Icarus 183 (2006) 283–295www.elsevier.com/locate/icarus

Combined modeling of thermal evolution and accretion of trans-neptunianobjects—Occurrence of high temperatures and liquid water

Rainer Merk ∗, Dina Prialnik

Department of Geophysics and Planetary Sciences, Tel Aviv University, P.O.B. 39040, Ramat Aviv, Tel Aviv 61390, Israel

Received 8 September 2005; revised 20 February 2006

Available online 5 April 2006

Abstract

We have calculated the early thermal evolution of trans-neptunian objects by means of a thermal evolution code that takes into account simulta-neous accretion. The set of coupled partial differential equations for 26Al radioactive heating, transformation of amorphous to crystalline ice andmelting of water ice was solved numerically for small porous icy (cometary-like) bodies growing to final radii between 2 and 32 km and accretingbetween 20 and 44 AU. Accretion within a swarm of gravitationally interacting small bodies was calculated self-consistently with a simple accre-tion algorithm and thermal evolution of a typical member of the swarm was tracked in a parameter-space survey. We find that including accretionin numerical modeling of thermal evolution leads to a broad variety of thermally processed icy bodies and that the early occurrence of liquid waterand extended crystalline ice interiors may be a very common phenomenon. The pristine nature of small icy bodies becomes thus restricted to aparticular set of initial conditions. Generally, long-period comets should be more thermally affected than short-period ones.© 2006 Elsevier Inc. All rights reserved.

Keywords: Accretion; Asteroids; Comets; Kuiper Belt objects; Thermal histories

1. Introduction

NASA’s Deep Impact mission to Comet P/Tempel 1 atteststo the increasing interest in questions related to internal thermalprocessing and the possible pristine nature of small icy bod-ies of the Solar System. Comets as well as Kuiper Belt objects(KBOs) formed far away from the Sun at heliocentric distancesof more than 20 AU. Given the low ambient temperature of thatregion (Bell et al., 1997), they are expected to reveal an original(or pristine) composition. Thus space missions to comets maybe considered a way to obtain information about the very earlystages of the Solar System.

Alterations of icy planetesimals, however, have taken place.Impacts, insolation and particle radiation are examples of fac-tors that can affect the surface and the outermost layers of icyplanetesimals. But more importantly, radioactive decay of iso-topes contained in dust, providing a volume-energy source, maylead to changes in the deeper interior, eventually progressing

* Corresponding author. Fax: +972 3 640 9282.E-mail address: merkrain@post.tau.ac.il (R. Merk).

0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2006.02.011

outward, such as crystallization of amorphous ice and phasetransitions of volatile species. In comparison to planets, radi-ogenic heating of comets (and asteroids) is less effective due totheir large surface-to-volume ratio. However, if the heat sourceis strong enough, this picture may change. An ideal candidatefor altering comets and asteroids is the radioactive isotope 26Al,abundant in the dust of the early Solar System (MacPherson etal., 1995). On the timescale of planetary evolution, this isotopeis short-lived (with a half-life of 0.72 Ma). Therefore, it cannotalter planets, which appear much later than planetesimals in theaccretion scenario of planetary bodies, after most of the 26Alnuclei have already decayed.

However, it was shown that an early heat pulse generatedby 26Al decay may have significantly modified asteroids (e.g.,Wood, 1979; Miyamoto et al., 1981; Ghosh and McSween,1998; Akridge et al., 1998; Merk et al., 2002). In the case ofcomets, the work by Irvine et al. (1980) and Wallis (1980)predicted possible melting of water ice and prompted a se-ries of studies devoted to radiogenic heating of comets and icysatellites (Schubert et al., 1981; Ellsworth and Schubert, 1983;Prialnik et al., 1987; Haruyama et al., 1993; Yabushita, 1993;De Sanctis et al., 2001; for a review cf. Podolak and Prialnik,

284 R. Merk, D. Prialnik / Icarus 183 (2006) 283–295

1997). A more recent work by Choi et al. (2002) led to the con-clusion that insolation and radiogenic heating might lead to asubstantial loss of volatiles within KBOs.

These investigations have shown that perhaps the pristine na-ture of small icy bodies should not be taken for granted. Rather,what is required is a closer study of the early stage of evo-lution of planetesimals, when formation (accretion) and earlyradiogenic heating by 26Al could have altered the original ma-terial out of which comets and KBOs eventually formed. Usu-ally, accretion of small bodies and heating by 26Al are treatedseparately in numerical calculations, although these processesactually take place in parallel. The half-life of 26Al and typicalformation times of small bodies are both of the order of 1 Ma(Wetherill and Stewart, 1989).

The common procedure adopted for including accretion inthe framework of thermal evolution calculations has been toimpose a time shift to the decay law of 26Al, allowing for thespan of time needed for the small bodies to accrete to their fi-nal sizes (e.g., Ghosh and McSween, 1998). The justificationwas that the surface-to-volume ratio of accreting seed bodies issuch that any alteration of the material during accretion couldbe neglected (Miyamoto et al., 1981). Furthermore, the longaccretion times calculated for objects in the outer Solar Sys-tem (Kenyon and Luu, 1998), led to the conclusion that majorchanges of small icy bodies could be neglected altogether. How-ever, more recently, both analytical and numerical calculationshave demonstrated the significant influence of the accretionprocess on the thermal history of small planetary bodies (Merket al., 2002; cf. Merk and Prialnik, 2003, in the case of trans-neptunian objects). Thus consideration of accretion in thermalevolution calculations may lead to a revision of the commonpicture of the early thermal behavior of these bodies and, con-sequently, of their pristine nature.

2. Modeling simultaneous internal heating and accretion

2.1. Estimates

In a previous work (Merk and Prialnik, 2003, hereafter Pa-per I), we addressed the question whether the combined effectof accretion and radioactive heating of icy planetesimals can beestimated analytically. To this purpose, it is sufficient to con-sider a simple accretion law that shows saturation for t → ∞.Such simple law for the planetesimal mass Mp(t) is, for exam-ple

(1)Mp(t) = Mpmax(1 − e−t/θ

).

Here, θ is the accretion time constant of the respective body.The accreted material contains radioactive 26Al within a massfraction

(2)X(t) = X0e−t/τ ,

where τ denotes the time constant of radioactive 26Al nuclei.Thus we showed in Paper I that, because planetesimal accretionand radioactive decay proceed in parallel and on the same timescale (θ ≈ τ ), effective heating starts already when a planetes-imal has yet to accrete half of its final mass while the accreted

material still contains half the original amount of live 26Al. Itis therefore necessary to treat radioactive heating and spatialgrowth (accretion) of planetesimals simultaneously.

