This document summarizes research measuring visible and infrared spectra of 10 large, dark asteroids in the mid-outer main asteroid belt that are spectrally similar to Ceres. Thermal evolution modeling shows these "Ceres-like" asteroids have highly porous interiors, accreted relatively late between 1.5-3.5 million years after calcium-aluminum inclusions formed, and experienced maximum interior temperatures under 900K. Dynamical modeling suggests these asteroids were likely implanted from more distant regions into their current orbits between 3.0-3.4 AU during dynamical instability of the giant planets.

1. Nature Astronomy
natureastronomy
https://doi.org/10.1038/s41550-023-01898-x
Article
LateaccretionofCeres-likeasteroidsand
theirimplantationintotheoutermainbelt
Driss Takir 1,7
, Wladimir Neumann 2,3,4
, Sean N. Raymond 5
,
Joshua P. Emery6
& Mario Trieloff 3
Low-albedoasteroidspreservearecordoftheprimordialSolarSystem
planetesimalsandtheconditionsinwhichthesolarnebulawasactive.
However,theoriginandevolutionoftheseasteroidsarenotwell
constrained.Herewemeasuredvisibleandnear-infrared(about0.5–
4.0 μm)spectraoflow-albedoasteroidsinthemid-outermainbelt.Weshow
thatnumerouslarge(diameter>100 km)anddark(geometricalbedo<0.09)
asteroidsexteriortothedwarfplanetCeres’orbitsharethesamespectral
features,andpresumablycompositions,asCeres.Wealsodevelopeda
thermalevolutionmodelthatdemonstratesthattheseCeres-likeasteroids
havehighlyporousinteriors,accretedrelativelylateat1.5–3.5 Myrafter
theformationofcalcium–aluminium-richinclusions,andexperienced
maximuminteriortemperaturesof<900 K.Ceres-likeasteroidsare
localizedinaconfinedheliocentricregionbetweenabout3.0 auand3.4 au,
butwereprobablyimplantedfrommoredistantregionsoftheSolarSystem
duringthegiantplanet’sdynamicalinstability.
Dark asteroids, most of which are located in the mid-outer main belt
(2.5 < a < 4.0 au,whereaisthesemimajoraxis)1
,arethoughttobelefto-
vers from the formation of the planets2
and remnants of the primary
accretion of the first Solar System planetesimals3
. These asteroids are
genetically linked to carbonaceous chondrites4
and are collectively
calledprimitiveasteroids.Primitiveasteroidshavebeenstudiedusing
variousobservationaltechniques,includingground-based(forexample,
refs. 5,6
) and space-based7
telescopes and spacecraft8
. Using the NASA
InfraredTelescopeFacility(IRTF)telescope,TakirandEmery5
measured
spectra(~1.9–4.1 µm)oflow-albedoasteroidsinthemid-outermainbelt
andidentifiedfourmainspectralgroupsbasedonthe3 µmbandshape:
(1) The sharp group has a 3 µm band consistent with CI or CM car-
bonaceous chondrites (for example, ref. 9
). Most of this group’s
asteroids are located closer to the Sun in the 2.5 < a < 3.3 au
region.
(2) A group of asteroids that are spectrally similar to Ceres, located
in the ~2.6 < a < 3.2 au region, and has a relatively narrow feature
centred at 3.05 µm superimposed on a much broader absorp-
tion feature from ~2.8 µm to 3.7 µm.
(3) A group of asteroids that are spectrally similar to asteroid (52)
Europa, located in the ~3.1 < a < 3.2 au region and exhibit a 3 µm
band centred at 3.15 µm also superimposed on a much broader
absorption feature from ∼2.8 µm to 3.7 µm. No meteorite match
was found for both Ceres- and Europa-like groups in the 3 µm
band10
.
(4) The rounded group is located in the ~3.4 < a < 4.0 au region and
has a 3 µm band that is possibly attributed to water ice (for ex-
ample, ref. 11
).
Here we present visible and near-infrared (NIR; ~0.5–4.0 µm)
reflectance spectra of 10 Ceres- and Europa-like asteroids (including
spectra of asteroid Europa) measured at the IRTF. We place the astro-
nomicalobservationsoftheselargedarkasteroidsinthecontextofthe
thermalevolutionanddynamicalmodelsandprovideinterpretations
fortheoriginandevolutionoftheseasteroids.
