Higher albedos and size distribution of large transneptunian objects

ARTICLE IN PRESS

0032-0633/$ - se

doi:10.1016/j.ps

�Correspond

fax: +81 78 803

E-mail addr

Planetary and Space Science 53 (2005) 1319–1330

www.elsevier.com/locate/pss

Higher albedos and size distribution of large transneptunian objects

Patryk Sofia Lykawka�, Tadashi Mukai

Graduate School of Science and Technology, Earth and Planetary System Sciences, Kobe University, 1-1 rokkodai, nada-ku, Kobe 657-8501, Japan

Received 14 October 2004; received in revised form 21 June 2005; accepted 25 June 2005

Available online 26 August 2005

Abstract

Transneptunian objects (TNOs) orbit beyond Neptune and do offer important clues about the formation of our solar system.

Although observations have been increasing the number of discovered TNOs and improving their orbital elements, very little is

known about elementary physical properties such as sizes, albedos and compositions. Due to TNOs large distances (440 AU) and

observational limitations, reliable physical information can be obtained only from brighter objects (supposedly larger bodies).

According to size and albedo measurements available, it is evident the traditionally assumed albedo p ¼ 0:04 cannot hold for all

TNOs, especially those with approximately absolute magnitudes Hp5:5. That is, the largest TNOs possess higher albedos (generally

40.04) that strongly appear to increase as a function of size. Using a compilation of published data, we derived empirical relations

which can provide estimations of diameters and albedos as a function of absolute magnitude. Calculations result in more accurate

size/albedo estimations for TNOs with Hp5:5 than just assuming p ¼ 0:04. Nevertheless, considering low statistics, the value

p ¼ 0:04 sounds still convenient for H45:5 non-binary TNOs as a group. We also discuss about physical processes (e.g., collisions,

intrinsic activity and the presence of tenuous atmospheres) responsible for the increase of albedo among large bodies. Currently, all

big TNOs (4700 km) would be capable to sustain thin atmospheres or icy frosts composed of CH4, CO or N2 even for body bulk

densities as low as 0.5 g cm�3. A size-dependent albedo has important consequences for the TNOs size distribution, cumulative

luminosity function and total mass estimations. According to our analysis, the latter can be reduced up to 50% if higher albedos are

common among large bodies.

Lastly, by analyzing orbital properties of classical TNOs (42 AUoao48 AU), we confirm that cold and hot classical TNOs have

different concentration of large bodies. For both populations, distinct absolute magnitude distributions are maximized for an

inclination threshold equal to 4.51 at 499.63% confidence level. Furthermore, more massive classical bodies are anomalously

present at ao43:5 AU, a result statistically significant and apparently not caused by observational biases. This feature would

provide a new constraint for transneptunian belt formation models.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Solar system; Kuiper belt; Transneptunian belt; Albedos; Size distribution

1. Introduction

For the last 13 years our knowledge about thetransneptunian belt has been increasing dramatically.From the first discovery of a transneptunian object(TNO) in 1992 (Jewitt and Luu, 1992), as of April 2005about 1000 TNOs have already been reported withorbital elements currently available at the Minor Planet

e front matter r 2005 Elsevier Ltd. All rights reserved.

s.2005.06.004

ing author. Tel.: +81 78 803 5740;

6483.

ess: [email protected] (P.S. Lykawka).

Center (MPC, 2005). Far to resemble an accretion diskleftover, the TNOs orbital characteristics point to acomplex structure (Fig. 1). These outer solar systemobjects can be tentatively classified as: (a) classicalTNOs: spread in a narrow region between semimajoraxes 42 AUoao48 AU, and supposed to be thedynamically most primitive objects. On the other hand,some of their features indicate a more evolved popula-tion of dynamically ‘‘cold’’ and ‘‘hot’’ classical TNOs(Morbidelli and Brown, 2005). We set a threshold atinclination i ¼ 4:51 to represent the division of classicalTNOs into the cold (io4:51) and hot populations

www.elsevier.com/locate/pss

ARTICLE IN PRESS

50494847464544434241Semimajor axis (AU)

40393837363534

50494847464544434241Semimajor axis (AU)

40393837363534

0

0.05

0.1

0.15Ecc

entr

icity

0.2

0.25

0.3

0.35

0.4

0.45

q = 35AU

q = 30AU

4:3 3:2 5:3 7:4 2:1

50

45

4035

30

25

20

15

10

50

4:3 3:2 5:3 7:4 2:1

Incl

inat

ion

(°)

(a)

(b)

Fig. 1. Orbital distribution of TNOs as of 11 April of 2005 taken from

the Minor Planet Center (MPC, 2005). Only objects with more than

one opposition observations are shown. Vertical dotted lines indicate

mean motion resonances with Neptune. In the upper panel, perihelion

distances of 30 and 35 AU are also indicated by dashed curves. We set

a threshold at 4.51 to represent the division of classical TNOs into the

cold (io4:51) and hot populations (i44:51) (see text for details). In this

plot, we emphasize the configuration of the largest bodies (Hp5:5) in

the transneptunian belt with circles (big hot classical TNOs), squares

(big cold classical TNOs) and triangles (big non-classical TNOs). Pluto

is shown by a gray triangle. Lastly, those objects with a ‘‘X’’ mark

represent ‘‘very large’’ TNOs with Hp4:5. Many big TNOs are located

at the 3:2 mean motion resonance, but this is likely to be a result of

observational bias. In the classical region, we notice a greater presence

of large bodies in the hot population when compared to the cold one

(lower panel). Also, we stress the mysterious concentration of very

large TNOs at ao43:5 AU. Both claims are statistically significant and

not likely to be caused by observational biases (see text).

1For instance, the high albedo of Chiron is clearly explained by

cometary activity (Hartmann et al., 1990).

P.S. Lykawka, T. Mukai / Planetary and Space Science 53 (2005) 1319–13301320

(i44:51) (Peixinho et al., 2004); (b) resonant TNOs:associated with mean motion resonances with Neptune.In particular, those trapped in the 4:3 (a�36:4 AU), 3:2(a�39:4 AU), 5:3 (a�42:3 AU), 7:4 (a�43:7 AU) and 2:1(a�47:8 AU) mean motion resonances; (c) scatteredTNOs: with no strict neither official definition, we setthose TNOs with a450 AU and perihelion distancesq430 AU as scattered TNOs. Scattered TNOs arebelieved to have been scattered during the early solarsystem, hence the name (Duncan and Levison, 1997); (d)extended scattered TNOs: those scattered TNOs withperihelion distances large enough (q440 AU) tobe considered a distinct class (for details, see Morbidelli

et al., 2004 and references therein). Another importantclass of outer solar system bodies are the centaurs,which are believed to be in transitional orbits fillingthe dynamical link between TNOs and Jupiter-family comets (Tiscareno and Malhotra, 2003). Inthis work we classify them as objects with qo30 AUand not in any external mean motion resonancewith Neptune.

Orbital elements of TNOs and their subpopulationsoffer valuable clues and constraints, but at the sametime limited information on the origin of the solarsystem. To get insight into a more complete view of theformation and evolution of our solar system, we mustrely on crucial physical properties such as sizes, albedos,compositions, rotational states, colors and so on.With current telescopical technology, these propertiescan be obtained only from the brightest objects dueto mainly two reasons: the large transneptuniandistances involved (average �43 AU) and lowalbedos. For instance, contrary to the number ofdetected transneptunian bodies so far, TNOs withmeasured diameters and albedos are very few. Likewise,the distribution of albedos among TNOs is unknown.Apart from allowing straight derivation of sizes, knowl-edge of albedos can provide fruitful constraints on thestudy of compositions, colors, lightcurves and otherfields. A list of TNOs and centaurs with sizes/albedosderived from optical and thermal observations ispresented in Table 1, according to several publisheddata. As one can note, among the diversity of albedos,there appears to be a systematic increase of albedos onlarger objects.