In technical terms, this means that the governing set of par-tial differential equations has to be formulated on a domainwhose boundary changes with time. Such boundary value prob-lems are often referred to as moving boundary problems andtheir mathematical and numerical treatment is known to be non-trivial (Ockendon and Hodgkins, 1975; Albrecht et al., 1982; cf.Merk et al., 2002, in the case of moving boundary problems ofasteroids).

2.2. Governing equations

The thermal evolution model used here was already de-scribed in Paper I. To summarize, we have developed a 1Dcode that numerically solves the heat transport equation writ-ten in terms of energy density u, depending on mass (m) andtime coordinate (t ). We assume a spherically symmetric body,consisting of ice (in a mass fraction Xice) and dust (in a massfraction Xd). We consider only water ice; the dust componentis assumed to include any non-volatile material present in icybodies. Given the specific densities of the components and theporosity p, the bulk density ρp is obtained. The model al-lows for amorphous-ice crystallization and melting of water ice,amorphous ice being contained within a fraction Xa and liq-uid water within a fraction Xw of the water ice. Heat sourcesare due to radioactive 26Al within the dust fraction (associ-ated with the radioactive energy per unit mass H) and to thelatent heat released in the transition from amorphous to crys-talline ice (associated with the energy Hac). Significant impactheating during formation can be ruled out as a first approxima-tion, as was already shown in earlier studies (Merk et al., 2002;Squyres et al., 1988; Orosei et al., 2001). This is justified by thelow relative velocities of planetesimals in comparison to ve-locities found in the belts of small bodies nowadays (Wetherilland Stewart, 1989). A rough estimate of the increase in surfacetemperature �T due to impact events during the accretion stagegives �T = v2/cp < 1 K, with v and cp denoting impact veloc-ity and specific heat of ice, respectively, assuming v ≈ 100 m/s(Wetherill and Stewart, 1989).

In the following, the local heat balance is expressed in termsof the divergence of the heat flux F(m, t), which is determinedby the temperature-dependent thermal conductivity K(T )

(3)∂u

∂t= −∂F (m, t)

∂m+ XiceXa(m, t)Hac + 1

τXdX0He−t/τ ,

(4)F(m, t) = −K(T )

[4π

(3m

4πρp

) 23]2

∂T

∂m.

The propagation of cystallization is described by an additionaldifferential equation, which is solved in parallel during thecourse of thermal evolution. With the crystallization rate λ(T )

(cf. Table 1 and Schmitt et al., 1989) and planetesimal mass Mp,the equation reads

(5)Xa + Mp

MXa = −λXa.

p

Combined thermal evolution and accretion of TNOs 285

Table 1Material properties

Property Value Unit

β 40ca, cc 7.49T + 90 J kg−1 K−1

cd 770 J kg−1 K−1

cw 4186 J kg−1 K−1

Hac 9 × 104 J kg−1

Hw 3.34 × 105 J kg−1

H 1.48 × 1013 J kg−1

Ka 2.11 × 10−3T + 2.5 × 10−2 W m−1 K−1

Kc 567/T W m−1 K−1

Kd 0.1 W m−1 K−1

Kw 0.55 W m−1 K−1

λ 1.05 × 1013e−5370/T s−1

p 0.5ρd 3500 kg m−3

ρice 900 kg m−3

ρp (1 − p)/(Xice/ρice + Xd/ρd) kg m−3

τ 3.345 × 1013 s

X0 6.7 × 10−7 from c(26Al)c(27Al)

= 5 × 10−5 (canonical)

Xa 1 (prior to onset of heating)

We note that the differential equations are linked and the sys-tem (3)–(5) is solved simultaneously.

Local energy densities uα are connected to the local tem-perature as integrals over the respective heat capacities cα ,uα = ∫

cα(T )dT + const. If indices are chosen as above, u(T )

reads

u(T ) = Xice{[

1 − Xw(T )]uice(T ) + Xw(T )[Hw + cwT ]}

(6)+ XdcdT .

Here, the latent heat needed to melt water ice is included in Hw.The last equation shows that melting of water ice is described inan energetically correct manner. In this study, we approximatesharp melt fronts by a smoothed profile for Xw (Weizman et al.,1997), depending on the local temperature. The liquid fractionreads (Tw: melting temperature of water ice)

(7)Xw(T ) = 1

1 + eβ(1−T/Tw).

This melt front is close to a step function (the steepness be-ing determined by β), i.e., it guarantees, in a mathematicallysmooth manner, Xw = 1 for T � Tw, Xw = 0 for T � Tw, andXw = 0.5 for T = Tw.

The thermal conductivity was calculated from the contri-butions of water ice, liquid water and dust by the followingformula, Ki denoting the thermal conductivities of the corre-sponding materials or phases, respectively (i = ice, dust, w, forwater ice, dust and liquid water)

(8)

K(T ) = ψ(p)[Xice

(1 − Xw(T )

) · Kice(T )

+ (1 − Xice) · Kdust] + XiceXw(T ) · Kw,

(9)

Kice(T (m, t)

) = Xa(m, t) · Ka(T (m, t)

)+ [

1 − Xa(m, t)] · Kc

(T (m, t)

).

The factor ψ(p) < 1 stands for a porosity-dependent correc-tion factor due to the grainy structure of the solid material. The

last equation shows the thermal conductivity of ice. It is builtas a weighted average from the contributions of amorphousand crystalline ice, Ka and Kc, respectively. Values and lawsfor the various thermal conductivities can be found in Table 1;Ka and Kc are taken from to the work by Klinger (1980). Theapproach taken in Eq. (9) for a mixture of materials is widelyused, but there are other ways of combining thermal conductiv-ities (Sirono and Yamamoto, 1997).

A change in porosity due to possible shrinkage effects is notincluded here. The effect of porosity on the thermal conduc-tivity of the material is still poorly known. Given the densitiesof ice and liquid water, if one assumes a porosity change uponmelting of about 10%, the resulting change in the thermal con-ductivity correction factor is well within the presently knownerror (cf. Prialnik et al., 2004). Assuming a hypothetical com-pletely molten body, a 10% volume loss due to shrinkage re-sults in shrinkage in terms of radius of about 3% only. In viewof the still existing solid silicate matrix, the porosity changeupon melting might be even smaller. Radial shrinkage as con-sequence of the phase transition can therefore be neglected asa first approximation. However, the phase transition to liquidwater alters the (bulk) values within the expression for K signif-icantly, since Kw � Kice. The model does not include internalsublimation of ice and possible advection of heat by flowingvapor; it is thus implied that the permeability of the medium isvanishingly low.

