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size andge. In thisent methodAlthoughclass, withrequencyd may also

Icarus 176 (2005) 184–191www.elsevier.com/locate/icaru

Diverse albedos of small trans-neptunian objects

W.M. Grundya,∗, K.S. Nollb, D.C. Stephensb,1

a Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff, AZ 86001, USAb Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA

Received 1 July 2004; revised 9 December 2004

Available online 17 March 2005

Abstract

Discovery of trans-neptunian object (TNO) satellites and determination of their orbits has recently enabled estimation of thealbedo of several small TNOs, extending the size range of objects having known size and albedo down into the sub-100 km ranpaper we compute albedo and size estimates or limits for 20 TNOs, using a consistent method for all binary objects and a consistfor all objects having reported thermal fluxes. As is true for larger TNOs, the small objects show a remarkable diversity of albedos.the sample is limited, there do not yet appear to be any trends relating albedo to other observable properties or to dynamicalthe possible exception of inclination. The observed albedo diversity of TNOs has important implications for computing the size-fdistribution, the mass, and other global properties of the Kuiper belt derived from observations of objects’ apparent magnitudes anpoint the way toward an improved compositional taxonomy based on albedo in addition to color. 2005 Elsevier Inc. All rights reserved.

Keywords: Kuiper belt objects; Trans-neptunian objects; Composition; Surfaces

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, buassingcru-ns-rib-uci-tive

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1. Introduction

Considerable progress has been made in understanthe dynamical structure of the trans-neptunian Solar Sysbut the physical characteristics of the small bodies thahabit that region remain poorly determined. Measuremof colors, absolute magnitudes, and lightcurves have amulated for a number of objects, and near infrared sptra have been reported for some of the brightest onesknowledge of fundamental properties such as size, malbedo, and density remain woefully sparse. Determinthese properties for a representative sample of TNOs iscial for estimating the total mass of material in the traneptunian region, for relating magnitude-frequency distutions to size- and mass-frequency distributions, for eldating patterns of compositional taxonomy, for quantita

* Corresponding author. Fax: +1-928-774-6296.E-mail address: w.grundy@lowell.edu(W.M. Grundy).

1 Now at Johns Hopkins University, Baltimore, MD 21218, USA.

0019-1035/$ – see front matter 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2005.01.007

g,

t,

interpretation of infrared spectra, and for constraininginternal compositions of these objects. All of these obtives have important implications for physical and chemconditions in the outer proto-planetary nebula and for thecretion of solid objects in the outer Solar System.

Data constraining TNO sizes, albedos, and colorscompiled in this paper in an effort to search for possible pterns related to TNO origins or subsequent surface procing. We use a consistent set of models to derive sizealbedo constraints from thermal emission observationsfrom binary orbits reported by various authors, therebypanding the range of diameters included in the samplmore than an order of magnitude.

Although they likely do derive from the TNO population, Centaurs (by which we mean non-resonant objwhich cross the orbits of major planets) and comet nuwere excluded from this study because we lack knowleabout what part of the trans-neptunian system they o

nated from. Comet nuclei also have systematically differentcolors from TNOs (e.g.,Jewitt, 2002), inferred to result fromvolatile loss processes which may also affect Centaurs.

TNO

diesys-rtiesthecessvere-nts or

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2. Size and albedo

Size and albedo are fundamental properties of bowhich constrain composition and internal structure. If stematic patterns were found to exist among these propethey could reveal much about the accretion of TNOs inproto-planetary nebula and about the subsequent proing of their surfaces. Different types of TNOs could haformed at different rates or in different source regionssulting in different bulk compositions. Objects in differetypes of orbits could experience different cratering rateradiolytic fluxes (e.g.,Stern, 2002a; Cooper et al., 2003).Smaller objects may see their surfaces eroded by impwhile larger objects retain impact ejecta (e.g.,Stern, 1995;Durda and Stern, 2000). Larger objects could also have thesurface compositions altered by thermal processes sucvolatile transport or differentiation (e.g.,De Sanctis et al.2001). It has been postulated that TNO colors reflect sface age; that their surfaces darken and redden over timradiolysis and photolysis, in contrast with fresher surfawhich feature recently exposed, bright ices, and so apmore gray (e.g.,Luu and Jewitt, 1996; Gil-Hutton, 2002Peixinho et al., 2003; Strazzulla et al., 2003; ThébaultDoressoundiram, 2003; Delsanti et al., 2004). Alternatively,gray surfaces could be so highly radiation damaged andvolatilized that they are extremely dark, with an almost pcarbon composition (e.g.,Johnson et al., 1987; Moroz et a2003). Impacts by micrometeoroids could also play an iportant role in churning up gray or red subsurface mate(Cooper et al., 2003). Comparing albedo with other paramters for a large sample of TNOs could potentially provuseful information for these types of inquiries.