2. Diameters and albedos of outer solar system objects

Measurements of size/albedo are available for bothcentaurs and TNOs, although the sample for the formeris rather small. Besides, the albedos of centaurs arepresumably distorted because of contamination bycometary activity.1 Compared to TNOs, centaurs havealso planet crossing orbits leading to enhanced proces-sing due to proximity to the Sun and the giant planets. Itis true that cometary activity could also be triggered attransneptunian belt distances though, depending on thevolatiles composition, internal structure and otherfactors (Hainaut et al., 2000 and references therein).But the extent at which cometary activity would affectthe albedo of TNOs and the fraction of objects currentlyundergoing this phenomenon is unknown. Only a fewalbedo measurements of TNOs are available (Table 1).These include four transneptunian binaries (in additionto the Pluto–Charon pair) with albedos constrained

ARTICLE IN PRESS

Table 1

Transneptunian objects and centaurs with diameter and albedo measurements sorted by sizes

Object a (AU) e i (1) Diametera (km) Hb Albedoa,c Classd Ref.e

(8405) Asbolus 17.942 0.619 17.6 6674 9.0 0.1270.03 C 1

(2060) Chiron 13.665 0.382 6.9 14878 6.5 0.1770.02 C 1

(5145) Pholus 20.431 0.573 24.7 190722 7.0 0.0470.03 C 2

(10199) Chariklo 15.869 0.176 23.4 273719 6.4 0.05570.008 C 3

(58534) 1997 CQ29

Component A 101–80f 7.20 0.23r–0.37rf

45.508 0.123 2.9 bTNO 13

Component B 83–66f 7.60 0.23r–0.37rf

1998 WW31

Component A 186–148f 7.95 0.034r–0.054rf

44.577 0.086 6.8 bTNO 16

Component B 155–123f 8.35 0.034r–0.054rf

(66652) 1999 RZ253

Component A 209–166f 6.85 0.076r–0.12rf

43.624 0.087 0.6 bTNO 14

Component B 173–137f 7.25 0.076r–0.12rf

(88611) 2001 QT297

Component A 247–196f 6.80 0.057–0.09f

43.870 0.031 2.6 bTNO 15

Component B 171–136f 7.60 0.057–0.09f

(15789) 1993 SC 39.355 0.183 5.2 328 (+58;�66) 6.9 0.022 (+0.013;�0.006) 3:2TNO 4

420 (+80;�120) 0.018 (+0.017; �0.005) TW

(38628) Huya 39.719 0.281 15.5 o540 4.7 40.08 3:2TNO 9

700 (+100;�160) 0.049 (+0.033;�0.011) TW

(15874) 1996 TL66 83.083 0.578 24.0 632 (+84;�98) 5.4 0.03 (+0.012;�0.007) STNO 4

600 (+90;�150) 0.035 (+0.027;�0.009) TW

(47171) 1999 TC36 39.233 0.221 8.4 609 (+93;�47) 4.9 0.0570.01 3:2bTNO 9

660 (+100;�150) 0.045 (+0.031;�0.011) TW

(24835) 1995 SM55 41.710 0.105 27.1 o701 4.8 40.04 TNO 9

680 (+100;�160) 0.047 (+0.032;�0.011) TW

(19521) Chaos 45.715 0.105 12.1 o742 4.9 40.04 TNO 9

660 (+100;�150) 0.045 (+0.031;�0.011) TW

(55565) 2002 AW197 47.471 0.130 24.3 700750 3.3 0.1770.03 2:1TNO 17

886 (+115;�131) 0.101r (+0.038;�0.022) 5

960 (+110;�180) 0.094 (+0.047;�0.018) TW

(19308) 1996 TO66 43.139 0.121 27.5 o897 4.5 40.04 TNO 9

740 (+100;�160) 0.054 (+0.035;�0.012) TW

(28978) Ixion 39.534 0.241 19.6 o804 3.2 40.15 3:2TNO 9

980 (+110;�180) 0.099 (+0.048;�0.019) TW

(20000) Varuna 43.070 0.051 17.2 1060 (+180;�220) 3.7 0.038 (+0.022;�0.010) TNO 6

0.049r (+0.029;�0.013) 6

900 (+130;�150) 0.07r (+0.030;�0.017) 12

880 (+110;�170) 0.078 (+0.043;�0.016) TW

(55636) 2002 TX300 43.081 0.121 25.9 o1110 3.3 40.06 TNO 11

960 (+110;�180) 0.094 (+0.047;�0.018) TW

(84522) 2002 TC302 55.139 0.293 35.1 o1195 3.9 40.04 5:2STNO 9

840 (+100;�170) 0.071 (+0.041;�0.015) TW

Charon 39.482 0.249 17.1 1250750 1.0 0.38b70.015 3:2bTNO 8

1620 (+110;�180) 0.274 (+0.070;�0.033) TW

(50000) Quaoar 43.440 0.034 8.0 12607190 2.6 0.092r (+0.036;�0.023) TNO 7

0.101b (+0.039;�0.024) 7

1120 (+110;�180) 0.130 (+0.055;�0.022) TW

(90377) Sedna 501 0.848 11.9 o1800 1.6 — STNO 10

1420 (+110;�180) 0.207 (+0.066;�0.029) TW

Pluto 39.482 0.249 17.1 2345755 �1.0 0.44–0.61b 3:2bTNO 8

2560 (+70;�90) 0.694 (+0.054;�0.036) TW

The original orbital data (a, e, i and H) as of 11 April of 2005 was taken from the Minor Planet Center (MPC, 2005).

References: (1) Fernandez et al. (2002); (2) Davies (2000); (3) Altenhoff et al. (2001); (4) Thomas et al. (2000); (5) Margot et al. (2002); (6) Lellouch et

al. (2002); (7) Brown and Trujillo (2004); (8) Tholen and Buie (1997); (9) Altenhoff et al. (2004); (10) Brown, M. E., private communication (2005);

(11) Ortiz et al. (2004); (12) Jewitt et al. (2001); (13) Noll et al. (2004a); (14) Noll et al. (2004b); (15) Osip et al. (2003); (16) Veillet et al. (2002); (17)

Cruikshank et al. (2005); TW ¼ this work.aUsually obtained by simultaneous thermal and optical observations. In the last row of each object, the values in italic are estimations calculated

using empirical Eqs. (3) and (5) (see text).bAbsolute visual magnitude.cGeometrical albedos with r and b referring to those at red (700 nm) and blue (450 nm) wavelengths, respectively. When no band is given, the

albedos refer to the V-band wavelengths (550 nm).dC ¼ centaur; TNO ¼ transneptunian object; bTNO ¼ binary TNO; STNO ¼ scattered TNO; p:q ¼ in the p:q mean motion resonance.eReference for diameter and albedo measurements.fObtained indirectly and constrained for assumed densities of 0.5 and 1 g cm�3, respectively.

P.S. Lykawka, T. Mukai / Planetary and Space Science 53 (2005) 1319–1330 1321

ARTICLE IN PRESSP.S. Lykawka, T. Mukai / Planetary and Space Science 53 (2005) 1319–13301322

from the determination of the components orbitalelements, total mass and assumed densities (for example,see Noll et al., 2004a). With the lack of a distribution ofalbedos, the standard albedo p ¼ 0:04 has been widelyassumed for TNOs following the measurements ofcometary nuclei (especially 1P/Halley) and dark cen-taurs (see e.g. Jewitt et al., 2001; Schulz, 2002). Very lowalbedos are also expected from space weathering studies(Gil-Hutton, 2002 and references therein). Nevertheless,as we will show later, it is quite possible that intrinsicactivity is contributing for a systematic increase ofalbedos well beyond 0.04 (Section 3.2).

Henceforth we will use diameter/albedo values basedon the criterion of most recent observations (first line ofeach object in Table 1). Taking the weighted averagedvalue of p for TNOs with measurements (Plutoand Charon not included), we obtain a crude approx-imation of 0.0570.02, slightly larger than 0.04. If wetake only the three TNOs with diameter D4700 km, theweighted average becomes 0.08570.045. This albedoincreasing tendency can be explained by the factthat large bodies can sustain icy patchy frosts on theirsurfaces, such as the plutonian moon Charon andlarge TNOs like Varuna (Jewitt and Luu, 1998; Jewitt,1999; Jewitt et al., 2001). Formation of fresh icedeposits would be feasible only in big bodies withenough gravity to retain volatiles near their surfaces orto force icy collisional ejecta to fall back on the object.Besides, intrinsic activity and temporary dusty/gaseousatmospheres can also raise the albedo. It should benoted too that bodies with critical size about D4100 kmcould have suffered differentiation by the concomitantaction of solar irradiation and internal radiogenicheating (De Sanctis et al., 2001; Choi et al., 2002)with important consequences for the volatile distribu-tion, albedos and relationship with centaurs and short-period comets.