The initial and boundary conditions are

(10)T (m,0) = Te(dH),

(11)F(0, t) = 0,

(12)

F(Mp(t), t

) = 4π

(3Mp(t)

4πρp

) 23 [

εσT 4(Mp(t), t) − σT 4

e (dH)],

where Te is the temperature of the ambient nebula at helio-centric distance dH, and ε and σ are the usual symbols foremissivity and Stefan–Boltzmann constant, respectively. In ourmodels, nebula temperatures Te decline from 20 K (20 AU) to10 K (44 AU) (Bell et al., 1997). The last equation shows thata moving boundary problem has to be solved. We thus employa coordinate transformation by dynamical scaling of the masscoordinate (Merk et al., 2002):

(13)η(m, t) = m

Mp(t),

(14)

(∂

∂m

)t

= 1

Mp(t)

(∂

∂η

)t

,

(15)

(∂

∂t

)m

=(

∂

∂t

)η

+(

∂η

∂t

)m

(∂

∂η

)t

(16)=(

∂

∂t

)η

− η

Mp(t)

dMp

dt

(∂

∂η

)t

.

The system of partial differential equations was solved numeri-cally by use of an implicit finite difference scheme.

A crucial ingredient of the model is the accretion ratedMp/dt of the planetesimal. Thus either an analytic law or a

286 R. Merk, D. Prialnik / Icarus 183 (2006) 283–295

set of data for dMp/dt has to be fed into the system of differen-tial equations given above. The ultimate goal is to calculate howaccretion interferes with radiogenic heating of planetesimals lo-cated in various regions of the accretion disk. Therefore, a moreelaborate treatment of accretion itself becomes necessary.

Current models of planetesimal accretion assume an accre-tion zone of about 1010 interacting planetesimals circling withinthe accretion disk around the early Sun. The evolution of thenumber spectrum is calculated numerically, usually by adopt-ing a statistical approach, which is due to the large number ofbodies in the accretion zone. Basic numerical studies date backto the work of Wetherill and Stewart (1989) and Spaute et al.(1991). It was only recently that planetesimal coagulation couldbe modeled as an N-body problem by means of supercomputers(Inaba et al., 2001). The work by Wetherill and Stewart (1989)showed that an embryo-sized protoplanetary body can form ona timescale of 105 years in the terrestrial zone at about 1 AU(runaway growth), much faster than predicted by earlier stud-ies (Safronov, 1969). Wetherill and Stewart (1989) concludedthat it is inevitable to include the evolution of velocities in sta-tistical accretion modeling. The same approach was adopted byKenyon and Luu (1998) to model planetesimal accumulation inthe Kuiper Belt zone.

For studying radiogenic heating of accreting planetesimals,the detailed evolution of the accretion disk or the runaway bodyis of no concern; rather, what one needs is a reliable accretionrate of an average planetesimal within the accretion disk at agiven heliocentric distance, since thermal evolution studies ofsmall bodies refer to a broad variety of planetesimals, later onto become comets, KBOs or transition objects. The aim is tohave a simple accretion algorithm that can be applied to any he-liocentric distance in order to produce a typical accretion ratedMp/dt for a representative small body within the swarm. Sucha simple accretion algorithm was described in Paper I. It con-tains the basic features of a numerical accretion model such asappropriate statistical treatment of small bodies and inclusionof velocity evolution. It reproduces results for planetesimal ac-cretion in the asteroid belt zone (e.g., Weidenschilling, 2000).Accretion time-scales produced with this algorithm are in fairagreement with what is presently known about KBO accretiontheory (Kenyon and Luu, 1998).

Briefly, the accretion algorithm starts with the set of coagu-lation differential equations (cf. Paper I for all details) for thenumber spectrum Ni(t) of an accretionally evolving swarm ofplanetesimals

(17)

dNi

dt= −

∑j

(1 + δij )Aij→k

V

NiNj

1 + δij

+∑l,k�l

Alk→i

V

NlNk

1 + δlk

.

These equations represent a system of I coupled nonlinear dif-ferential equations of first order. Planetesimal masses are dis-tributed over a discrete spectrum {mi}, where Ni representsthe number of planetesimals in the corresponding mass bin i.Mass bins correspond to size bins so that planetesimal radii be-tween 100 m and 500 km can be covered, with mass bins mi andmi−1 typically separated by a factor of 1.1 (yielding I ≈ 300).The coefficients Aij→k denote accretion cross-sections (reac-

tion rates within a volume V ) of merging collisions betweenplanetesimals of masses mi and mj (Wetherill and Stewart,1989)

(18)Aij→k = π(ri + rj )2vi,j (1 + 2θi,j ).

Here, ri stands for the radius of a planetesimal and vi,j = (v2i +

v2j )

1/2 is the relative velocity of the particles. In addition, thegeometrical cross-section is enhanced by the Safronov-factordue to gravitational focusing (Greenzweig and Lissauer, 1990;Wetherill and Stewart, 1989)

(19)θi,j = G(mi + mj)

(ri + rj )v2i,j

.

As a crude approximation, equipartition of kinetic energy is as-sumed to calculate particle velocities during the run of the code.An accretion law for a typical representative of the planetesimalswarm can be defined by taking an averaged value

(20)〈Mp〉(t) =∑I

i=1 Ni(t)mi∑Ii=1 Ni(t)

.

Planetesimal accretion is therefore described in an entirely sta-tistical way and leads to spherically symmetric growth of a testbody in the swarm. This is basically a consequence of the sym-metric nature of the coagulation equations and of the law ofgravity used therein. Later during the evolution of planetesi-mals, after accretion was terminated, planetesimals could haveobtained their irregular shape due to mutual high-speed colli-sions. This assumption holds for chunks that did not reaccumu-late. They would continue their existence as fragments with anirregular shape. For example, SP comets are thought to repre-sent fragments of larger KBOs (Farinella and Davis, 1996). It isknown that both the asteroid belt and the Kuiper Belt went into acollisional stage after the termination of accretion (Farinella etal., 2000). However, detailed questions concerning disruptionand shaping of accretional and post-accretional planetesimalscan only be answered by a three dimensional model that alsoconsiders material-strength arguments and is beyond the scopeof the present paper.