Size and albedo are, unfortunately, extremely difficulmeasure for TNOs. To date, data enabling estimates or lifor 20 TNOs have been obtained from a variety of sourand methods. Despite potential risks in comparing dataing different systematic uncertainties, the growing bodyobjects having constrained size and albedo offers an optunity to look for potential correlations between albedo aorbital parameters, size, or color. In the following substions we describe the sources of size and albedo constrused in this paper along with their characteristic uncertties.

2.1. Thermal observations

Simultaneously observing thermal emission and reflesunlight is a well-established technique which has bwidely used to estimate asteroid size and albedo (Lebofsky and Spencer, 1989). A thermal model (subject tovarious assumptions) can be inverted to solve for a sizean albedo which are consistent with observed emitted

reflected fluxes. Principal sources of uncertainty in TNOradiometric diameters include lack of knowledge of pole ori-entation and thermal inertia.

albedos 185

,

-

s

s

Thermal emission from trans-neptunian objects istremely difficult to detect, owing to their great distancsmall size, and low surface temperatures. Blackbody ration from TNOs typically peaks in the vicinity of 100 µmwavelength where ground-based observations are preclby the opacity of the terrestrial atmosphere. Neverthelthermal flux measurements have now been reported fTNOs, and upper limits have been reported for 9 moThomas et al. (2000)reported a 90 µm thermal measument from the ISO spacecraft for (15789) 1993 SC alwith a tentative detection of (15874) 1996 TL66 which wetake to be an upper limit. Additionally, various grounbased observers have detected the Rayleigh–Jeans tthermal emission from TNOs at sub-mm wavelengths,cluding (20000) Varuna, observed byJewitt et al. (2001)andby Lellouch et al. (2002). Margot et al. (2002)have reported1.2 mm observations of (55565) 2002 AW197. Altenhoff etal. (2004)reported 1.2 mm observations of (47171) 19TC36 and upper limits for (28978) Ixion, (24835) 199SM55, (19308) 1996 TO66, (19521) Chaos, (38628) Huyand (84522) 2002 TC302. Ortiz et al. (2004)have reportedan upper limit for (55636) 2002 TX300. Brown et al. (2004)have reported an upper limit for (90377) Sedna. Manyditional thermal observations of TNOs can be expected othe next few years from the Spitzer Space Telescope (Salthough SST targets tend to be biased towards the largenearer objects which are more readily detected at theinfrared wavelengths. An additional advantage of Spiobservations is its ability to observe more than one thmal wavelength, which can provide the additional constrneeded to overcome many of the uncertainties assocwith thermal properties and pole orientation (e.g.,Lebofskyand Spencer, 1989; Stansberry et al., 2004).

For this paper, we fitted a consistent suite of thermal mels to reported thermal fluxes in conjunction with publishvisual photometry (from sources detailed in Section3). Up-per limits on diameters (and lower limits on albedos) wderived by using an infinite thermal inertia (“fast-rotatomodel without beaming, in equator-on orientation, whileopposite limits were derived from a zero thermal ine(“slow-rotator”) model augmented with a beaming paramter of 0.8. These two cases conservatively encompasgamut of plausible thermal models. The most probable tmal model was taken to be a fast-rotator tilted 30◦ away fromequatorial orientation.