Received: 3 January 2022
Accepted: 18 January 2023
Published online: xx xx xxxx
Check for updates
1
Jacobs, NASA Johnson Space Center, Houston, TX, USA. 2
Institute of Geodesy and Geoinformation Science, Technische Universität Berlin, Berlin,
Germany. 3
Klaus-Tschira-Labor für Kosmochemie, Institut für Geowissenschaften, Universität Heidelberg, Heidelberg, Germany. 4
Institute of Planetary
Research, German Aerospace Center (DLR), Berlin, Germany. 5
Laboratoire d’Astrophysique de Bordeaux Université de Bordeaux, Pessac, France.
6
Northern Arizona University, Flagstaff, AZ, USA. 7
Present address: NASA Infrared Telescope Facility, University of Hawaii, Mauna Kea, HI, USA.
e-mail: driss.takir@nasa.gov

2. Nature Astronomy
Article https://doi.org/10.1038/s41550-023-01898-x
Ceres-likeasteroids’thermalevolution
Primitiveasteroidsarethoughttobecomposedinitiallyofmixturesof
anhydrousmaterialsandwatericethatwaslatermeltedbyheatsources
such as the decay of 26
Al, reacting with anhydrous materials to form
H2O/OH-richminerals15
,andacarbonaceouschondriticCM-orCI-like
composition. The temperature and bulk density evolution of initially
water-richsmallbodieswerecalculatedusingaone-dimensional(1D)
finitedifferencesthermalevolutionmodel16,17
forplanetesimalsheated
by 26
Al, 60
Fe and long-lived radionuclides. An ice-rich initial composi-
tionthatleadstoamaterialdominatedbyphyllosilicatesafteraqueous
alteration (with an initial ~13 wt% H2O consumed completely for the
aqueous alteration leading to a composition with ~60 vol% hydrated
silicates as suggested by the water content and modal mineralogy of
CM and CR chondrites) was assumed.
Inparticular,thermallyactivatedcompactionduetohotpressing
of asteroids from an initially low density (that is, highly unconsoli-
dated porous structure) and a bigger size to a higher density and a
smallersizewasmodelledtofitthebulkdensitiesandsizesofthestudied
largedarkasteroids.Tothisend,atypicalinitialporosityof50%(ref.17
)
was reduced following the change of the strain rate calculated as
Voigt approximation from the strain rates of components17
. Mate-
rial properties (thermal conductivity, density, heat capacity and so
on) corresponded to the composition assumed and were adjusted
with temperature and porosity. For illustration and comparabil-
ity, we associate bodies of an equal mass but different porosities
(that is, different bulk densities and sizes obtained after a model cal-
culation) with a ‘reference’ mass. The reference mass and accretion
time intervals covered by our estimates are 1015
kg to 1021
kg (which
would correspond to diameters of ~10 km to 1,000 km at a grain
density of 2,460 kg m−3
and zero porosity) and 1 Myr to 5 Myr rela-
tive to the formation of calcium–aluminium-rich inclusions (CAIs),
respectively. Models with a low initial density (that is, a high initial
porosity) were calculated for all resulting pairs of parameters. The
massesandbulkdensitiesobtainedfromcompactionweresearched
formatcheswiththemassesandbulkdensitiesofobservedasteroids.
From those matches, accretion times were derived. Figure 2 shows
the maximum temperature and the average density calculated as
2.5 3.0 3.5 4.0
100
1,000
Semimajor axis (au)
Diameter
(km)
Themis
Cybele
Europa
Euphrosyne
Patientia
Carlova
Germania
Diotima
Loreley
Nephele
Alethiesa
Palma
Aurora
Aqueously altered asteroids Unaltered asteroids
Ceres
Hygiea
Pulcova
91
324
34
54
187
36
308
704
48
120
130
104
511
1015
121
334
41
211
98
13
190
153
361
107
401
790
76
Fig.1|Orbitaldistributionoflargedarkasteroids.Theidentifiedlargedark
asteroids(redsquares)thatwerefoundtobespectrallysimilartothedwarf
planetCeresarelocatedinthe~3.0–3.4 auheliocentricregion(grey).TheCM/CI-
likeandaqueouslyalteredasteroids(sharpgroup;bluetriangles)fromref. 5
are
plottedatlowersolardistancesandunalteredasteroids(roundedgroup;black
stars)atgreatersolardistances.
OrbitaldistributionofCeres-likeasteroids
Inthiswork,weareupdatingtheclassificationofref.5
andcombining
Ceres-andEuropa-likegroupstogetherinonegroup,aCeres-likegroup.