3. Numerical calculations

3.1. General approach

The present paper describes a detailed 2-parameter studyfor the early evolution of icy planetesimals. One free parame-ter is the formation distance, taken to vary between 20 and44 AU, i.e., between the orbit of Uranus and the present-day Kuiper Belt zone. The second free parameter is the finalradius, Rpmax, upon completion of accretion, over the range2 km � Rpmax � 32 km. The basic parameter space of this studyis thus the (dH,Rpmax)-parameter plane. Results are presentedas third coordinate over this parameter space in the form ofcontour plots. Another parameter for which different genericvalues are assumed relates to the initial composition. How-ever, since a numerical parameter study using a moving gridis a time-consuming task, we decided to restrict it to three ini-tial homogeneous compositions, i.e., three values for the mass

Combined thermal evolution and accretion of TNOs 287

fraction of ice, equally spaced logarithmically: Xice = 0.9 (ice-rich), Xice = 0.45 (ice and dust in about equal parts), andXice = 0.225 (ice-poor). Cometary models usually assume a 1:1composition of dust and ice and hence in the following, the caseXice = 0.45 shall be referred to as the nominal composition.As the composition of KBOs is not yet known, we decided tostudy the compositional extreme cases in order to quantify devi-ations from a median composition. For input parameters such asporosity, thermal conductivity, specific heat and latent heat, weassume standard values commonly used in numerical model-ing of comets and asteroids. They are listed in Table 1 (adaptedfrom Klinger, 1980; Schmitt et al., 1989; Haack et al., 1990;Alexiades and Solomon, 1993; Bennett and McSween, 1996).

3.2. Accretion times of the average TNO in the accretion disk

Using the accretion algorithm described above, we may cal-culate average accretion times for bodies located in the para-meter space spanned by maximal radius Rpmax and heliocentricdistance dH, cf. Fig. 1 for the compositions Xice = 0.9, 0.45and 0.225 (Fig. 1, top to bottom). We used the model by Bellet al. (1997) as an input for ρ(dH), Te(dH), the spatial mid-plane density of material in the accretion disk and the ambienttemperature, respectively. This model gives a declining spatialplanetesimal density with increasing heliocentric distance.

The relatively long accretion times of KBOs in compari-son to asteroids could be confirmed by this survey (Kenyonand Luu, 1998; Wetherill and Stewart, 1989; Weidenschilling,2000). Accretion times range between 1 and more than 20 Ma(for a nominal composition). In general, ice-rich planetesimalsaccrete faster than the ice-poor ones. This is a material-densityeffect and explained if one looks at equal final sizes but differentcompositions. The effect has contributions due to the coeffi-cients Aij→k that contain the radii. A full theoretical analysisof the accretion algorithm presented above requires scaling ofthe system of differential equations. The only free parametersof this model are the total mass M of planetesimals within acontrol volume, the size of the control volume and the bulk (in-herent) density of the material. Alternatively, total mass, spatialdensity ρ of planetesimals in the midplane of the accretion diskand bulk density ρp were used in this study. Analysis of the co-agulation equations then leads to the following scaling law forthe mass accretion rate m of an accreting planetesimal

(21)m ∝ Mρ7/5ρ−9/10p .

Furthermore, the scaling shows that planetesimals locatedcloser to the Sun accrete faster than the more distant ones, asthis is what one would expect in a nebula with radially decreas-ing spatial density.

For the extreme ice-poor composition (Xice = 0.225), themost distant and largest KBOs need up to 50 Ma to reachtheir final size. It is therefore clear that a thermal evolutioncalculation based on a mere time shift in the activity of 26Al,would completely miss any internal changes of such bodies.The smallest bodies of 2 km size, however, can always be ac-creted within less than 2 Ma. Accretion times vary considerably

Fig. 1. Duration of accretion of icy planetesimals for Xice = 0.9 (top),Xice = 0.45 and Xice = 0.225 (bottom), calculated with a self-consistent accre-tion algorithm (cf. Section 2.2 for details). The abscissa denotes the radius ofplanetesimals upon completion of accretion. The ordinate is the location withinthe protoplanetary cloud.

for bodies around 30 km radius. The steep gradients in the con-tours already indicate that a variety of thermal evolution pathscan be expected, provided internal heating is sufficient.

288 R. Merk, D. Prialnik / Icarus 183 (2006) 283–295

3.3. Peak temperatures

Temperatures obtained over the parameter plane can be con-siderably high except for the Xice = 0.9 case. In comparisonto former studies considering 26Al heating of icy small bod-ies (e.g., Choi et al., 2002), this is the most obvious new fea-ture. The assumption that, being originally very small, accretingcomets cannot be efficiently heated by 26Al is shown to fail insome cases. An early heat pulse, when the accreting body isstill relatively small can lead to an early increase in temper-ature provided the amount of live 26Al is high enough (read:the dust fraction is high enough while the duration of accretionis short enough). The heat pulse cannot be properly resolvedin long-term evolution models if it is modeled by a mere timeshift imposed on the decay law of 26Al in order to account forthe accretion time.

Temperatures were already discussed in Paper I for the nom-inal case. This composition results in peak temperatures be-tween 140 and about 350 K, depending on the location of theplanetesimal. Almost all icy planetesimals originally locatedbetween the present-day orbits of Uranus and Neptune attainpeak temperatures allowing for liquid water. However, an icefraction of Xice = 0.9 leads to overall peak temperatures be-low 110 K. In case the ice-to-dust ratio approaches the nominal1:1 composition, liquid water is obtained. If the dust content isfurther increased, temperatures rise considerably. Upon passinga certain threshold, the 26Al-energy supply appears to becomeunbounded. This effect is well known from modeling accretingasteroids (Merk et al., 2002), where in some cases the interiorcan melt almost up to the surface.

For icy planetesimals, additional effects (like steam, openingof cracks and so forth) become important if temperatures fur-ther increase to the boiling point of water. The present modelis not adapted to deal with these conditions. Therefore, resultsobtained upon reaching a threshold of about 370 K have to beregarded with caution. However, the calculations do show thatan icy planetesimal has the potential to undergo even extremeinternal metamorphism in some cases.