2.2. Direct imaging

The diameter of the large Classical KBO (50000) Quahas been determined via direct observation byBrownand Trujillo (2004), using the Hubble Space TelescopAdvanced Camera for Surveys High Resolution Cam(HST/ACS HRC). An upper limit to the diameter of (9037

Sedna can be set from HRC observations that failed to re-solve that object. At the time of the HST observation, Sednawas at a geocentric distance of 90.375 AU. At this distance,

carus

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teret’s

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186 W.M. Grundy et al. / I

the ACS/HRCy-axis pixel scale of 0.0247 arcsec pixel−1

corresponds to a linear distance of 1620 km. Therespondingx-axis values are 0.02855 arcsec pixel−1 and1870 km. An object of this size or larger would show etension perpendicular to the motion vector (the observatdid not track Sedna). An approximate upper limit todiameter can be set atd < 1800 km from the ACS/HRCdata, similar to the upper limit diameter inferred from treported non-detection by SST(Brown et al., 2004). Theprincipal source of uncertainty in direct imaging diamemeasurements comes from lack of knowledge of a targcenter-to-limb brightness profile.

2.3. Binaries

An exciting new source of TNO sizes and albedos istrometric observations of TNOs with natural satellites (eNoll, 2003). Determining a satellite’s orbital period ansemimajor axis yields the system mass. Total system volcan then be computed for an assumed density. For this pwe used densities of 0.5 and 2 g cm−3 to bracket the plausible range of system densities. We then used relative vphotometry between primary and secondary to computerelative sizes, assuming both have the same albedo, andpublished absolute photometry to constrain that albedo.cause the majority of the surface area in a binary is preseby the primary body, its diameter and albedo are betterstrained than are those of the secondary. For this reasizes and albedos of binary secondaries are not considin this paper.

Binaries are especially valuable in providing data forjects much too small to detect with current thermal infraor direct imaging technologies. The first binary orbit wasported byVeillet et al. (2002)for 1998 WW31. Since then,orbits have been determined for (66652) 1999 RZ253 (Nollet al., 2004a), (58534) 1997 CQ29 (Margot et al., 2004Noll et al., 2004b), (88611) 2001 QT297 (Osip et al., 2003),(26308) 1998 SM165, (47171) 1999 TC36, and 2001 QC298(Margot et al., 2004). Future observations of thermal emsion from binaries, mutual events, or stellar occultatiwould greatly help in constraining TNO densities, by pviding independent determinations of their sizes (e.g.,Noll,2003; Elliot and Kern, 2003).

3. Data processing

By using a consistent set of thermal models to re-compsizes and albedos from reported thermal and visual fluand a consistent set of densities to estimate sizes and albfrom system masses and visual photometry we attemto provide as consistent as possible a basis for comson. We also used photometry from the literature to com

the spectral slope parameters, defined as the percent in-crease in reflectance per 100 nm of wavelength relative tothe V central wavelength 550 nm, for wavelengths ranging

176 (2005) 184–191

r

l

d

,d

s

from V to I (e.g.,Boehnhardt et al., 2001). We computeds from all available photometry in that wavelength rancombined according to reported uncertainties. Valuessfor TNOs range from less than 5 for gray objects to grethan 10 for red objects.Table 1lists dynamical class, spectrslopes, method of constraining size and albedo, diameted ,and R albedo for the 20 TNOs having published sizealbedo constraints, as well as the planet Pluto and its slite Charon. Data sources for specific objects are detaileTable 2and for objects requiring non-standard treatmenthe remainder of this section.

For (15874) 1996 TL66, we took the radiometric flux reported byThomas et al. (2000)to be an upper limit becausnothing was seen at the object’s ephemeris location.

For (20000) Varuna, we used radiometric fluxes frJewitt et al. (2001)andLellouch et al. (2002)separately, andthen took the resulting albedo and diameter limits to encpass the range of possible values.

For the binary (47171) 1999 TC36, we used theMargot etal. (2004)mass and differential photometry. A radiometflux measurement byAltenhoff et al. (2004)offers an in-dependent measure of the projected surface area of (471999 TC36 which can be combined with the system masscompute an apparently absurd density of 0.15+0.17

−0.05 gcm−3

for the primary. However, theAltenhoff et al. (2004)sizehas been called into question byStansberry et al. (2004,who find a size consistent with our size estimates fromsystem mass (Stansberry, personal communication, 200

For (50000) Quaoar, we used the direct imaging diamof Brown and Trujillo (2004).