Diameter and albedo are normally calculated usingthe formula derived by Russell (1916):

pD

2

� �2

FðaÞ ¼ 2:25 � 1016r2D2100:4ðmn�mÞ, (1)

where p is the geometric albedo, D is the object diameter(km), FðaÞ is the phase function, r is the heliocentricdistance (AU), D is the geocentric distance (AU) and m

is the apparent magnitude of the object. Taking theorigin in the object, the phase angle a is formed by thevectors pointing to the Earth and the Sun. Fð0Þ ¼ 1 andD ¼ r � 1 are assumed when the body is at opposition.The apparent magnitude of the Sun m

*is �27.1, �26.74

and �26.07 in red, visible and blue wavelengths,respectively. The apparent magnitude m is related tothe absolute magnitude H, distances and the phase angleas

m ¼ H þ 5 logðrDÞ þ bjaj, (2)

where b is a parameter of the phase function. For sakeof simplicity, we will assume that the last term isnegligible for the purposes of this study.

3. What clues can large TNOs and their dynamical

populations reveal?

Important information can be extracted from the sizedistribution of TNOs. For example, distribution of mass,accretion conditions and collisional evolution in thetransneptunian region. Normally the size distribution isderived from the cumulative luminosity function (CLF)under the assumptions of constant heliocentric distanceand constant albedo (0.04) (Elliot et al., 2005). The firstassumption is reasonable, but the second is moreproblematic, because the TNOs distribution of albedos isunknown. In terms of collisional evolution, only TNOswith diameters larger than about 100 km would havesurvived since formation over the age of the solar system(Stern, 1995). For the entire transneptunian region,although the largest size (which can tell about the growthend) has not been constrained yet, it must be larger than1000 km (Trujillo et al., 2001a). Concerning statisticalpredictions of the number of large classical TNOs, Trujilloet al. (2001b) have estimated that there would exist 1–6TNOs with �2000 km sizes (Pluto-like) and 18–46 bodieswith �1000 km sizes among the classical TNOs.

Our knowledge about the size distribution is stillobservationally limited to TNOs with sizes larger thanabout 100 km. Among them, many large-scale TNOs(600–1800 km) have been observed (Fig. 1). Potentialimportance of large TNOs can be resumed as:
According to accretion models, TNOs withD4100 km must be primordial reflecting the end ofaccretion phase. Therefore, knowing the distributionof big TNOs can help to find the largest diameterproduced during the accretion, since a cut off at largesize (after runaway growth) is expected. Besides, largeTNOs can also yield fruitful information about theoriginal distribution of mass in the early solar nebula(Kenyon and Luu, 1998, 1999a, b). With current observational technology, as big TNOsare brighter, it is possible to collect spectra moreeasily in order to probe compositions and structure. Knowledge about color and albedo distributions oflarge TNOs can help to constrain collisional modelsand to understand surface dynamics (e.g., processesresponsible for the dispersion in colors). Having a significant sample of big TNOs, dynamicalmodels can be constrained (e.g., hot classical TNOsorigin), correlations with orbital elements can beproved or disproved, and the dependence on masscan be better understood considering differentpopulations.

ARTICLE IN PRESSP.S. Lykawka, T. Mukai / Planetary and Space Science 53 (2005) 1319–1330 1323

3.1. Large TNOs with measurements and implications for

the size and albedo distributions

Objects used in this section are those with diametermeasurements as shown in Table 1 and with absolutemagnitudes taken from the MPC database. Althoughthis database is primarily astrometric (rather thanphotometric), all the objects possess more than threeopposition observations, so we assume that the values ofabsolute magnitude have small errors (o0.1mag).

In Fig. 2, we show the sizes and absolute magnitudesof these objects together with curves representingconstant values of albedo: 0.02, 0.04, 0.08, 0.12, 0.25and 0.50. It is clear that for any large TNO with Hp4:5,assuming albedo 0.04 to calculate the diameter wouldimply a large overestimation. For example, Quaoarwould have 2000 km for an albedo of 0.04. Moreover,big TNOs have the tendency to fall off from the p ¼ 0:04curve to higher albedos as their sizes increase (decreas-ing H). As we saw in Section 2, there are physicalreasons that explain this tendency observed on the plot.Pluto has a very high albedo, thanks mainly to itsatmosphere with correlated surface dynamics (Yelle andElliot, 1997). The position of Charon on the plot is moreproblematic to interpret though. It suggests the presenceof icy frosts and perhaps the existence of a tenuousatmosphere helping to enhance the albedo. Water ice

Absolute magnitude-2 -1 0 1 2 3 4 5 6 7 8 9 10 11

10000

1000

100

10

Dia

met

er (

km)

Centaurs TNOs Scattered TNOs Charon Pluto Binary TNOs

albedos0.020.040.080.120.250.50

Fig. 2. Relation of diameter with absolute magnitude for bodies with

size measurements. Diagonal dotted lines show values of constant

albedo. From the top they are 0.02, 0.04, 0.08, 0.12, 0.25 and 0.50. The

typically assumed p ¼ 0:04 albedo is indicated by the long dashed

diagonal line. Two curve fittings were derived: the light gray line

represents 13 TNOs in the range 1:5oHo5:5 and 1993 SC. The dark

line is the same fitting but also including Pluto and Charon. Deviations

caused by uncertainties are also shown with two thinner dark lines for

this fitting in particular. Note that big bodies tend to fall off from the

assumed line towards higher albedos as their sizes increase (smaller H).

This tendency is probably caused by patchy frosts, temporary dust

clouds, atmospheres or intrinsic activity. We also notice that small

bodies (centaurs and binary TNOs) have albedos greater than 0.04.

Errors in absolute magnitude were assumed to be o0.1 for all but

binary TNOs. Arrows indicate upper limits constrained for an assumed

p ¼ 0:2.

frosts have been found (Nakamura et al., 2000) but it isnot clear if this moon really possesses a tenuousatmosphere (Elliot and Young, 1991). At the faint end,note that for H46:026:5, binary TNOs and centaursstrongly do not follow the typical p ¼ 0:04 curve, withalmost all of them falling off towards higher albedos.From the above, evidently assuming albedo 0.04 is notadequate for large TNOs, transneptunian binaries andcentaurs (see also Section 3.3.1).

We derived two curve fittings from the objects withdiameter measurements data. We neither includedcentaurs nor transneptunian binaries in the followingderivation. The light gray line shows the best fitting for13 TNOs in the range 1:5oHo5:5 and 1993 SC(H ¼ 6:9). The black line is the same fitting but alsoincluding Pluto and Charon. It is not clear howsignificant is taking Pluto and Charon together withother large TNOs, but we preferred to do so becauseboth probably are just typical TNOs, as evidenced in theliterature (Stern and Levison, 2000; Davies, 2001). For apower law function, considering the fitting includingPluto and Charon, we got the diameter as a function ofabsolute magnitude:

DðHÞ ¼ fgH, (3)

with f ¼ ð2:039þ0:094�0:149Þ � 103 and g ¼ ð7:96þ0:15

�0:30Þ � 10�1.Parameter f tells us the domain of sizes for theconsidered albedo distribution, while g defines the rateof albedo change with absolute magnitude. We havealbedo increasing proportionally to sizes within the�0:2o log go0 interval, whereat �0.2 sets the limit forconstant albedo. Larger values in the interval implysteeper albedo changes.