As an example, temperatures obtained for the lowest icecontent (Xice = 0.225) are shown in Fig. 2 (top), demonstrat-ing that very high temperatures are possible well within theKuiper Belt zone. In the neptunian zone, such high dust con-tents would probably result in a disruption of bodies above 4 kmradius. Nearly horizontal contours for larger radii result fromthe inability of planetesimals to compensate for progressive ra-dioactive decay of 26Al by further accretion of material duringthe late stage of accretion. The decline in temperature towardhigher heliocentric distances is caused by the slower accretionalgrowth of the more distant bodies as compared to those accretedcloser to the Sun: the more distant planetesimals accrete slowly,hence they remain small for a prolonged period of time and can-not store the heat provided by radioactive decay. Fig. 2 (bottom)demonstrates how temperatures decline if the ice content is in-creased to 90%. The thermodynamic behavior shows similartrends over the parameter space but it is obvious that no melt-ing is possible for this composition.

Fig. 2. Example of high peak temperatures in accreting planetesimals (cf. Fig. 1)in case the dust fraction is brought to the maximal value of 0.775 (top; ice-poorcomposition). The other extreme is shown below: a minimal dust content of 0.1only (bottom; ice-rich composition) results in less 26Al and therefore in lowertemperatures throughout. Planetesimals are located in the parameter space ofmaximal radius upon completion of accretion and original heliocentric distance.Axes are the same as those in Fig. 1.

3.4. Transition from amorphous to crystalline ice

Transition from amorphous to crystalline ice is a well-knownenergy source in cometary thermal evolution (Patashnik et al.,1974; Prialnik and Bar-Nun, 1987). With some justification,crystallization fronts could also be regarded as indicators ofa transition zone from pristine to more processed cometarymaterial. Jewitt and Luu (2004) reported evidence for crys-talline water ice on the surface of Kuiper Belt Object (50000)Quaoar. This discovery suggests possible exposure of formerlyprocessed internal ice by an impact event or by cryovolcanicoutgassing. It is an example showing the necessity to study thecrystallization process in the framework of radiogenic heatingand accretion.

Transition occurs around 100 K (Schmitt et al., 1989), wherethe timescales of crystallization and radioactive decay becomecomparable. We focus on the model with highest ice content

Combined thermal evolution and accretion of TNOs 289

Fig. 3. Crystalline-ice fraction inside accreting icy planetesimals (top) and du-ration of the crystallization process (bottom), both calculated for ice-rich smallbodies (Xice = 0.9). The contours in the top part of the figure show the fraction0 < Rac/Rpmax < 1, where Rac is the radius of the interior crystallized zoneand Rpmax denotes the radius of the planetesimal upon completion of accretion(cf. Section 3.4 for a description). Axes are the same as those in Fig. 1.

(Xice = 0.9), as this is the one with the lowest peak temper-atures. In the top part of Fig. 3, the level of crystallization isshown as contours over the parameter plane. Crystallizationis triggered by radioactive heating, which is a volume-energysource. Thus the crystallization front will progress outward,leaving interior crystalline ice behind and advancing into anamorphous-ice ‘mantle.’ The contour levels show the fraction0 < Rac/Rpmax < 1, where Rac is the radial location of thefront.

We note that over the entire parameter space the 2 km plan-etesimals retain the initial amorphous ice. For bodies with lowerice content on the other hand, one can always expect somecrystalline ice in the interior. We further note the occurrenceof a peak in all contours, located between final radii of 8 and12 km. This apparently unexpected result can be understoodby comparing the duration of accretion (Fig. 1, top) and that ofcrystallization (Fig. 3, bottom). Our calculations show that crys-tallization always starts within the first few 105 yr of the evolu-

tion, when accretion is not yet completed and thus the durationof accretion and crystallization are comparable. In particular,the contours are similar in that region of the parameter spacewhere the peak in the contours of the crystalline ice fraction,Fig. 3 (top), is observed. Prialnik (1993) found an expressionfor the velocity of the crystallization front by comparing thecharacteristic width of the front with the time-constant τac ofthe crystallization process. The velocity depends on a charac-teristic temperature θ within the front and can be estimated byvF(θ) = (κ/τac(θ))1/2, with an experimentally determined con-stant κ . Choosing θ � 100 K gives roughly vF = 6 km/Ma.A similar value is obtained for the average accretion rate in themedium range of the parameter space. Hence advancing accre-tion and crystallization fronts move at about the same speedoutward. This coupling can be broken in two ways: either accre-tion will outlive crystallization, as may happen for large bodies,since crystallization depends on the amount of live 26Al andthus will eventually cease, as seen in the top-right corner ofthe parameter plane; or crystallization will outlive accretion (asseen in the bottom part of the figure), meaning that accretionwill stop while the crystallization front is still advancing. Thecrystallization front will eventually stop, too, when it will reachcolder regions closer to the surface, since the surface will nolonger be moving.

In conclusion, the behavior of Rac/Rpmax over the parame-ter space leads to a broad variety of possible internal zoningsof small icy bodies, when accretion is taken into considerationalong with radiogenic heating. A larger radius can mean lessalteration of pristine material, a conclusion otherwise valid forsmaller radii. Furthermore, an entirely pristine interior is diffi-cult to preserve even in the case of the smaller members of theplanetesimal family, located in the colder regions of the outerSolar System. Fig. 3 shows that the zone of entirely pristine icybodies is restricted to a narrow region close to the Rpmax = 2 kmiso-line between 20 and 44 AU in the parameter space. We haveshown earlier (Paper I) that such zones vanish completely if thedust content is increased.

3.5. Liquid water

One of the most important issues when dealing with the ther-mal evolution of small icy bodies is the possible production ofliquid water. It is evident that this question is crucial for as-trobiological studies. Especially the span of time during whichwater can be expected to be liquid is of interest here. It is knownthat comets may contain large organic molecules and may evenhave contributed to the evolution of life (Thomas et al., 1997;Lewis, 1995). If, in addition, water would be (moderately)warm, an energy source to trigger bio-organic reactions wouldbe available. It would thus be interesting to correlate the cal-culated duration of the liquid-water stage with minimum-timespans necessary to maintain basic biochemical reactions. Liq-uid water in comets has long been addressed: Irvine et al. (1980)and Wallis (1980) showed that the potential to melt water ice ex-ists. Later studies, although more detailed, usually neglected theeffect that accretion might have on the early thermal evolutionof icy bodies. In a study by Prialnik and Podolak (1995), melt-

290 R. Merk, D. Prialnik / Icarus 183 (2006) 283–295

ing of water ice for a non-porous, non-accreting 20 km cometnucleus was investigated, and melting proved to be possible.However, considering large porosity led to substantially low-ered temperatures. The authors used 26Al as heat source butimposed a time-shift to the radioisotope in order to account foraccretion. Due to the very different accretion times of bodiesin the outer range of the Solar System (see Fig. 1), the inves-tigation of possible liquid water inside icy planetesimals mustconsider accretion in a self-consistent manner, as we attempt inthis paper.