For (55565) 2002 AW197, Margot et al. (2002)reported aradiometric diameter and R albedo but did not report theserved thermal flux, so we could not apply our standard tmal models to this object, and instead used the albedosize reported by Margot et al. Recent results from SpiSpace Telescope reported byStansberry et al. (2004)sug-gest that this object has a somewhat smaller diameterhigher albedo than found byMargot et al. (2002).

For (84522) 2002 TC302, we were unable to find photometric colors to compute a spectral slope. The only availphotometry for this object was reported in MPECs 20V26 and 2002-X65.

For (90377) Sedna we used theBrown et al. (2004)radio-metric limits and photometry, which are consistent withrect imaging limits based on HST/ACS observations. Broet al. did not report their thermal flux limits, so we were uable to run our own thermal models for this object.

For the binary 2001 QC298, color photometry in the V-Iinterval was unavailable so we had to use V–J photomfrom Stephens et al. (2003)to estimate the spectral slopThe object is likely to be somewhat more red in the V–Iterval than it is over the broader V–J interval.

For Pluto and Charon, we took diameters fromTholen

et al. (1987)andBuie et al. (1992)to bound possible sizes.Albedos were taken fromBuie et al. (1997)andBuie andGrundy (2000). Pluto’s albedo envelope reflects its rotational

Tis

Diverse TNO albedos 187

Table 1TNO size and albedo

Object Dynamical classa Spectral slope Method Diameter (km)b R albedo (%)

(15789) 1993 SC 3:2 35± 9 Thermal (90 µm) 398+108−171 3.5+1.6

−1.3(15874) 1996 TL66 Scattered 0.7± 1.5 Thermal (90 µm) �958 �1.8(19308) 1996 TO66 3:2 1.3± 1.3 Thermal (1.2 mm) �902 �3.3(19521) Chaos Classical 19± 1 Thermal (1.2 mm) �747 �5.8(20000) Varuna Classical 18± 1 Thermal (0.9, 1.2 mm) 936+238

−324 3.7+1.1−1.4

(24835) 1995 SM55 Scattered 2.2± 0.6 Thermal (1.2 mm) �704 �6.7(26308) 1998 SM165 2:1 21± 1 Binary orbit 238± 54 14± 6(28978) Ixion 3:2 17± 1 Thermal (1.2 mm) �822 �14.8(38628) Huya Scattered 16± 6 Thermal (1.2 mm) �548 �8.4(47171) 1999 TC36 3:2 23± 1 Binary orbit 301± 68 22± 10(50000) Quaoar Classical 20± 1 Direct imaging 1260± 190 10± 3(55565) 2002 AW197 Scattered 17± 1 Thermal (1.2 mm) 886+115

−131 10.1+3.8−2.2

(55636) 2002 TX300 Scattered −0.5± 1.4 Thermal (1.2 mm) �709 �19(58534) 1997 CQ29 Classical 18± 3 Binary orbit 77± 18 39± 17(66652) 1999 RZ253 Classical 25± 3 Binary orbit 170± 39 29± 12(84522) 2002 TC302 Scattered – Thermal (1.2 mm) �1211 �5.1(88611) 2001 QT297 Classical 20± 2 Binary orbit 168± 38 10± 4(90377) Sedna Scattered 36± 2 Thermal & imaging �1800 �4.61998 WW31 Classical 0.5± 3.0 Binary orbit 152± 35 6.0± 2.62001 QC298 Scattered 4± 1 Binary orbit 244± 55 2.5± 1.1Pluto 3:2 11± 2 Various 2200± 90 72± 12Charon 3:2 −2± 2 Various 1260± 90 37± 2

a “3:2” and “2:1” indicate objects orbiting in 3:2 and 2:1 mean motion resonances with Neptune. “Classical” indicates non-resonant objects havingserand

parameters with respect to Neptune greater than 3 and mean eccentricities less than 0.2 over 10 Myr orbital integrations (e.g.,Chiang et al., 2003; Elliot et al.,

ssum

a

oes-dokelyllerec-tesare

exuc-ize.

allers to

torger

Os

Myrdy-ula-bitRes-with

icitiesnant

d as

olored

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2005). “Scattered” indicates all other objects.b For binary objects, diameter is for the brighter/larger component, a

lightcurve. Spectral slopess were computed from spectrfrom Fink and DiSanti (1988)andGrundy and Fink (1996).