Substituting Eq. (2) into Eq. (1) and solving for p, wehave

pðH;DÞ ¼K � 100:4ðmn�HÞ

D2, (4)

with K ¼ 9 � 1016. One can derive the albedo as afunction of absolute magnitude putting (3) into (4) tofinally get

pðHÞ ¼K � 100:4ðmn�HÞ

f 2g2H, (5)

for Hp5:526:0; Or the albedo as a function of size

pðDÞ ¼K � 100:4½mn�logg ðD=f Þ�

D2or

pðDÞ �K � 100:4ðmnþ10 log ðD=f ÞÞ

D2

simplifying log g for � 0:1, ð6Þ

for DX5002600 km. Determination of diameters andalbedos based on the absolute magnitudes for the samebodies in Table 1 resulted in reasonable estimates.Taking again Quaoar as an example, our estimated size

ARTICLE IN PRESS

Table 2

Large transneptunian objects sorted by absolute magnitudes with diameter and albedo values estimated by this work

Object a (AU) e i (1) Diameter (km) Ha Albedo Classb

(90482) Orcus 39.453 0.218 20.6 1200 (+110;�180) 2.3 0.150 (+0.058;�0.024) 3:2TNO

(55637) 2002 UX25 42.562 0.144 19.5 900 (+110;�170) 3.6 0.082 (+0.044;�0.016) TNO

2002 MS4 41.758 0.142 17.7 840 (+100;�170) 3.9 0.071 (+0.041;�0.015) TNO

2003 AZ84 39.598 0.177 13.6 840 (+100;�170) 3.9 0.071 (+0.041;�0.015) 3:2TNO

(90568) 2004 GV9 42.238 0.083 22.0 820 (+100;�170) 4.0 0.068 (+0.040;�0.014) 5:3TNO

(42301) 2001 UR163 51.330 0.283 0.8 780 (+100;�170) 4.2 0.062 (+0.038;�0.014) 5:2STNO

(84922) 2003 VS2 39.361 0.074 14.8 780 (+100;�170) 4.2 0.062 (+0.038;�0.014) 3:2TNO

2002 KX14 38.925 0.041 0.4 740 (+100;�160) 4.5 0.054 (+0.035;�0.012) TNO

2003 QW90 43.267 0.034 10.4 740 (+100;�160) 4.5 0.054 (+0.035;�0.012) TNO

2002 KW14 46.877 0.203 9.8 720 (+100;�160) 4.6 0.051 (+0.034;�0.012) TNO

(26375) 1999 DE9 56.046 0.423 7.6 700 (+100;�160) 4.7 0.049 (+0.033;�0.011) STNO

2001 QF298 39.223 0.114 22.4 700 (+100;�160) 4.7 0.049 (+0.033;�0.011) 3:2TNO

2003 FY128 49.897 0.257 11.8 680 (+100;�160) 4.8 0.047 (+0.032;�0.011) TNO

2000 CN105 44.809 0.094 3.4 660 (+100;�150) 5.0 0.043 (+0.030;�0.010) TNO

2000 YW134 58.134 0.291 19.8 660 (+100;�150) 5.0 0.043 (+0.030;�0.010) STNO

2001 KA77 47.558 0.093 11.9 660 (+100;�150) 5.0 0.043 (+0.030;�0.010) TNO

2002 WC19 47.875 0.264 9.2 660 (+100;�150) 5.0 0.043 (+0.030;�0.010) 2:1TNO

2002 XV93 39.359 0.128 13.3 660 (+100;�150) 5.0 0.043 (+0.030;�0.010) 3:2TNO

The orbital data as of 11 April 2005 was taken from the Minor Planet Center (MPC, 2005).aAbsolute magnitude.bTNO ¼ transneptunian object; STNO ¼ scattered TNO; p:q ¼ in the p:q mean motion resonance.


and albedo would be around 1120 km and 0.13,respectively, within the limits of measured values. Wealso estimated diameters and albedos of other big TNOsfor which no measurements are available yet (Table 2).

Although estimations using Eqs. (3), (5) or (6) haveconsiderable uncertainties (limited sample, measurementerrors, discordance among different observers, etc.), inour sense it is much better than just assuming p ¼ 0:04indiscriminately for all sizes. Our present analysissuggests that for large TNOs (say, Hp5:5), the diametershould not be estimated by any assumed constantalbedo, but from the tendency observed in the best fitof all large TNOs with diameter measurements. Hence-forth we will use our empirical relations to estimate sizesand albedos. We note too that the error bars of our fitinclude errors of size measurements, uncertainties forobjects with diameter upper limits and variations in theabsolute magnitudes (70.1) for all objects. If thecentaurs were considered in the fitting, we would havea size overestimation for Ho2:5 and a severe under-estimation for 3:5oHo6:5. The size overestimationeffect would be enhanced at the bright end if oneallowed an intrinsic population dominated by smallbodies with 0:04opo0:3. From this simple exercise, it isclear that the fit cannot be extrapolated to all sizes,justifying our choice to limit H and D in the derivationof the empirical equations.

An intrinsic increase of albedo for TNOs with H

smaller than a critical absolute magnitude Hcrit willprovoke changes in the number of TNOs observed persky area. What implications for the CLF and sizedistribution should we expect from an albedo changing

as described previously? Basically, TNOs withHoHcrit�5:5 would have greater probabilities to befound by surveys because of their intrinsic largerbrightness as the albedos get higher. That is, the CLFwould shift to a shallower slope for apparent magni-tudes approximately o21mag. According to ourestimates, discovery would be favored implyingsky densities 50–100 times larger for objects withm�15mag (Pluto-class) and 2–10 times for m�19:5mag(1000 km-class). There are two possible interpretations:(1) the TNOs size distribution follows a single power lawdistribution, so that the CLF slope change at the brightend is real but observations are too scarce for this to bedistinguishable; or (2) the TNOs size distributionfollows a broken power law distribution, whereat bodiesbigger than a critical size would have a steeper slope.Thus, the number of bright objects with mo21mag mustbe small enough in order to explain a CLF following asingle slope until the bright end, otherwise we would seethe slope change in the CLF at o21 mag. According topublished data from surveys, very few bright objectshave been observed so far (Bernstein et al., 2004 andreferences therein). Therefore, it is still not possible toconfirm the CLF slope change at the bright end.

Another implication is that the total mass, which isproportional to p�3=2, will be somewhat smaller for arange of diameters larger than 500–600 km and trun-cated to the maximum size in the distribution. Asignificant fraction of the total mass must be containedin larger bodies, especially those in more excited orbits(Bernstein et al., 2004). Assuming constant bulk densityand a single power law size distribution, the decrease of

ARTICLE IN PRESS

2rcrit [AU] is a constant given by ð4205m0=7kÞ2.

P.S. Lykawka, T. Mukai / Planetary and Space Science 53 (2005) 1319–1330 1325

the total mass could reach roughly 50% for this sizerange if the albedos are in fact systematically larger than0.04.

In the opposite direction of the curve (H45:5), thingsare more difficult with the lack of data and mixing ofTNOs (mostly binaries) with centaurs, dynamical classesthat surely suffer different processing. Even then, in thisregion of smaller objects there is an obvious tendency ofhigher albedos than the usual 0.04. Therefore, anyassumption of albedos for smaller objects shouldseriously consider p40:04 (see Grundy et al., 2005 fora discussion).

3.2. Outgassing in large TNOs: tenuous atmospheres and

icy frosts

The environment in the transneptunian region favorsthe formation of tenuous permanent or transient atmo-spheres. This is supported by diverse evidences: (a) theatmospheres of Pluto (Yelle and Elliot, 1997) and Triton(Yelle et al., 1995); (b) abundance of volatiles withsublimation temperatures (Tsub) comparable to the localtemperature; (c) intrinsic and/or induced activity onsome bodies. Intrinsic activity has been attributed to theoutgassing of embedded volatiles, namely HCN(T sub ¼ 95 K), CO2 (T sub ¼ 72 K), CH4 (T sub ¼ 31 K),CO (T sub ¼ 25 K) and N2 (T sub ¼ 22 K), and could betriggered by diverse mechanisms, such as heat releasedfrom the change of amorphous to crystalline water ice,decay of radioactive nuclides, collisions, etc. (Sekiguchiet al., 2002). In fact, activity has been reported forcomets at large heliocentric distances and much beyondthe water ice sublimation limit (Hainaut et al., 2000;Sekiguchi et al., 2002). At transneptunian distancestemperatures are around 30–50 K, so that activity couldbe playing an important role with sublimation ofsupervolatiles and surface changes, and hence significantchanges of albedo. Furthermore, Delsanti et al. (2004)have already shown that intrinsic activity must have animportant role for the colors, albedos and other surfaceproperties of TNOs. According to spectra measure-ments, Pluto is known to have H2O, CH4, CO and N2

ices on its surface (Brown, 2002). Recently, it has beenreported that Quaoar possesses ices identified as H2O(amorphous and some part in crystalline form), CH4

and ammonia hydrate (Jewitt and Luu, 2004; de Berghet al., 2005). Consequently, this would have relationwith icy frosts or potential sublimation of supervolatilesto account for the albedo reported (about 0.1).