Weidentifiednineadditionalasteroids(inadditiontoasteroidEuropa)
thatarespectrallysimilartoCereshavediametersgreaterthan~100 km
withdifferentspectralclasses,includingC,B,P,FandD,andgeometric
albedosoflessthan0.09(SupplementaryTable1).SpectraofCeres-like
asteroidsexhibitabandcentredaround3.05–3.15 µm(Supplementary
Table 2, column 2) mainly superimposed on a much broader absorp-
tion feature from ~2.8 µm to 3.7 µm and a broad feature centred at
~1–1.5 µmthatgenerallyhasaconcave-upshapeatshorterwavelengths
(~0.6–2.0 µm) (Supplementary Fig. 1). The absorption band intensi-
ties at 3 µm for these asteroids range from ~2% to 8% (Supplementary
Table 2, column 3). The 3 µm band areas range from 0.012 µm−1
to
0.015 µm−1
(Supplementary Table 2, column 4). Previously published
visiblespectra(0.4–0.93 µm;https://sbnapps.psi.edu/ferret/)arealso
includedinthisstudytoprovideadeeperunderstandingofthesurface
compositionoftheseasteroids.SupplementaryFig.2showsprocessed
spectra of all the identified large dark asteroids that are found to be
consistent with those of the dwarf planet Ceres.
Figure1illustratesthatallidentifiedCeres-likeasteroidsarecon-
centratedbetween~3.0 auand3.4 au.Twoasteroids,(24)Themisand
(65) Cybele, which were classified by ref. 5
in the rounded group, are
reclassified in this work in the Ceres-like group because of their spec-
tral similarity to Ceres’ spectra. Asteroid (324) Bamberga is grouped
by refs. 5,12,13
as a Ceres-like object; however, more recent work has
shown that this asteroid is classified in the sharp group14
. Bamberga’s
spectralshapeinthe~0.5–2.5 µmregion,characterizedbyasteepslope
with a slight upwards curvature around 1.5 µm, further suggests the
classification of Bamberga in the sharp group. Bamberga may have a
heterogeneoussurfacerepresentingbothgroups,Ceres-likeandsharp.
ExceptforasteroidCybelelocatedat3.4 au,allCeres-likeasteroids
arelocatedinanarrowheliocentricregionbetween~3.0 auand~3.2 au,
beyondCeres’orbitat~2.8 au.Figure1alsoshowsbodieslocatedcloser
to the Sun whose ice melted, leading to aqueous alteration (sharp
group), and those farther from the Sun that contain unmelted ice
(roundedgroup)5
.

3. Nature Astronomy
Article https://doi.org/10.1038/s41550-023-01898-x
functions of reference masses and accretion time, where the mass
and the accretion time t0 were varied as stated above. Furthermore,
the accretion times for several of the asteroids studied that result
fromthebulkdensityandmassfitsareshown.SeeMethodsformore
information about the fitting procedure of bulk densities for the
studiedlargedarkasteroidsandtheircorrespondingaccretiontimes
and uncertainties.
The availability of 26
Al determines the heating and compaction
ofplanetesimals,thatis,bytheaccretiontimet0,suchthatmaximum
temperatures and structures vary enormously for t0 < 3 Myr relative
toCAIs.However,foralateraccretion,onlythemass(moreprecisely,
the surface-to-volume ratio, that is, the size that corresponds to this
massatagivengraindensityandbulkporosity)ofthebodydetermines
itsmaximumtemperatureanddensityduetonearlyconstantheating
bylong-livedradionuclides.Themodelsfittheasteroidbulkdensities
as an observational parameter and calculate bulk porosities consist-
ent with these densities. We find that most highly porous interiors
characterize the large and dark asteroids (Fig. 3) and, consequently,
accretedrelativelylate,thatis,at1.5–3.5 Myrrelativetotheformation
ofCAIswithamaximumtemperatureof<900 K(Fig.2).Lowerbounds
onthemaximumtemperaturescanbeprovidedbycomparingmasses
withmaximumcentraltemperaturesinFig.2aforthosefiveasteroids
for which observational constraints (that is, the density) do not suf-
fice for producing accretion time fits. These lower bounds are 300 K,
450 K,550 K,620 Kand650 Kfor(762)Pulcova,(31)Euphrosyne,(360)
Carlova, (165) Loreley and (241) Germania, respectively. The range of
maximumtemperaturesagreeswiththehydrationofdrysilicatesand
is insufficient for dehydration, in agreement with the spectra of large
darkasteroids.
Contrarytowhatwasassumedbyref.15
,state-of-the-artaccretion
models do not produce a correlation between accretion times and
heliocentricdistance.Thecurrentsemimajoraxesshouldnotbeused
to derive such objects’ accretion times. However, this includes such a
correlation at the original accretion location of these asteroids that
mighthavedifferedconsiderablyfromthepresentonesaccordingto
ourdynamicalmodels.