4. Comparisons

Comparing R-band albedo with sized , spectral slopes,and inclinationi (with respect to the invariable plane), nclear albedo trends are evident with size or with color,pecially if the planet Pluto is excluded (Pluto’s high albebeing attributed to surface–atmosphere interactions unlito affect the smaller TNOs). Higher albedos among smaTNOs and among TNOs having higher inclinations andcentricities could result from higher collisional erosion raon such objects, if more pristine sub-surface materialsbrighter than space-weathered surfaces (e.g.,Stern, 1995;Durda and Stern, 2000; Strazzulla et al., 2003). Below somethreshold diameter, erosion rates could be expected toceed photolytic and radiolytic darkening timescales, proding a characteristic signature in a plot of albedo versus sThe two highest albedos in our sample are for objects smthan 200 km, but there are as yet too few small objectmake a convincing case for what may eventually provebe distinct albedo distributions between smaller and laTNOs.

The existence of distinct dynamical classes of TN

could potentially obscure trends affecting particular sub-populations coming from different source regions or ex-periencing different thermal, collisional, or radiation envi-

ing the two components have equal albedos.

-

ronments. Based on their average behavior during 10orbital integrations, we divided our sample into threenamical classes to help distinguish possible source poptions or environmental influences. Objects found to inhamean motion resonances with Neptune were classed asonant. Non-resonant objects with Tisserand parametersrespect to Neptune greater than three and mean eccentrless than 0.2 were classified as Classical, and non-resoobjects with greater mean eccentricities were classifieScattered (e.g.,Chiang et al., 2003; Elliot et al., 2005). Thesethree classes: Classical, Resonant, and Scattered, are cred, blue, and green, respectively, inFig. 1. All three groupsare seen to have diverse albedos, and we do not see evifor systematic albedo differences between Classical objwith their small inclinations and eccentricities, and Scatteand Resonant objects, which have larger inclinations andcentricities, and thus higher mean collision speeds.

A dark, 4% albedo has historically been assumedTNOs by analogy to comet nuclei (e.g.,Campins and Fernández, 2002). While low albedos do exist among our saple, much higher albedos are also seen, with the mR albedo of our sample being 14%, excluding Pluto aCharon and objects having only lower limits. These higalbedos are consistent with models for impact formationbinary TNOs, which need smaller, brighter objects to pduce enough binaries(Stern, 2002b).

Distinguishing size effects from effects of duplicity, dy-namical class, or other possible influences is a potentiallyserious difficulty. The seven smallest objects in our sam-

try

102

try

3

)

188 W.M. Grundy et al. / Icarus 176 (2005) 184–191

Table 2Data sources

Size and albedo from thermal observations

Object Source of thermal flux Sources of reflected photome

(15789) 1993 SC Th00 LJ96, TR97, Da00, JL01(15874) 1996 TL66 Th00 (upper limit only) Ba99, Da00, Bo01, JL01(19308) 1996 TO66 Al04 (upper limit only) Ba99, Da00, Bo01, GL01, JL0(19521) Chaos Al04 (upper limit only) Ba00, Da00, Bo01, De01, Do(20000) Varuna Je01, Le02 Do02(24835) 1995 SM55 Al04 (upper limit only) Bo01, De01, GL01, Do02(28978) Ixion Al04 (upper limit only) Do02, Bo04(38628) Huya Al04 (upper limit only) Do01, JL01, Bo02(55565) 2002 AW197 Ma02 (see text) Fo04(55636) 2002 TX300 Or04 (upper limit only) Ba00, Bo01, GL01, JL01(84522) 2002 TC302 Al04 (upper limit only) (see text)(90377) Sedna Br04 (see text) Br04 (see text)