We mentioned in Paper I that temperatures inside small icybodies with an ice fraction of less than 0.45 allow for the exis-tence of liquid water in a broad region of the parameter space.For a nominal (1:1) composition of dust and ice, all planetes-imals above a final radius of 4 km, originally located betweenthe present-day orbits of Uranus and Neptune, produce liquidwater cores. Melt zones can comprise 10–90% of the interior ofa spherical body.

At 20 AU, planetesimals above a final radius of 8 km ex-perience a boost in melting and core temperatures close to theboiling point of water are easily reached. That the energy sup-ply by 26Al decay is sufficient to melt an icy planetesimal canbe shown by a simple estimate. Integrated over the entire evo-lution of a 32 km planetesimal, the energy supply of 26Al canbe estimated as (

∫ ∞0 Qrad(t)dt) · Mp = O(1023 J). However,

the amount of energy required for melting all the water ice in-side this body is smaller by one order of magnitude. It can beassumed that upon reaching a value of about 370 K, the iceof the outer layers of an icy planetesimal cannot withstand thebuildup of internal pressure. In all likelihood, this results in thedisruption of the planetesimals as a whole or at least in frag-mentation into larger chunks accompanied by rapid re-freezing.This is especially to be expected when the interior is alreadymolten to a large extent. A lower estimate for the tensile stresslevel causing an ice crust to burst was provided by Sirono andYamamoto (1999) as 106 dyn/cm2 (105 Pa). For H2O, the pres-sure of steam associated with 370 K on the Clausius–Clapeyroncurve is in the same range.

We calculated for how long a liquid interior can be expected.For the nominal composition of dust and ice, the result is shownin Fig. 4 (top): the liquid-water zone in the parameter space isapproximately located between 20 and 30 AU and final radiiin excess of about 6 km. The case of planetesimals that expe-rienced fierce internal heating deserves special consideration.Since there is reason to assume that temperatures above approx-imately 370 K lead to a disruption of the body, the computercode was designed to interrupt the calculation at this point.Otherwise, the span of time, �t , for liquid water to exist wasobtained from the time difference between first occurrence ofliquid water and total refreezing.

Heating and warm-water interiors can only be maintainedby sufficient 26Al activity and by sufficient accumulation ofradioactive material due to accretion. Accretion, furthermore,increases the thermal insulation of the warm interior. The 26Alactivity eventually ceases, and thus upon passing a maximumin the energy input, the thermal evolution proceeds regardlessof the body’s final radius. This holds for any given heliocen-

Fig. 4. Time spans during which accreting planetesimals can be assumed tocontain liquid water, calculated for a ≈1:1 (top) composition of ice and dust.The bottom part of the figure shows the same span of time for ice-poor plan-etesimals (Xice = 0.225). Axes are the same as those in Fig. 1.

tric distance and explains the horizontal contours in Fig. 4.Along a constant-Rpmax-line, a maximum for �t is obtainedat about 26 AU. The liquid-water zone in the parameter spaceis therefore demarcated by the present-day orbits of Uranusand Neptune. Within the present-day orbit of Uranus, plan-etesimals experienced internal heating too fierce to allow for aprolonged existence of liquid water. On the other hand, beyondthe present-day orbit of Neptune, bodies accreted too slowly toenable a sufficient amount of warm material to be accumulated,thus resulting in frozen interiors during the entire evolution.The more interesting zone, in this respect, is in-between, wherebodies were neither too cold nor too hot. Here, for the nomi-nal composition, liquid water can last for up to 5 Ma. No liquidwater whatsoever is obtained for the ice-rich composition.

From Fig. 2 it can clearly be seen that in the compositionallimit of high dust contents (ice-poor composition), liquid watercannot be ruled out over the entire parameter-space region stud-ied here. In our computer-runs, liquid water is always observedafter less than 1.5 Ma and in the ice-poor models, melting is ac-companied by a steep increase in temperature, characteristic for26Al. Thus not only can the liquid-water zone be shifted well

Combined thermal evolution and accretion of TNOs 291

into the EKB-region, but also planetesimals located closer tothe Sun may experience fierce internal processing in this case.The early occurrence of liquid water at such high temperaturesquestions the stability of these objects and thus also limits theduration of the liquid-water stage. The time spans for the ice-poor case Xice = 0.225 are shown in Fig. 4 (bottom).

From the accretion times calculated (Fig. 1), it is evident thatfarther away from the Sun, melting must cease at some helio-centric distance, especially given the longer accretion times fordust-rich compositional models. Therefore, in Fig. 4 (bottom)an interesting competition of opposite trends can be observed:deeper in the Kuiper Belt, around 44 AU, long accretion timeslead to colder interiors and hence shorter time spans for theliquid-water stage when compared with the nominal composi-tion. Yet, the very reason for prolonged accretion in this case isthe increased dust content, in turn leading to much higher tem-peratures where accretion times are sufficiently low. Closer tothe Sun this leads to an early disappearance of the liquid waterand in average to shorter time scales during which liquid watercan be expected. Liquid water can thus persist for up to 5 Ma inthe nominal case but only for up to 3 Ma in the ice-poor model,cf. Fig. 4 (bottom). Note however, that then the most stable zonein the parameter space retreats by more than 12 AU. Also interms of radii, the interaction of the various effects acting to-gether is not trivial. Increasing the dust content shifts highertime differences toward the smaller bodies between 2 and 12 kmin the parameter space: smaller bodies retain liquid water for alonger span of time. This is not surprising due to more live 26Al,but in comparison to the nominal model, the scenario proceedsmuch farther away from the Sun. Models with high dust con-tent reveal a kinship to accreting asteroids (Merk et al., 2002).Here, the parameter combination is such that 26Al unfolds itsfull potential as a heat source. The dust content could be fur-ther increased to model planetesimals with only traces of ice.Fig. 4 (bottom) holds for an ice content of about 23%. Thiscomposition seems to constitute an upper limit in terms of in-ternal heating. The conclusions drawn from Fig. 4 (top) holdfor Xice = 0.45, hence for a cometary-like composition.