DynamicsofCeres-likeasteroids’orbital
implantation
Theplanets’growthanddynamicalevolutioncausedwidespreadradial
mixing of small bodies2
. Volatile-rich asteroids were implanted from
moredistantorbitsbybeingscatteredinwardsbythegiantplanetsand
thentrappedonstableorbitswithinthebelt.Thisprobablyhappened
in multiple episodes (Fig. 4).
(1) The giant planets’ rapid gas accretion destabilized the orbits
of nearby planetesimals and scattered them in all directions.
A fraction was trapped in the belt under gas drag18
.
(2) The giant planets’ orbital migration acted to scatter and shep-
herd planetesimals. In the Grand Tack model context, the gi-
ant planets’ late outwards migration scattered volatile-rich
planetesimals inwards and implanted a fraction into the belt19
.
Other migration pathways—such as those dominated by the
inwards migration of the giant planets—would also have led to
implantation18,20
.
(3) The ice giants’ accretion—from the inwards migration and colli-
sional growth of a population of about five Earth-mass cores21
—
scattered planetesimals inwards, implanting a fraction in the
asteroid belt due to gas drag22
.
(4) The giant planet dynamical instability scattered the bulk of
the primordial outer planetesimal disk through the inner Solar
System to be ejected by Jupiter23
. A small fraction of these very
volatile-rich objects were captured onto stable orbits in the in-
ner Solar System: Jupiter’s co-orbital region24,25
and the asteroid
belt26,27
.
These four implantation mechanisms form a rough temporal
sequence: giant planet growth, migration and instability. There is an
implied gradient in the accretion ages of implanted asteroids by dif-
ferent mechanisms simply because planetesimals must have formed
before being implanted. The feeding zones of the other mechanisms
alsoformaroughradialprogression.JupiterandSaturn’sinsitugrowth
(assuming no migration) implants asteroids from a zone ~5 au wide,
from ~4 au to 9 au (ref. 18
). Accounting for the gas giants’ migration
and the ice giants’ growth, the source region of dark asteroids would
have extended from a few to ~20 au, yet with a strong preference for
objectsoriginatingbetween~5 auand10 au(refs.18,20,28
).Theicegiants’
growth implanted planetesimals from ~10 au to at least 20–30 au
(ref.22
).Finally,thedynamicalinstabilityimplantedplanetesimalsthat
accretedat~20–40 au(ref.25
).
Although the exact timing of giant planet growth, migration and
instabilityremainuncertain,weexpectlaterasteroidaccretiontimesto
Maximum
temperature (K)
400
4
0
0
600
600
6
0
0
800
800
8
0
0
1,0
00
1
,
0
0
0
27
3
1 2 3 4 5
Accretion time (Myr after CAIs)
Planetesimal
mass
(kg)
400
600
800
1,000
1,200
Average density
(kg m
–3
)
1,300
1
,
3
0
0
1,300
1,500
1,500
1
,
5
0
0
1,500
1,800
1,800
1
,
8
0
0
1,800
2,000
2,000
2
,
0
0
0
2,000
2,200
2,200
2
,
2
0
0
2
,
2
0
0
2,400
1 2 3 4 5
Accretion time (Myr after CAIs)
10
16
10
17
10
18
10
19
10
20
10
21
Planetesimal
mass
(kg)
1,200
1,400
1,600
1,800
2,000
2,200
2,400
a
b
(431)
(52)
(10)
(423)
(372)
(94)
(259)
(65)
(10)
(52)
(423)
(372)
(24)
(431)
(451)
(65)
(94)
(451)
(259)
10
16
10
17
10
18
10
19
10
20
10
21
80
0
(24)
Fig.2|Maximumtemperatureandaveragedensityforinitiallywater-rich
planetesimalsasafunctionoftheaccretiontimerelativetoCAIsandthe
referencemass.a,Maximumtemperature.b,Averagedensity.Thesquaresshow
fittedasteroidscentredattheirreferencemassesandaccretiontimesandthe
verticalerrorbarsshowthemassuncertainty.Thestudiedasteroids’numbersare
alsoincludedintheplots.SeeMethodsformoredetailsaboutthermalevolution
modelling.SupplementaryTable3summarizeskeyobservedpropertiesof
asteroidsfittedwiththermalevolutionmodels,theirinitialandintermediate
propertiesinvolvedinthemodellingprocedureandthefinalcalculated
propertiesofasteroidfitsandresultingaccretiontimesderived.Theerror
barsplottedshowthemassuncertaintiesofthefits(Methods)thatresultfrom
themassestimateobservationuncertainties.Fortheaccretiontimeestimate
uncertainty,seeSupplementaryTable3.