Size and albedo from binary orbit

Object Source of binary orbit Sources of reflected photome

(26308) 1998 SM165 Ma04 De01(47171) 1999 TC36 Ma04 Bo01, De01, Do01, Do03, Te0(58534) 1997 CQ29 Ma04, No04b Ba00, Bo01, GL01, JL01(66652) 1999 RZ253 No04a De01, Do01(88611) 2001 QT297 Os03 Os031998 WW31 Ve02 Ve02, St032001 QC298 Ma04 St03 (see text)

References

LJ96 Luu and Jewitt (1996) GL01 Gil-Hutton and Licandro (2001) Al04 Altenhoff et al. (2004)TR97 Tegler and Romanishin (1997) Bo02 Boehnhardt et al. (2002) Bo04 Boehnhardt et al. (2004Ba99 Barucci et al. (1999) Do02 Doressoundiram et al. (2002) Br04 Brown et al. (2004)Ba00 Barucci et al. (2000) Ma02 Margot et al. (2002) Fo04 Fornasier et al. (2004)Da00 Davies et al. (2000) Ve02 Veillet et al. (2002) Ma04 Margot et al. (2004)Bo01 Boehnhardt et al. (2001) Do03 Dotto et al. (2003) No04a Noll et al. (2004a)De01 Delsanti et al. (2001) Os03 Osip et al. (2003) No04b Noll et al. (2004b)

ns etet al.

uldrag-ingwniesin-onforthe

si-edo

tionpat-e totion

2

d

thedur-

nres-

BOs

allsta-utofow-tion,

ntric

Do01 Doressoundiram et al. (2001) St03 StepheJL01 Jewitt and Luu (2001) Te03 Tegler

ple are all primaries of binary systems. Binary objects coconceivably have unusual albedos resulting from the fmentation of larger, differentiated objects in binary-formimpact events or from the re-accretion of the debris throoff during such violent events. A sample of larger binarwould provide a useful experimental control to help distguish size effects from the effects of duplicity, but basedthe limited data in hand, we see no compelling evidencedifferences between the albedos of small binaries andlarger, singular objects probed by thermal observations.

Curiously, the lowest mean inclinations among Clascal KBOs in our sample correspond to the highest albobjects, as seen in red in the bottom panel ofFig. 1, sug-gesting an anti-correlation between albedo and inclinaamong the small, Classical KBO sub-population. Such atern, if confirmed by additional data, could perhaps relatwell-established correlations between color and inclina(or mean impact speed) among these objects (e.g.,Hainautand Delsanti, 2002; Stern, 2002a; Trujillo and Brown, 200).

One might expect the albedos of Resonant TNOs (inblue in Fig. 1) to differ from those of the lower inclina-tion Classical objects, based on the broader range of col-

al. (2003) Or04 Ortiz et al. (2004)(2003)

ors among 3:2 Resonant TNOs (e.g.,Doressoundiram anBoehnhardt, 2003; Fulchignoni and Delsanti, 2003) as wellas the possibility that Resonant objects formed closer tosun and were propelled outward by resonance sweepinging the outward migration of Neptune (e.g.,Malhotra, 1995;Morbidelli and Levison, 2003). The five Resonant TNOs iour sample (four in the 3:2 resonance and one in the 2:1onance) exhibit diverse albedos, just as the Classical Kdo, ranging from very dark (15789, R albedo 3.5± 1.7%) torather bright, with the binary (47171, R albedo 22± 10%)being one of the brighter Resonant TNOs. From this smsample, the range of R albedos of Resonant TNOs ististically indistinguishable from that of Classical KBOs, bif there is any trend with inclination, it is the oppositethat suggested by the data for Classical KBOs, with the lest albedo Resonant TNO also having the lowest inclinaas shown in the bottom panel ofFig. 1. Inclinations of 3:2Resonant TNOs are thought to be related to the heliocedistances at which individual objects formed (e.g.,Gomes,

2000, 2003), but there is little evidence in our data for cor-relation of albedo with inclination among objects inhabitingthis resonance.