Taking the evidences together, it appears reasonableto expect the formation of thin gaseous and/or dustyatmospheres in large TNOs, because they would havethe mass needed to avoid direct escape of materials intospace. Thus, volatile outgassing could sustain ahypothetical atmosphere and contribute to eject dustor/and fresh icy grains on the surface. Besides, volatiles

condensing near the surface can also form icy frosts. Allthese processes working together could explain thesystematic higher albedos on large TNOs. Following thisinterpretation, we analyzed the feasibility of existence ofsuch gaseous structures according to some of the mostcommon chemical species in the outer solar system: CH4,CO and N2. We assumed that if the thermal velocity vth

of molecules in the atmosphere is less than the escapevelocity vesc of the same molecules from a parent body,such object could be capable to keep an atmosphere. Thevth and vesc are defined as

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2kT=mM

pand

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GM=R

p,

where G is the universal gravitational constant and k isthe Boltzmann’s constant. M denotes the mass of theparent body with radius R and mean density r. Lastly, T

represents the temperature in an atmosphere consisting ofa molecule with mass mM. For simplicity, we assumedTðKÞ ¼ 280r�1=2, where r is the heliocentric distance ofthe object in units of AU. In general, TNOs larger thanabout 700 km have the possibility to harbor atmospheresconsisting either of CH4, CO or N2, even assumingdensities of TNOs as low as 0.5 g cm�3 (Fig. 3).

Our simple treatment assumes that the gas is at thermalequilibrium, a condition that may be not necessarily truefor all TNOs. Indeed, the gas may escape from thesurface via sublimation following an expansion velocitygiven by vexp ¼ 580r�1=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim0=mM

p, where r is given in

AU and m0 is the water molecular mass (Bobrovnikoff,1954; Delsemme, 1982). Besides, as dust and icy grainsshould be well coupled with the gas, it is likely that somemacroscopic material will be released with a velocitynearly described by vexp. Analyzing the dependence of vth

and vexp with heliocentric distance, we found that thelatter dominates only inside rcrito1:7 AU for a particulargas constituent.2 That is, if we use the expansion velocityinstead of thermal velocity in our investigation above(assuming vexpovesc), our previous conclusion becomestrue for TNOs larger than �300–400 km (Fig. 3). In otherwords, assuming vexp would imply a reduction of theapproximate minimal diameter to maintain an atmo-sphere. This decrease is proportional to r

�1=4crit r1=4 �

0:88r1=4. For typical TNOs distances (30260 AU), theminimal diameter would reduce within a factor of 2–2.5,while for scattered TNOs this could reach up to �5around 1000 AU.

Concluding, the minimum size of TNOs to keep thinatmospheres consisting either of CH4, CO or N2 wouldbe the largest when assuming thermal velocity andbody’s mean density of 0.5 g cm�3, both of which weconsider quite conservative assumptions. Therefore,according to observations, all the known largest TNOswould be capable of sustaining bound thin atmospheresand/or to form associated icy frosts on their surfaces(Fig. 3).

ARTICLE IN PRESS

Heliocentric distance (AU)

10100

1000

10000

100 1000

Dia

met

er (

km)

No atmosphere

AtmosphereCH4

CO, N2 1.0 gcm-30.5 gcm-3

1.0 gcm-30.5 gcm-3

Centaurs TNOs Scattered TNOs Charon Pluto Binary TNOs�

Fig. 3. Existence of a hypothetical atmosphere around a TNO with

size D and mean density r at heliocentric distance r. The region above

the lines indicates where a body can possess an atmosphere consisting

of either CH4 (black lines), CO or N2 (gray lines). Dashed and solid

lines represent assumed TNOs densities for 0.5 and 1 g cm�3,

respectively. Two cases are considered for the gas molecules: thermal

velocity (thick lines) and expansion velocity (thin lines). Note that

there is strong support for the existence of permanent or temporary

tenuous atmospheres in TNOs larger than about 700 km, thus

including all the known largest TNOs.

0 500 1000 1500 2000 2500Diameter (km)

Alb

edo

0.01

0.1

1

(3:2)

(3:2)

(3:2)(3:2)

(2:1)

hot

hot hothot

hot

hot scat

scat

scat

TritonTNOs Scattered TNOs Charon Pluto Binary TNOs

Fig. 4. Bodies with diameter and albedo measurements. Some

dynamical groups are indicated by ‘‘3:2’’ and ‘‘2:1’’, representing

objects respectively in the 3:2 and 2:1 mean motion resonances with

Neptune. Also, ‘‘hot’’ are hot classical TNOs and ‘‘scat’’ indicate

scattered TNOs. The horizontal dotted line marks the typically

assumed albedo p ¼ 0:04. Some objects with arrows indicate albedo-

lower/diameter-upper limits. The black curve was traced by using Eq.

(6) with parameters derived as explained in the text. Note that larger

objects tend to have higher albedos following roughly the curve.

Notice too that Charon possesses a quite high albedo, whose origin is

not clear yet. The current position of transneptunian binaries poses a

puzzle with no apparent link with the general tendency observed for

larger TNOs. Finally, we realize the tendency of resonant bodies to

present higher albedos when compared to hot and scattered TNOs,

possibly indicating physical differences between resonants and non-

resonants as a result of different collisional and orbital histories.


3.3. Albedos and dynamical populations

In Fig. 4, we show TNOs with diameter/albedomeasurements together with the largest neptuniansatellite Triton. Among the TNOs, some dynamicalgroups are indicated: ‘‘3:2’’ (3:2 resonants), ‘‘2:1’’ (2:1resonants), ‘‘hot’’ (hot classicals) and ‘‘scat’’ (scatteredbodies). Transneptunian binaries are also shown. Theblack curve represents the tendency of increasingalbedos for larger diameters according to Eq. (6).

Curiously, resonant TNOs seem to have higheralbedos when compared to other objects in the hotclassical and scattered populations. To assert thevalidity of this tendency, we applied the Kolmogor-ov–Smirnov statistical test (K–S test). Basically, the K–Sstatistic is non-parametric and can tell if two particulardistributions are derived from the same parent distribu-tion (i.e., they are the same) or represent two distinctdistributions (see Press et al., 1992 for details). Employ-ing the two-dimensional (2D) K–S test, the difference ofresonants and non-resonants according to sizes andalbedos is 98.20% statistically significant. A criticalproblem is that the expected changes for objects withlimits (indicated with arrows) could diminish the 2DK–S statistic to �90% or even less. Besides, contrary tothe 1D K–S test, the total sample is still too small (13objects) to get a strong answer from the 2D K–S test.Nevertheless, if the difference is confirmed with futureobservations, this may be the first physical evidence thatresonant TNOs and non-resonants have been evolvingdifferently since their formation. One potential cause for

the slight differences of albedos could be attributed todistinct collisional ambient for both resonants and non-resonants (Gil-Hutton, 2002). Another evidence comesfrom the simulations of Thebault and Doressoundiram(2003), where they have found that 3:2 resonants have amore excited collisional ambient than other TNOs.Lastly, the results of Dell’Oro et al. (2001) also confirmthat the collisional regimes for non-resonants vs. non-resonants, non-resonants vs. 3:2 resonants and 3:2resonants vs. 3:2 resonants are comparable, butdifferent. They have also found average greater impactvelocities for cases involving 3:2 resonants in agreementwith the other mentioned investigations. All thesestudies support our hypothesis that resonant TNOscould present systematically higher albedos than otherpopulations in the transneptunian region, assumingalbedos dependent on the collisional excitation and/orenhanced intrinsic activity caused by their smallerperihelion distances and more frequent perihelionpassages.