4. Nature Astronomy
Article https://doi.org/10.1038/s41550-023-01898-x
correlatewithamoredistantoriginandimplantationbyalater-occurring
process. The giant planet’s dynamical instability (mechanism 4) is the
strongest candidate for implanting large dark asteroids. The critical
piece of evidence is that these objects are concentrated in the outer-
most parts of the main belt, mostly between 3.0 au and 3.2 au (Fig. 1).
Gas-drivencapture(mechanisms1,2and3)producesabroaderdistribu-
tionofimplantedasteroidsinwhichitisstatisticallyunlikelynottohave
capturedanyobjectsinteriortoCeres’present-dayorbit18,19,22
.Forboth
mechanisms1and3,thepeakinthedistributionofimplantedCeres-sized
planetesimals is close to Ceres’ actual orbit18,22
. However, suppose we
assume that Ceres and the large dark asteroids are part of the same
populationandthatnolargedarkasteroidsexistclosertotheSunthan
Ceres.Inthatcase,itbecomesapparentthatthesemechanismscannot
explaintheimplantationofthelargedarkasteroids.Incontrast,implan-
tation of asteroids during the giant planet instability (mechanism 4)
is almost entirely confined to the outer belt, beyond 2.5 au and with a
steep radial number density gradient (although the exact distribution
of implanted objects depends on the detailed evolution of scattered
planetsduringthedynamicalinstability26,27
).Thisimpliesthatthelarge
dark asteroids originated in the 20–40 au region26,27
. The outstanding
questioniswhythedwarfplanetCeresshouldbetheinnermost.
Despite their overlapping orbital distributions, dark asteroids
and their more refractory-dominated counterparts (such as S types)
probably originated in disconnected regions of the Solar System2,29
.
Thecarbonaceous/non-carbonaceousisotopicdichotomymeasured
inmeteorites30
suggeststhattheirparentbodiesformedconcurrently
butnotnearby31
.Instead,thediskofplanetesimal-formingsolidswas
dividedintwo,perhapsbyJupiter’sgrowingcore,anon-planet-related
pressurebumpinthediskorotherprocessesrelatedtotheplanetesi-
malformation32
.Darkprimitiveasteroidsprobablyrepresentplanetary
buildingblocksintheoutermostpartsofthedisk.
Surfaceandinteriorcompositionoflargedark
asteroids
The nature of the surface compositions of Ceres, and also Ceres-like
asteroids,isstillunderdebate,anddifferentinterpretationshavebeen
putforthtoexplaintheabsorptionfeaturesintheseobjects33–35
.Labo-
ratoryandspectroscopicexperimentsonmeteoritesrepresentingall
nine carbonaceous chondrite types found no spectral matches for
theselargeasteroids36
.PreviousstudiesofCereshavebeenconducted
to constrain and estimate its surface composition. Using linear mix-
ing, ref. 35
found hydroxide brucite, serpentines and carbonates con-
sistent with Ceres’ ground-based spectra. Another study33
estimated
the surface composition of Ceres and found evidence of widespread
NH3-phyllosilicatesacrossitssurfaceusingbest-fitsolutionstoDawn’s
NIRspectra.ThepresenceofNH3-phyllosilicatesimpliesthatmaterial
fromtheouterSolarSystemwasincorporatedintolargedarkasteroids,
eitherduringtheirformationatagreatheliocentricdistanceorincor-
porating material transported into the main belt region33
.
Spectra of large dark asteroids are similar to the spectra of
Himalia37
,thelargestirregularsatelliteofJupiterat5.2 au.Theirregular
satellite’s spectra exhibit 1 µm and 3 µm bands consistent with those
found in Ceres-like asteroids. In addition, NIR spectroscopic meas-
urements of comet 67P/Churyumov–Gerasimenko by the Rosetta
spacecraft38
revealed that this comet’s spectra exhibit a 3 µm feature
that is similar to the spectra of Ceres and other large asteroids. The
3 µmfeatureincomet67Pwasattributedtoammoniumsalts38
.Another
study39
alsosuggestedthaticyammonia,condensedintheouterSolar
System beyond 5 au, could have migrated inwards and incorporated
intoCeresandpresumablyotherlargedarkasteroidsinthemainbelt.