Diverse TNO albedos 189

Fig. 1. R albedo is plotted versus estimated diameterd (top left panel), spectral slopes (top right panel), and mean inclinationi over the past 10 Myr (bottom

ciated d fosical

aveor-

. Asul-ongjor-its,her

er-ns.ze,ncyithpu-eab-tionin

thus

esra-.g.,otion,

allg tonot

etersrre-oflassi-graysses

panel) for 20 TNOs plus the planet Pluto and its satellite Charon. Assohaving only limits. Colors indicate orbital characteristics: red for Clasgreen for Scattered objects.

All of the Scattered objects except (90377) Sedna hTisserand parameters below three, indicating that theirbits are unstable with respect to perturbation by Neptunea result, their population could have been drawn from mtiple sources, potentially obscuring trends detectable amthe Classical or Resonant populations. Although the maity of the Scattered objects in our sample only have limthey appear to exhibit albedo diversity similar to that of otdynamical classes.

Determination of TNO albedos is necessary for convsion of magnitude-frequency to size-frequency distributioIf albedo were eventually found to correlate with object siit would imply changes in the shape of the size-frequecurve relative to that of the magnitude-frequency curve, wimplications for the total mass of the trans-neptunian polation (e.g.,Bernstein et al., 2004). The existence of diversalbedos implies that the lower albedo objects in eachsolute magnitude bin represent a disproportionate fracof the mass in that bin, while the higher albedo objectsa given mass bin have lower absolute magnitudes and

higher probabilities of being discovered.

TNO albedos could prove highly revealing of their com-positional taxonomy, potentially breaking ambiguities be-

uncertainties are approximated by boxes and error bars, and are dotter objectsobjects, blue for objects inhabiting mean motion resonances with Neptune, and

tween similarly-colored but compositionally distinct classof objects. Analogies can be drawn to the impact ofdiometric albedos on asteroid taxonomy in the 1980s (eTholen and Barucci, 1989). Albedo determinations are alsneeded to enable quantitative compositional interpretaof infrared spectra of TNOs (e.g.,Grundy and Stansberry2003).

5. Conclusion

Statistical study of TNO albedos is limited by the smnumber of measurements, but useful hints are beginninemerge. Contrary to expectation, convincing evidence isseen for dependence of albedo on object size for diamspanning an order of magnitude. Similarly, no clear colation of color with albedo is observed. A wide rangealbedos is evident among Scattered, Resonant, and Ccal objects, as well as among both small and large, andand red objects. Models of size-dependent surface proce

such as impact erosion and volatile loss being proposed tointerpret TNO colors need to accommodate the existenceof bright and dark objects of diverse sizes, colors, and dy-

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190 W.M. Grundy et al. / I

namical classes. Visible wavelength albedos of most obare higher than the 4% value once assumed, calling forsion of mass and size estimates for TNO populations bon 4% albedos. Based on this sample (excluding PlutoCharon and the objects having only lower limits), a bevalue would be the median R albedo of 10%, or perhapR albedo distribution with a mean of 14% and an averdeviation from the mean of 10%.

Spitzer Space Telescope observations can be expecplay a valuable role in future TNO size and albedo stud(e.g., Stansberry et al., 2004). However, Spitzer’s instruments are not sensitive enough to detect the smallerhigher albedo TNOs that binary studies are beginning toveal, so binaries will continue to offer unique opportunitfor physical studies, especially of smaller TNOs. Resolvpossible ambiguities between effects of duplicity and scalls for more sensitive thermal capabilities and/or mustation stellar occultation observations to provide size emates of small, non-binary TNOs.

Acknowledgments

This work was made possible by NASA/ESA HubbSpace Telescope programs #9386, #9585, and #9991,port for which was provided by NASA through a grant frothe Space Telescope Science Institute, which is operatethe Association of Universities for Research in AstronomInc., under NASA contract NAS5-26555. Two anonymoreferees contributed useful input. We are also gratefuM.W. Buie and E.I. Chiang for help with dynamical clasification, and to the free and open source software comnities for providing essential tools used in this work, notaLinux, the GNU tools, MySQL, OpenOffice.org, Tcl/Tk, anFVWM.

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