Concerning cold and hot classical TNOs, according tothe literature both populations differ not only in sizedistribution, but also in inclination and color distribu-tions (Brown, 2001; Levison and Stern, 2001; Bernsteinet al., 2004; Peixinho et al., 2004) and possibly incompositions (Gomes, 2003). All these characteristics


may be mainly related to distinct formation sites forboth populations during the early solar system. If this isthe case, we could expect cold and hot classical TNOshaving different albedo distributions as well. Severalobjects with diameter and albedo measurements are hotobjects, while only transneptunian binaries are withinthe cold population (Table 1). Thus, a comparisonaccording to observational data is extremely proble-matic.

3.3.1. Transneptunian binaries: some facts and clues on

their origin

The albedo weighted average of the four transneptu-nian binaries is �0.10 and �0.16 assuming densities of0.5 and 1 g cm�3, respectively.3 Such values are 2.5–4times greater than the long assumed p ¼ 0:04. Inparticular, the albedo obtained (0.37) for 1997 CQ29

assuming 1 g cm�3 density would be almost one order ofmagnitude bigger (Noll et al., 2004a).

Physically it is difficult to explain the reason for highalbedos on these binaries. With components typicallyless than 250 km, we cannot apply here our approachdiscussed for large TNOs in previous sections. On theother hand, Stern (2002) has demonstrated the possibi-lity of formation of binary TNOs4 via collisions with thecondition of albedos equal to 0.15 or more. Thus,current albedo values constrained so far match thepredictions of Stern’s model, which also allows theformation of transneptunian binaries even in morerecent periods of the solar system history. If collisionsare indeed the primary mechanism for their formation,Stern’s model would offer an explanation for the highalbedos observed, assuming components are fragmentscomposed of fresh ices from the interior of a largeparent body. Within the same scenario, anotherpossibility is the deposit of fresh materials on thesurface of either one or both the components raising thealbedos.

3.4. Size distribution of the main transneptunian

populations

In this section, we investigate the relation of orbitalelements with absolute magnitudes for the maintransneptunian populations focusing on large bodies.We used only objects with more than one oppositionobservations, thus having more reliable orbits and withlittle danger of dynamical misclassification.

In Fig. 1, the TNOs orbital elements distribution withemphasis on the brightest bodies (i.e., largest objects) isillustrated. From our discussion in Section 3.1, we took

3Densities of TNOs indicate values greater than 0.5 g cm�3 and

increasing for larger sizes (Sheppard and Jewitt, 2002).4See Petit and Mousis (2004) for a more detailed discussion about

the formation and evolution of binary TNOs.

H ¼ 5:5 (D�600 km) as reference to define large TNOs(Hp5:5). We also show both the big hot and coldclassical TNOs and large non-classical bodies. Mostly,large TNOs concentrate for q435 AU except several bigones in the 3:2 mean motion resonance, although oneshould recall observational bias playing a role here.That is, with smaller perihelion distances, these objectsare more likely to be detected by standard surveys(Bernstein and Khushalani, 2000). For the 2:1 meanmotion resonance, there are apparently three big objectstrapped in.

In the classical region, we notice a greater presence oflarge bodies in the hot population when compared to thecold one. We investigated the absolute magnitudedistributions of cold and hot classical TNOs fordifferent threshold inclinations with steps of 0.51. Forthe best inclination threshold i ¼ 4:51, the probabilitythat both populations are the same is 0.37% (199 coldand 117 hot objects). Assuming other definitions ofclassical TNOs, such as only classical bodies withq435 AU or/and excluding 5:3 and 2:1 resonants fromthe sample resulted in even smaller probabilities(o0.1%). Apart from the small uncertainties causedby arbitrary definitions, the presence of two distinctpopulations in the classical region according to sizes andinclinations with confidence level 499.63% is verylikely. The division of cold and hot populations at 4.51 isin accordance with previous investigations and is notcaused by observational biases (Levison and Stern,2001; Bernstein et al., 2004; Peixinho et al., 2004).Therefore, the criterion for division of both populationsseems to be well established and should not affect ouranalysis of subpopulations. Furthermore, note thatwhile the largest hot classical TNOs are spread acrossthe entire classical region from low to very highinclinations and show diverse sizes (from nearly600 km up to 1260 km, the size of Quaoar), the biggestcold ones seem to be located in a narrow region�44–45 AU with sizes mostly ranging 600–650 km. Weperformed a K–S test to check the significance of bothsamples having different semimajor axes distributions(six large cold and 23 large hot bodies). The statisticresulted 24.66% for equal parent populations, implyingit is statistically not significant to affirm that large coldclassical TNOs are distributed in semimajor axesunequally when compared to their counterparts in thehot population. On the other hand, the samples are verysmall and only more observations will solve definitelythis issue with better statistics. Interestingly, Chiang(2002) have suggested the existence of a collisionalfamily whose boundaries in phase space roughly matchthose of all large cold classical bodies.

After close inspection of Fig. 1, it is intriguing thatinside a�43:5 AU the distribution of sizes appear to bepeculiar. We stress the exclusive concentration of ‘‘verylarge’’ TNOs (Hp4:5) in the same region. Indeed, four


of them have already diameter measurements as shownin Table 1: 1996 TO66, Varuna, 2002 TX300 and Quaoar;other four have only our diameter estimates as shown inTable 2: 2002 UX25, 2002 MS4, 2004 GV9 and 2003QW90. Once again we applied the K–S test to assert thesignificance of this claim. We considered all classicalTNOs with Hp5:5 and arbitrarily divided the popula-tion into two groups with a threshold at 43.5 AU: GroupI for ao43:5 AU and Group II for a443:5 AU. Thestatistics gave us 99.98% of confidence that theconcentration of larger classical TNOs at ao43:5 AUseems indeed to be a real feature. This conclusion couldbe the result of observational bias though, becauseobjects at smaller distances are easier to be discovered.Accordingly, if the objects from Group I have periheliaor distance at discovery distribution significantly differ-ent from that of Group II then our claim would be aconsequence of observational bias. We applied the K–Stest for the distributions of perihelia and distance atdiscovery of both groups finding that they cannot beconsidered distinct (K–S statistic ¼ 94.27% and22.23%, respectively). This argues in favor of ourhypothesis. Different distributions of large classicalbodies for ao43:5 AU and a443:5 AU could also becaused by an uneven concentration of cold and hotpopulations within each group. That is, if one group isdominated by cold classical TNOs and vice-versa, ourclaim would be a direct consequence from the fact thatcold and hot populations possess different brightnessdistributions. Group I contained 10 objects exclusivelyfrom the hot population. Group II contained 19 objects,from which six were cold classical bodies. We repeatedthe K–S test excluding the six objects from Group IIfinding 99.85% of confidence that both groups havedistinct absolute magnitude distributions again strength-ening our claim. We also stress that this positive result isachieved only for absolute magnitudes Hp5:5 and doesinvolve semimajor axes with the best threshold around�43.5 AU, therefore excluding any influence of otherorbital parameters.

Finally, we also checked the discovery circumstancesof each very large TNO within Group I using publishedMinor Planet Circulars. We found these big objects wereobserved by different telescopes focusing in distinctregions of the sky during the respective diverse epochs.Moreover, except two objects,5 all of them werediscovered by different teams of observers. A word ofcaution is necessary though: observers follow similarprocedures for the detection of TNOs so that a biascannot be completely ruled out. On the other hand, thispossibility is unlikely. Taking together the uncorrelateddiscovery circumstances of these objects with our

5Only Quaoar and 2002 MS4 were discovered by the same team

using the Palomar/NEAT. Both objects had different discovery

circumstances though.

investigations, we can affirm that large classical TNOsare distributed differently inside ao43:5 AU anda443:5 AU, with the largest bodies being preferentiallylocated in the inner part of the classical region. Thisresult is intriguing because no scenario can explain whythere should be a preference for concentration of largerTNOs in the inner region of the classical belt.