Cereshasaspecificcompositionthatappearstodifferfrommost
other large dark asteroids in the main belt40
. In particular, Ceres has a
higher density at present than most other large dark asteroids, had,
potentially, a higher H2O fraction in the past that led to differentia-
tion41
and might have experienced a loss of a past water ocean42
. Both
modelling and observations suggest a small porosity for Ceres40,43
,
in agreement with more vital compaction due to its larger size and
moreenergeticthermalevolution44
.Incontrast,currentobservations
indicate no free water and higher porosity, and lower metamorphic
temperatures for the other large dark asteroids, supported by our
modellingthermalevolutionsection.Beingmuchmoreevolved,Ceres
owes its impressive geological evolution and past to its dwarf planet
sizeandamuchmoreextensivewateraction.
IsasteroidHygiea,thefourthlargestmainbeltasteroid,thesecond
dwarf planet in the main belt? The Dawn mission revealed that Ceres
is geologically evolved, with evidence of tectonic and cryovolcanic
activitiesandaheavilycrateredsurface8
.Previousobservationalresults
showedthatthedwarfplanetCeresandasteroidHygieaarespectrally
similar in that they both have a 3 µm band centred at ~3.05 µm (ref. 5
),
unlikemostofthestudiedlargedarkasteroidsthathavea3 µmfeature
centredat~3.15 µm.Inaddition,Hygieawasfoundtohaveabasin-free
sphericalshapecomparabletoCeres44
.Theaccretiontimeof2.65 Myr
after CAIs derived for Hygiea is earlier than the accretion times of
≥5 MyrafterCAIssuggestedforCeresbydifferentstudies(forexample,
ref.16
andreferencestherein).Thisisconsistentwithlessefficientcool-
ingofCeresthroughthesurfacethanforHygiea.IfCereshadaccreted
earlier, this would have led to elevated temperatures, dehydration
and, potentially, a loss of its water content. However, reducing the
radiogenic energy for late accretion provides less energetic heating
and compensates for a weaker cooling for Ceres. As Ceres probably
had, and still has, a more significant water fraction than large dark
asteroidsaddressedhere,itwasexplicitlynotfitted.However,models
withaCeres-likewaterfractionwouldnecessitatealowergraindensity,
shifting the density isolines in Fig. 2b to more enormous reference
massesandtolateraccretiontimessincethewaterfractionwouldnot
containradioactiveheatsources.Theshapesofthedensityisolinesin
Fig.2bimplyanaccretiontimeclosetoorlaterthan~5 MyrafterCAIs.
SupposeCeresandHygieahaveasimilarsurfacecompositionandare
ofasimilarorigin.Inthatcase,theaccretionofplanetesimalsmusthave
occurred over an extended time interval of more than 2.5 Myr in the
regionoftheSolarSystemwherebothobjectsformed.Thediscovery
oflargedarkasteroidssmallerthanCeresnearitsorbitalvicinitysug-
geststhatthisdwarfplanetispossiblynotuniqueinthemainbeltand
itssurfacecompositionisnotdrivenbyitsvastsize.
Most evolved
structure
25% ≥ φc
≥ 10%:
10% > φc
> 0%:
(372) Palma
(423) Diotima
(451) Patientia
(52) Europa
(65) Cybele
(431) Nephele
(24) Themis
(94) Aurora
φ = 0% for innermost:
30 vol% (10) Hygiea
40 vol% (259) Aletheia
a
b
c
d
Hydrated and partially
compacted
Partially
compacted
Fully
compacted
Structure evolution with time
Hydrated
surface
Fig.3|Evolutionoftheasteroidinteriorstructurefromlefttoright,as
wellasfinalstructuresobtained. a,Asteroidsformaslooseagglomerates
ofdrydustandiceparticles.b,Heatingoftheinteriortriggershydrationand
progressivecompaction.c,Grazingimpactsthenremovetheremainingloose
surficiallayerexposingahydratedsurface.d,Someasteroidsevolvetoastage
thatischaracterizedbyfullycompactedcentralregions.Finalstructuresrange
fromstructuresthatareporousthroughout(thoughpartiallycompactedtoa
varyingdegreefordifferentasteroids)withahighcentralporosityofϕc ≈ 25%(c),
tostructureswithstronglyreducedcentralporositiesofdownto3%(c),tofully
compactedinteriorsoverlainbyhighlyporousouterlayers(d).

5. Nature Astronomy
Article https://doi.org/10.1038/s41550-023-01898-x
Methods
Observations and data reduction
We measured asteroid spectra of large and dark asteroids with the
Prism (0.7–2.52 µm) and long-wavelength cross-dispersed (LXD;
1.9–4.2 µm) modes of the SpeX (0.8 × 15 arcsec slit) spectrograph/
imager at the IRTF45
. Supplementary Tables 4 and 5 summarize the
observing parameters for the studied asteroids observed between
2015 and 2020 with the prism and LXD modes of SpeX. We used the
Interactive Data Language-based spectral reduction tool Spextool
(v4.0)toreducethedata46
.