4. Possible assignment of primordial to present-dayplanetesimal families

In some sense, the possible production of liquid water withincomets constitutes the analogue to melting of iron within as-teroids. Both processes are signs of heavy internal processingof small bodies, both processes give reason to distinguish be-tween more and less altered small planetary bodies. In the caseof asteroids, early differentiation due to thermal evolution ismost likely the reason why very different classes of meteoritescan be studied in laboratories. If one assumes that meteoritesare nothing but debris of asteroidal collisions, then an ironmeteorite would originate from the core region of a differen-tiated, hence once molten, asteroid. Similarly, a more primitivemeteorite would come from a less processed asteroidal parentbody. By this assignment, together with surface spectral analy-sis of asteroids, a rough classification of the respective sourcezones in the asteroid belt becomes possible (Lewis, 1995;

McSween, 1999). It is therefore natural to ask for a similarassignment of more and less internally processed icy planetesi-mals to the zones where those bodies can be observed.

With the accumulated knowledge about orbital dynamics ofthe outer Solar System (for an overview, cf. Mannings et al.,2000), it is clear that one must distinguish between the accretionzones of small planetary bodies (shown in our contour plots)and the orbits of icy planetoids as they are observed nowadays.Thus, it is interesting to investigate how planetesimals studiedin this work correspond to known families of planetesimals.The following shall refer to some of the main classes of icyplanetoids and is meant as a very rough sketch of what has tobe completed by more elaborate future studies. Mannings et al.(2000) give a modern overview of icy planetesimal classes ac-cording to their activity pattern, surface composition and orbitaldynamics. Besides the various sub-categories of KBOs, differ-ent comet families and transition objects (to more asteroidalcharacteristics) are known, the main distinction between cometsreferring to short-period (SP) and long-period (LP) comets.

Fig. 5 shows an attempt to assign planetesimals located invarious regions of the parameter space to known small bodyfamilies. Since the most interesting outcome of internal meta-morphism is the occurrence of liquid water, Fig. 5 is based onthe contour plot that shows the duration of the liquid-water frac-tion over the parameter plane (for the nominal composition, cf.Fig. 4), embedded in a sketch showing parts of the outer So-lar System, ranging from the present-day orbit of Uranus tothe Oort cloud. The vertical axis of the sketch represents he-liocentric distance and the contour plot ‘zooms’ into the regionbetween 20 and 44 AU. The sketch does not contain an abscissa;the location of various known planetesimal classes is indicatedsuccessively by elliptical symbols.

Several typical internal structures are considered, labeled Ato D, and structure sketches show the internal zonings in liquidwater, crystalline and amorphous ice, respectively. They weredrawn to scale, according to the results obtained from the nu-merical study (with the exception of the differentiation processthat is inferred rather than calculated). Arrows point from thesource regions in the parameter space (dH,Rpmax) to the re-spective sketches of planetesimals located there.

The basic idea is that, by gravitational scattering, planetes-imals were redistributed over the outer Solar System. Theseprocesses started during formation of Uranus and Neptune andit is known that gravitational perturbation of planetoid orbitshas lasted since then (Mannings et al., 2000). Scattering ofcountless small bodies caused migration of the jovian planetsto their present locations and can be explained by the exchangeof angular momentum. Accretion of proto-Neptune, migrationto its present position and accretion of small icy bodies in theneptunian zone is possible on the same timescale (Pollack et al.,1996; Malhotra et al., 2000). Thus, symbols of migrating Nep-tune and Uranus were added to the dH-axis in Fig. 5. Arrowspointing from the planetesimal sketch to various heliocentricdistances indicate possible perturbations of the original orbitsin the accretion disk that led to scattering to new locations. Sim-ilar considerations, without thermal modeling of planetesimals,can be found in an article by Jewitt (2004).

292 R. Merk, D. Prialnik / Icarus 183 (2006) 283–295

Fig. 5. Possible assignment of planetesimals as investigated in this study to planetesimal families as observed nowadays. The embedded figure represents theduration of liquid water inside accreting icy planetesimals (Fig. 4). Elliptical symbols indicate the location of known or suspected planetesimal families. Arrowswere included to indicate locations of planetesimals in the parameter space and possible scattering scenarios. The vertical axis stands for the heliocentric distance,cf. Section 4 for all details.

Classical KBOs constitute 2/3 of the well-observed KBOsand can be defined according to orbital parameters as KBOswith semimajor axes �42 AU, perihelion >35 AU and mod-erate eccentricity (Jewitt and Luu, 2000). Most probably, clas-sical KBOs originated and remained in the region �42 AU oftheir very accretion (Malhotra et al., 2000). Objects with radii<50 km are expected to form the bulk of KBOs (Jewitt andLuu, 2000). Although Neptune caused ‘dynamical heating’ ofKBO orbits, Davis et al. (1999) calculated that objects withradii larger than 25–50 km should be largely immune to col-lisional disruption. The ‘typical’ classical KBO could thereforebe similar to object A in Fig. 5: an icy object with a thickamorphous-ice mantle, enclosing a crystalline-ice core and con-

taining no traces of former liquid water, therefore revealing anoriginal (primitive) structure.

It is believed that SP comets originate in the Kuiper Belt(Weissman, 1999) and that they can be regarded as fragmentsof larger KBOs (Farinella and Davis, 1996). A large number ofSP comets could therefore represent mantle fragments of KBOslike object A in Fig. 5. However, it should be noted that theexact source zone of SP comets is yet unknown (Malhotra etal., 2000). As far as internal structure is concerned, SP cometsmight therefore represent the least altered cometary objects.

A very different picture emerges if one looks at planetesi-mals accreted between 20 and 30 AU. Even smaller membersof this population had a chance to undergo melting and crystal-

Combined thermal evolution and accretion of TNOs 293

lization. In Fig. 5, these objects are labeled B and D. Numericalmodels show that the region between 20 and 30 AU contributedconsiderably to populate the Oort cloud via scattering by earlyNeptune and Uranus (Fernandez and Ip, 1981, 1983; Duncan etal., 1987; for an overview cf. the review article by Mumma etal., 1993). The Oort cloud is believed to represent the sourcezone of LP comets (Weissman, 1999). Planetesimals of radiibetween 4–8 km are best suited to grow Neptune and simul-taneously populate the Oort cloud via scattering (Greenberg etal., 1984; Mumma et al., 1993). Comparison of accretion timesfor small icy bodies as calculated within this study (Fig. 1) withtime spans necessary to accrete proto-Neptune (Pollack et al.,1996) shows that these processes overlap. It is even assumedthat Neptune interrupted further accretion within the KuiperBelt by initiating the collisional epoch of this belt (Farinellaet al., 2000). It is therefore highly plausible that bodies like theone labeled D in Fig. 5 are common members of the Oort cloud.This implies that—very likely—LP comets had liquid interiorsand could be assumed to have lost their pristine character wellduring accretion.