4. Summary and conclusions

Using the currently available limited observationaldata sample, simple theoretical approaches and therobust K–S statistical test, we analyzed the size/albedoand absolute magnitude distributions of TNOs and itsmain subpopulations. The main results of this work aresummarized below:
Large TNOs (Hp5:5) have in general higher albedos(X0.04) that seem to increase systematically withsize. Empirical equations to estimate sizes/albedoswere derived and can offer testable predictions.Together with recent works (Noll et al., 2004a, b;Grundy et al., 2005), the long-assumed p ¼ 0:04cannot hold for the majority of TNOs. Moreover,volatile sublimation (CH4, CO or N2) at transneptu-nian distances supports the idea of a significantcontribution of thin gaseous atmospheres and/or icyfrosts in determining higher albedos for TNOs largerthan 700 km. Resonant TNOs have possibly higher albedos whencompared to other TNOs. The main reason would bea more excited collisional ambient for the former. Inthis way, resonant TNOs surfaces would be morerejuvenated by collisions itself (surface resurfacing)or/and by supervolatile outgassing provoked bycollisional excitation. Furthermore, as those bodieshave smaller perihelion distances and more frequentperihelion passages, this could also help to triggeroutgassing activity contributing for an average biggeralbedo. Big cold classical TNOs (�600 km) appear to beconcentrated between 44 and 45 AU. These bodiesmight constitute the remnants of a collisional family,as suggested by Chiang (2002). Larger classical TNOs are anomalously concentratedin the inner part of the classical region (ao43:5 AU)with 499.85% of confidence. This surprising result isunlikely to be the effect of observational biases andtherefore suggests a new puzzling constraint for theformation and evolution of the entire transneptunianregion.
Finally, we expect that new observations will bringlight to our understanding and reduce the uncertaintiesin general. For example, it is quite simplistic to assume


that the albedo will depend only on the absolutemagnitude or diameter, since it has clearly dependenceon several factors such as chemical composition,thermal evolution, surface structure, atmospheres andso on. Also, it is worth noting that all TNOs with sizeand albedo measurements belong to several dynamicalclasses, such as hot classicals, resonants and scatteredbodies. In our analysis, there is no single cold classicalTNO in the sample (we did not consider binaries, Table1), so that our discussions are valid only for the formerdynamically excited classes. In conclusion, our approachshould be seen as a starting point offering some testableprevisions concerning sizes and albedos.

Acknowledgments

We would like to thank Olivier R. Hainaut forcomments and suggestions that greatly improved thiswork. Comments from an anonymous referee alsohelped to give more consistency to our results. We alsothank Mike E. Brown for his kind communication of thesize of Sedna. Finally, we appreciated the commentsfrom Wilhelm J. Altenhoff and Jose L. Ortiz givingsome light about thermal observations. This researchwas supported by ‘‘The 21st Century COE Program ofOrigin and Evolution of Planetary Systems’’ in theMinistry of Education, Culture, Sports, Science andTechnology of Japan.

References

Altenhoff, W.J., Menten, K.M., Bertoldi, F., 2001. Size determination

of the Centaur Chariklo from millimeter-wavelength bolometer

observations. Astron. Astrophys. 366, L9–L12.

Altenhoff, W.J., Bertoldi, F., Menten, K.M., 2004. Size estimates of

some optically bright KBOs. Astron. Astrophys. 415, 771–775.

Bernstein, G.M., Khushalani, B., 2000. Orbit fitting and uncertainties

for Kuiper belt objects. Astron. J. 120, 3323–3332.

Bernstein, G.M., Trilling, D.E., Allen, R.L., Brown, M.E., Holman,

M., Malhotra, R., 2004. The size distribution of trans-neptunian

bodies. Astron. J. 128, 1364–1390.

Bobrovnikoff, N.T., 1954. Reports of observations 1953–1954: Perkins

Observatory—Physical properties of comets. Astron. J. 59,

356–358.

Brown, M.E., 2001. The inclination distribution of the Kuiper belt.

Astron. J. 121, 2804–2814.

Brown, M.E., 2002. Pluto and Charon: formation, seasons, composi-

tion. Annu. Rev. Earth Planet. Sci. 30, 307–345.

Brown, M.E., Trujillo, C., 2004. Direct measurement of the size of the

large Kuiper belt object (50000) Quaoar. Astron. J. 127,

2413–2417.

Chiang, E.I., 2002. A collisional family in the classical Kuiper belt.

Astrophys. J. 573, L65–L68.

Choi, Y.-J., Cohen, M., Merk, R., Prialnik, D., 2002. Long-term

evolution of objects in the Kuiper belt zone—effects of insolation

and radiogenic heating. Icarus 160, 300–312.

Cruikshank, D.P., Stansberry, J.A., Emery, J.P., Fernandez, Y.R.,

Werner, M.W., Trilling, D.E., Rieke, G.H., 2005. The high-albedo

Kuiper belt object (55565) 2002 AW197. Astrophys. J. 624,

L53–L56.

de Bergh, C., Barucci, A., Doressoundiram, A., Dotto, E., 2005.

Spectroscopy of Kuiper Belt Objects and Centaurs. 35th COSPAR

Scientific Assembly, p. 1572.

Davies, J.K., 2000. Physical characteristics of trans-neptunian objects

and centaurs. In: Fitzsimmons, A., Jewitt, D., West, R.M. (Eds.),

Proceedings of the ESO Workshop Minor Bodies in the Outer

Solar System (1998). Springer, Berlin, New York, pp. 9–24.

Davies, J., 2001. Beyond Pluto. Exploring the Outer Limits of the

Solar System. Cambridge University press, Cambridge.

De Sanctis, M.C., Capria, M.T., Coradini, A., 2001. Thermal

evolution and differentiation of Edgeworth-Kuiper belt objects.

Astron. J. 121, 2792–2799.

Dell’Oro, A., Marzari, F., Paolicchi, P., Vanzani, V., 2001. Updated

collisional probabilities of minor body populations. Astron.

Astrophys. 366, 1053–1060.

Delsanti, A., Hainaut, O., Jourdeuil, E., Meech, K.J., Boehnhardt, H.,

Barrera, L., 2004. Simultaneous visible-near IR photometric study

of Kuiper Belt Objects surfaces with the ESO/very large telescopes.

Astron. Astrophys. 417, 1145–1158.

Delsemme, A.H., 1982. Chemical composition of cometary nuclei. In:

Wilkening, L.L. (Ed.), Comets. University of Arizona Press,

Tucson (p. 85).

Duncan, M.J., Levison, H.F., 1997. A disk of scattered icy objects and

the origin of Jupiter-family comets. Science 276, 1670–1672.

Elliot, J.L., Young, L.A., 1991. Limits on the radius and a possible

atmosphere of Charon from its 1980 stellar occultation. Icarus 89,

244–254.

Elliot, J.L., Kern, S.D., Clancy, K.B., Gulbis, A.A.S., Millis, R.L.,

Buie, M.W., Wasserman, L.H., Chiang, E.I., Jordan, A.B., Trilling,

D.E., Meech, K.J., 2005. The deep ecliptic survey: a search for

Kuiper belt objects and centaurs. II. Dynamical classification, the

Kuiper belt plane, and the core population. Astron. J. 129,

1117–1162.

Fernandez, Y.R., Jewitt, D.C., Sheppard, S.S., 2002. Thermal

properties of centaurs Asbolus and Chiron. Astron. J. 123,

1050–1055.

Gil-Hutton, R., 2002. Color diversity among Kuiper belt objects:

the collisional resurfacing model revisited. Planet. Space Sci. 50,

57–62.

Gomes, R.S., 2003. The origin of the Kuiper belt high-inclination

population. Icarus 161, 404–418.

Grundy, W.M., Noll, K.S., Stephens, D.C., 2005. Diverse Albedos of

Small Trans-Neptunian Objects. Preprint: astro-ph/0502229.

