008 (Thomas et al. 1989). Sizes of minor satellites other than Puck may have been underestimated by some 10%. The uranian rings have an interesting history. Elliot and Nicholson (1984) considered ring particles to be extremely dark, with geometric albedos in the visible of about 0.02. Cuzzi (1985) discovered an error of factor 2 in determined optical depths, which made the ring particles almost twice as bright as considered before. The only accurate data so far came from Voyager, yielding a geometric albedo of 0.032 6 0.003 by Ockert et al. (1987). The current study discovered an error of factor 2 in the Voyager-based determination. This makes the rings twice as bright again. New observations presented in this work give a geometric albedo of 0.061 6 0.006 for the « ring and similar values for other rings. The uranian rings, once considered to be among the very darkest objects in the Solar System, are now brighter than the median geometric albedo in the Solar System, based on all objects with known measured geometric albedos, most of them asteroids. The Uranian rings belong to the brighter half of Solar System objects. The future will tell if the uranian rings can gain more factors of 2. The observed longitudinal variation of the « ring yields a mean separation of ring particles of four to five times

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their diameter. A similar study of Voyager data was interpreted by Svitek and Danielson (1987) with a simpler model, assuming a separation of ring particles toward infinity. The consideration of the finite separation of ring particles determined here yields agreement with occultation-based determinations of the optical depth (French et al. 1986). Ground-based data found Titania and Oberon to be gray (Harris 1961, Anderson 1974). Voyager data of all five major satellites gave global colors consistent with gray with the possible exception of Titania, which hinted a positive spectral slope (Buratti et al. 1990). There were no useful data on the color of the minor satellites (Thomas et al. 1989). The rings were found to be all gray (Porco et al. 1987). Recent Hubble Space Telescope data by Pascu et al. (1995) yielded the two largest minor satellites to be gray also. In contrast, this study shows that the uranian system exhibits a variety of subtle colors. This finding was made possible by the wider wavelength range of this study compared with previous investigations. Rings and minor satellites have a significant spectral slope, close to the average slope among Solar System objects. Spectrally, they belong to M-type asteroids. The major uranian satellites display different spectral slopes which are among the smallest spectral slopes observed in the Solar System. The spectral slopes of these five satellites are correlated with their sizes and, thus, also with distance from Uranus. Jupiter and Saturn are yellow, and their satellite systems and the major rings of Saturn all have a similar color hue. Uranus is blue-green. It is surrounded by brown rings and minor satellites. Further out comes blue Miranda, yelloworange Ariel, red Umbriel, and yellow Titania and Oberon. A dark, gray system has become brighter and colorful! This study was based on six images taken in less than 30 min. Filter selection and exposure times were optimized for Uranus. Only the minor part of the information in these images, the data on rings and satellites, is presented here. Further observations of Uranus with the Hubble Space Telescope look promising. ACKNOWLEDGMENTS I thank Martin Tomasko, principal investigator on the observations, for his support and his suggestions on the manuscript. Dan Pascu provided further improvements. Tony Roman and Keith Noll helped in retrieving calibration data from the Space Telescope Science Institute. Support for this work was provided by NASA through Grant number G0060300194A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA Contract NAS5–26555.

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