A similar conclusion would hold for bodies of type B(Fig. 5). They form the most interesting population emergingfrom this study, since their structure is stratified: they retain partof their original pristine structure close to the surface within azone of amorphous ice, to be followed by a crystalline-ice man-tle and a liquid core region. Such stratified bodies could havecontributed to the KBO sub-category of Scattered Kuiper BeltObjects (SKBOs) and to the Plutino population. The formergroup was accreted beyond Uranus and scattered by Neptuneto orbits with large semi-major axes and high eccentricities, theprototype Scattered Disk Object being 1996 TL66 (Malhotra etal., 2000; Jewitt and Luu, 2000). According to a suggestion byDuncan and Levison (1997), Jupiter-family comets (with an or-bital period of less than 20 years; Weissman, 1999) originatedin the Scattered Disk. Furthermore, a possible path to generatethe Centaur population may lead through the SKBO-group ofplanetesimals (Jewitt and Luu, 2000; Horner and Evans, 2002).This could mean that many Centaurs once have been internallyactive, since they would have belonged to the stratified group B.

The Plutino group, on the other hand, is constituted by KBOsin a 3:2 mean-motion resonance with Neptune and semi-majoraxes around 39 AU. Their origin is frequently explained bythe Resonance Sweeping mechanism (Jewitt and Luu, 2000;Malhotra et al., 2000). According to this model, a migratingNeptune pushed its orbital resonances like a bow wave throughthe outer disk with the effect that objects in these resonancesbecame trapped and were thus pushed back to locations fartheraway from the Sun. Neptune’s orbit could have expanded byup to 9 AU (Malhotra et al., 2000). Finally, stratified icy ob-jects might have contributed to a faint stability zone between24 and 26 AU (Holman, 1997) and to Neptunian Trojans (thefirst member of this dynamically stable group is Object 2001QR 322, discovered by Chiang, 2003). In conclusion, it seemspossible that a subdivision of the Kuiper Belt according to or-bital elements may be reflected by a compositional subdivisionas well.

The numerical calculations show that close to 20 AU, hightemperatures can be obtained, resulting in nearly overall melt-ing of the interior. This evolution path is indicated by bodiesof type C in Fig. 5. It is possible that within extended moltenregions—provided the duration of the liquid water stage is longenough—sedimentation of dust may occur. Thus the silicatefraction within a molten (‘muddy’) zone can be expected tomigrate inward, leaving a differentiated planetesimal behind.Convection may disturb this process, but for small bodies, thecritical Rayleigh number is usually very large and thus in-hibits convection for radii below several hundreds of kilometers(Wood, 1979; Merk et al., 2002). If these planetesimals shoulddisrupt due to high temperatures, the core region could sepa-rate to form an asteroidal body with traces of ice. Such bodiescould be trapped to become Uranus-Trojans; if scattered, theymight also contribute to the Centaur population. This could ex-plain the asteroidal behavior of some Centaurs (Mannings et al.,2000).

5. Conclusion

The parameter-space survey of small icy bodies formed inthe outer Solar System presented here has confirmed our ear-lier estimate (see Paper I) that accretion and thermal evolutionshould be considered simultaneously. It has also confirmed pre-viously published results on 26Al heating of asteroids consider-ing accretion (Merk et al., 2002). In the case of asteroids, thequestion was mainly whether accretion may prevent melting ofasteroids (due to the surface-to-volume ratio during the earlystages of accretion). For small icy bodies, however, the ques-tion was whether consideration of accretion would allow anysubstantial 26Al heating of the interior.

The parameter study covered a wide range of heliocentricdistances and final radii (20 AU � dH � 44 AU and 2 km �Rpmax � 32 km). An important result is that properties of smallbodies, such as the fraction of the interior that is crystallineor the duration of internal processes change over the parame-ter space in a manner that cannot be easily foreseen by simpleargumentation. Thus the evolution course may turn out to bemore involved than obtained by ad hoc assumptions. In particu-lar, the common argument that 26Al cannot alter the interior ofsmall icy bodies due to their long accretion time and to their re-duced dust content (in comparison to asteroids) is misleading.Thermal evolution during and after accretion leads to a broadvariety of thermal evolution paths. The two major conclusionsare that (a) melting of water ice is a common phenomenon in-side small icy bodies, and that (b) even when temperatures arenot sufficiently high for melting the ice, they may still be highenough to induce crystallization of amorphous ice and, possi-bly, other processes as well. Nevertheless, we find that entirelypristine bodies can exist, but they are restricted to a narrow re-gion of the parameter space, that is, they require rather finelytuned initial conditions. Partly pristine bodies can be common,where the outer part retains its initial structure and composi-tion, while the interior part may have been significantly alteredby crystallization and melting.

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In more detail, our numerical calculations have shown thefollowing results. Small icy bodies with an ice fraction of about50% and below will always contain interior crystalline ice. En-tirely pristine interiors (with respect to crystallization) can beexpected only for 2 km bodies with an ice-rich composition(Xice = 0.9 and more). Crystallization fronts progress concomi-tantly with the accretion process; as a result, larger planetesi-mals may contain less crystalline ice, contrary to expectationbased on their final size. For a nominal cometary composition(dust:ice ≈ 1:1) and for all models with a higher dust frac-tion, melting of water ice can be expected. For a large regionof parameter space, liquid water turns out to be the rule ratherthan the exception. In particular, for a nominal composition,the liquid-water zone is found between the present-day orbitsof Uranus and Neptune, for final radii above 4 km. Extensivethermal processing is expected close to the present-day Uranusorbit. In the intermediate zone, water can be liquid for about5 Ma. In general, objects accreted in the Kuiper Belt zone showless alteration than those originally located closer to the Sun(between 20 and 30 AU).

We have pointed out a possible link between classes of ob-jects defined by their internal structure and the classification ofpresent-day icy planetesimals according to orbital parameters,but such a link requires further investigation, both theoreticallyand observationally. In this context, there is reason to assumethat LP comets contained liquid water in the distant past, andthat SP comets, coming from the Kuiper Belt zone, have pre-served a largely pristine interior. Stratified icy objects with bothformer liquid and pristine regions may perhaps be found amongSKBOs, Plutinos and Centaurs.

Acknowledgments

We thank Sin-iti Sirono for a constructive and useful reviewof this paper. Support for this work was provided by the IsraelScience Foundation grant No. 942/04.

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