Hainaut, O.R., Delahodde, C.E., Boehnhardt, H., Dotto, E., Barucci,

M.A., Meech, K.J., Bauer, J.M., West, R.M., Doressoundiram, A.,

2000. Physical properties of TNO 1996 TO66 lightcurves and

possible cometary activity. Astron. Astrophys. 356, 1076–1088.

Hartmann, W.K., Tholen, D.J., Meech, K.J., Cruikshank, D.P., 1990.

2060 Chiron—colorimetry and cometary behavior. Icarus 83, 1–15.

Jewitt, D.C., 1999. Kuiper belt objects. Annu. Rev. Earth Planet. Sci.

27, 287–312.

Jewitt, D.C., Luu, J.X., 1992. IAUC 5611: 1992 QB1.

Jewitt, D.C., Luu, J., 1998. Optical-infrared spectral diversity in the

Kuiper belt. Astrophys. J. 115, 1667–1670.

Jewitt, D.C., Luu, J., 2004. Crystalline water ice on the Kuiper belt

object (50000) Quaoar. Nature 432, 731–733.

Jewitt, D.C., Aussel, H., Evans, A., 2001. The size and albedo of the

Kuiper-belt object (20000) Varuna. Nature 411, 446–447.

Kenyon, S.J., Luu, J.X., 1998. Accretion in the early Kuiper belt. I.

Coagulation and velocity evolution. Astron. J. 115, 2136–2160.

Kenyon, S.J., Luu, J.X., 1999a. Accretion in the early Kuiper belt. II.

Fragmentation. Astron. J. 118, 1101–1119.

Kenyon, S.J., Luu, J.X., 1999b. Accretion in the early outer Solar

System. Astrophys. J. 526, 465–470.


Lellouch, E., Moreno, R., Ortiz, J.L., Paubert, G., Doressoundiram,

A., Peixinho, N., 2002. Coordinated thermal and optical observa-

tions of trans-neptunian object (20000) Varuna from Sierra

Nevada. Astron. Astrophys. 391, 1133–1139.

Levison, H.F., Stern, S.A., 2001. On the size dependence of the

inclination distribution of the main Kuiper belt. Astron. J. 121,

1730–1735.

Margot, J.L., Trujillo, C., Brown, M.E., Bertoldi, F., 2002.

The size and albedo of KBO 2002 AW197. Bull. Am. Astron.

Soc. 34, 871.

Morbidelli, A., Brown, M.E., 2005. The Kuiper belt and the

primordial evolution of the Solar System. In: Festou, M., et al.

(Eds.), Comets II. University of Arizona Press, Tucson, pp.

175–191.

Morbidelli, A., Emel’yanenko, V., Levison, H.F., 2004. Origin and

orbital distribution of the trans-Neptunian scattered disc. Mon.

Not. R. Astron. Soc. 355, 935–940.

MPC: Minor Planet Center, 2005. http://cfa-www.harvard.edu/cfa/ps/

mpc.html

Nakamura, R., Sumikawa, S., Ishiguro, M., Mukai, T., Iwamuro, F.,

Terada, H., Motohara, K., Goto, M., Hata, R., Taguchi, T.,

Harashima, T., Kaifu, N., Hayashi, M., Maihara, T., 2000. Subaru

infrared spectroscopy of the Pluto-Charon system. Publ. Astron.

Soc. Jpn 52, 551–556.

Noll, K.S., Stephens, D.C., Grundy, W.M., Osip, D.J., Griffin, I.,

2004a. The orbit and albedo of trans-neptunian binary (58534)

1997 CQ29. Astron. J. 128, 2547–2552.

Noll, K.S., Stephens, D.C., Grundy, W.M., Griffin, I., 2004b. The

orbit, mass, and albedo of transneptunian binary 1999 RZ253.

Icarus 172, 402–407.

Ortiz, J.L., Sota, A., Moreno, R., Lellouch, E., Biver, N., Doressoun-

diram, A., Rousselot, P., Gutierrez, P.J., Marquez, I., Gonzalez

Delgado, R.M., Casanova, V., 2004. A study of trans-neptunian

object 55636 (2002 TX300). Astron. Astrophys. 420, 383–388.

Osip, D.J., Kern, S.D., Elliot, J.L., 2003. Physical characterization of

the binary Edgeworth-Kuiper Belt Object 2001 QT297. Earth,

Moon, Planets 92, 409–421.

Peixinho, N., Boehnhardt, H., Belskaya, I., Doressoundiram, A.,

Barucci, M.A., Delsanti, A., 2004. ESO large program on Centaurs

and TNOs: visible colors—final results. Icarus 170, 153–166.

Petit, J.-M., Mousis, O., 2004. KBO Binaries: how numerous were

they? Icarus 168, 409–419.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992.

Numerical RECIPES in FORTRAN. The Art of Scientific

Computing. Cambridge University press, Cambridge.

Russell, H.N., 1916. On the albedo of the planets and their satellites.

Astrophys. J. 13, 173–196.

Schulz, R., 2002. Trans-neptunian objects. Astron. Astrophys. Rev. 11,

1–31.

Sekiguchi, T., Boehnhardt, H., Hainaut, O.R., Delahodde, C.E., 2002.

Bicolour lightcurve of TNO 1996 TO66 with the ESO-VLT. Astron.

Astrophys. 385, 281–288.

Sheppard, S.S., Jewitt, D.C., 2002. Time-resolved photometry of

Kuiper belt objects: rotations, shapes, and phase functions. Astron.

J. 124, 1757–1775.

Stern, S.A., 1995. Collisional time scales in the Kuiper disk and their

implications. Astron. J. 110, 856–868.

Stern, S.A., 2002. Implications regarding the energetics of the

collisional formation of Kuiper belt objects. Astron. J. 124,

2300–2304.

Stern, S.A., Levison, H.F., 2000. Regarding the criteria for planethood

and proposed planetary classification schemes. Trans. IAU 2000.

Thebault, P., Doressoundiram, A., 2003. Colors and collision rates

within the Kuiper belt. Problems with the collisional resurfacing

scenario. Icarus 162, 27–37.

Tholen, D., Buie, M.W., 1997. Bulk properties of Pluto and Charon.

In: Stern, S.A., Tholen, D. (Eds.), Pluto and Charon. University of

Arizona Press, Tucson, pp. 193–219.

Thomas, N., Eggers, S., Ip, W.-H., Lichtenberg, G., Fitzsimmons, A.,

Jorda, L., Keller, H.U., Williams, I.P., Hahn, G., Rauer, H., 2000.

Observations of the trans-neptunian objects 1993 SC and 1996

TL66 with the Infrared Space Observatory. Astrophys. J. 534,

446–455.

Tiscareno, M.S., Malhotra, R., 2003. The dynamics of known

centaurs. Astron. J. 126, 3122–3131.

Trujillo, C.A., Jewitt, D.C., Luu, J.X., 2001a. Properties of the trans-

neptunian belt: statistics from the Canada–France–Hawaii Tele-

scope survey. Astron. J. 122, 457–473.

Trujillo, C.A., Luu, J.X., Bosh, A.S., Elliot, J.L., 2001b. Large bodies

in the Kuiper belt. Astron. J. 122, 2740–2748.

Veillet, C., Parker, J.Wm., Griffin, I., Marsden, B., Doressoundiram,

A., Buie, M., Tholen, D.J., Connelley, M., Holman, M.J., 2002.

The binary Kuiper-belt object 1998 WW31. Nature 416, 711–713.

Yelle, R.V., Elliot, J.L., 1997. Atmospheric structure and composition:

Pluto and Charon. In: Stern, S.A., Tholen, D. (Eds.), Pluto and

Charon. University of Arizona Press, Tucson, pp. 347–390.

Yelle, R.V., Lunine, J.I., Pollack, J.B., Brown, R.H., 1995. Lower

atmospheric structure and surface–atmosphere interactions on

Triton. In: Cruikshank, D.P. (Ed.), Neptune and Triton. The

University of Arizona Press, Tucson.

http://cfa-www.harvard.edu/cfa/ps/mpc.html

http://cfa-www.harvard.edu/cfa/ps/mpc.html

Documents

Higher albedos and size distribution of large transneptunian objects