Forasteroids’LXDandPrismobservations,wefollowedthesame
technique used in ref. 5
. The spectral image frames were divided by
a flat field frame measured using an internal integrating sphere. To
correct for the contributions of the OH line emission and the thermal
emission from the sky (longwards of ~2.3 µm), we subtracted spec-
tral image frames of asteroids and the solar analogue standard stars
in Supplementary Tables 4 and 5 (G-type stars close to asteroids on
the sky at similar airmass) at beam position A from spectral image
framesatbeamBofthetelescope.Afterthissubtraction,theresidual
background was removed by subtracting the median background
outside the data aperture for each channel. Spectra were extracted
by summing the flux at each channel within a user-defined aperture.
Asteroid spectra were divided by spectra of the solar analogue meas-
ured close in airmass to remove telluric absorptions (mostly water
vapouratthesewavelengths).Wavelengthcalibrationwasconductedat
λ < 2.5μmusingargonlinesmeasuredwiththeinternalcalibrationbox
andatλ > 2.5 µmusingtelluricabsorptionlines.
Thermalfluxmodellingandcorrection
The measured LXD spectra of dark asteroids show a steep increase of
apparent reflectance longwards of ~2.5 μm due to thermal radiation
from the asteroids’ surfaces. Removing the thermal excess in spec-
tra is essential for adequately characterizing mineral absorptions in
asteroids.WeusedtheNear-EarthAsteroidThermalModel(NEATM)47
to constrain the model thermal flux longwards of 2.5 μm in asteroids.
NEATM is based on the Standard Thermal Model (STM) of ref. 48
. The
(1) Planetesimals and
planetary embryos form
with a gradient of
compositions
Increasingly volatile-rich
Gaseous disk
Rocky
(2) Jupiter and Saturn's
rapid gas accretion
implants volatile-rich
planetesimals in the
outer main belt
(3) Jupiter and Saturn's
outwards migration (if it
happened) implants
volatile-rich planetesimals
into the outer main belt
(4) The ice giants accrete
from inwards-migrating
icy cores beyond the
gas giants and scatter
outer planetesimals to
the outer main belt
(5) The giant planet
instability clears out
the outer planetesimal
disk and implants very
volatile-rich objects
into the outer belt
Extra ice giant
ejected
Fig.4|Implantationofplanetesimalsintotheasteroidbeltduringthe
planets’growthanddynamicalevolution.Thedisk’stemperatureprofile
establishedagradientinthecompositionofsmallbodiesduringplanetesimal
formation(forexample,ref. 15
).Thepresenceofammoniatedphyllosilicates33
indicatesthatCeres(andpresumablyalsothelargedarkplanetesimals)probably
originatedbeyondSaturn’sorbitandperhapsmuchfartherout.Planetesimals
fromtheJupiter–Saturnregionwereimplantedduringthegasgiants’rapidgas
accretion18
.Themigrationofthegasandicegiantscausedthesourceregion
ofimplantedplanetesimalstoexpandoutwards18,19
.Theicegiants’growth
implantedadditionalplanetesimals22
.Thegiantplanet’sinstabilitythen
implantedsomeasteroidsfromtheouterplanetesimaldisk25,26
—thisisthelikely
sourceofthelargedarkasteroids.Theinstabilitymayhavebeentriggeredbythe
dispersalofthegaseousdisk68
,suchthattheseimplantationmechanismswere
separatedintimebyonlyafewtotenmillionyears.Manyvolatile-poorasteroids
wereprobablyimplantedfromtheterrestrialplanet-formingregion29
.

6. Nature Astronomy
Article https://doi.org/10.1038/s41550-023-01898-x
measuredthermalexcesswasfittedwithamodelexcess(Supplemen-
tary Fig. 3) that was then subtracted from the measured thermal flux
relativespectraoftheasteroids(SupplementaryFig.4).
Inthethermalmodel,weusedparametersthatincludeheliocen-
tric and geocentric distances, visible geometric albedo and phase
angle at the time of observation obtained from the Jet Propulsion
Laboratory Horizon online ephemeris generator (Supplementary
Table 2). A default value for the slope parameter G of 0.15 was used
for all asteroids49
. Because we used the V-band albedo in the thermal
model, we applied a K to V scale (derived using Prism spectra) for all
asteroids to reconcile the two reflectance values at the two different
wavelengths.ThebeamingparameterwasincorporatedintheNEATM
modeltoaccountfordifferencesinsurfaceroughness.Tominimizea
chi-squared fit to asteroids’ observational data and find the surface
temperaturethatbestmatchesthemeasuredthermalflux,theNEATM
model iterates through several approximations of the beaming and
geometric albedo. We assumed both bolometric and spectral emis-
sivity to be 0.9 and the night sides of the asteroids to emit no thermal
energyinthemodel.
Calculationofthe3 µmbandparameters
The absorption feature at ~3 µm in the studied asteroids was isolated
and divided by a straight-line continuum in wavelength space fol-
lowing the methodology used in ref. 50
. Two maxima determined the
absorption feature’s continuum at ~2.85 µm and 3.25 µm. The 3 µm
band depth, Dλ, at a given wavelength, was calculated relative to the
continuumusingthefollowingequation:
Dλ =
Rc − Rλ
Rc
, (1)
whereRλ isthereflectanceatagivenwavelengthλ,andRc isthereflec-
tance of the continuum at the same wavelength as Rλ. Band depth
uncertaintywascalculatedusingthefollowingequation:
𝛿𝛿Dλ = Dλ ×
√
√
√
√
(
δR1
R1
)
2
+ (
δRc
Rc
)
2
, (2)
where
R1 = Rc − Rλ, (3)
and
𝛿𝛿R1 = √(𝛿𝛿Rc)
2
+ (𝛿𝛿Rλ)
2
, (4)
δRc and δRλ were derived using each wavelength’s uncertainty calcu-
latedduringthedatareductionprocess.
The 3 µm band area was calculated by integrating the spectral
curvebelowthecontinuumoftheabsorptionfeature.Thebandcentre
was computed by applying a sixth-order polynomial fit to the central
partoftheabsorptionfeature.Anaverageofatleastfivemeasurements
made by varying the positions of band maxima was used for the band
area and band centre calculations. Uncertainties for the band area
andcentrewerecalculatedbythe2σstandarddeviationrepresenting
variabilityfromtheaverage.
Thermalevolutionmodeldescription
Thetemperatureandbulkdensityevolutionofinitiallywater-richsmall
bodieswerecalculatedusinga1Dfinitedifferencesthermalevolution
model16,17
for planetesimals heated by 26
Al, 60
Fe and long-lived radio-
nuclides.Inparticular,thermallyactivatedcompactionduetothehot
pressing of bodies with an initially unconsolidated porous structure
was modelled to fit the bulk densities of large low-albedo asteroids
underconsiderationand,therefore,constraintheiraccretiontime.
Energybalance
A 1D finite differences thermal evolution model for planetesimals
heatedmainlyby26
Alpresentedinrefs.16,17
wasadaptedforthecurrent
study. It calculates the heating of small porous bodies, their thermal
evolution,andthecompactionofamixtureofdryandhydratedmate-
rialfromaninitiallyunconsolidatedstateduetohotpressingbysolving
several equations that describe these processes. A non-stationary 1D
heat conduction equation in spherical coordinates is discretized by
the finite differences method along the spatial and temporal domain
andsolvedforthetemperature:
ρcp (1 + xiceSice)
∂T
∂t
=
1
r2
∂
∂r
(kr2 ∂T
∂r
) + Q (r, t) , (5)
with the bulk density ρ, the heat capacity cp, the initial fraction xice
and the Stefan number Sice for water ice, the temperature T, the time
t, the radius variable r, and the energy source density Q. The energy
source for the temperature change is the radioactive decay of typical
short-lived radionuclides 26
Al and 60
Fe and long-lived 40
K, 232
Th, 235
U
and238
U:
Q (r, t) = (1 − vice) ρ ∑
i
fiZi
Ei
τi
exp (−
t − t0
τi
) , (6)
with the initial water ice volume fraction vice, the porosity-dependent
bulk density ρ, the number of atoms of a stable isotope per 1 kg of the
primordialmaterialf,theinitialratioofradioactiveandstableisotope
Z, the decay energy E, the mean life τ = λ/log(2), the half-life λ and the
accretiontimet0 oftheplanetesimal.SeeSupplementaryTable6forthe
associatedparametervalues.Ahomogeneousheatsourcedistribution
within the material is assumed, while the heat source density scales
furtherwiththeporosityϕ.Theporosityisinitiallyconstantthrough-
out the interior but develops heterogeneously with depth during the
thermal evolution under the action of temperature and pressure.
The temperature calculation starts from an initial value of TS = 230 K
throughouttheplanetesimalwithaconstantsurfacetemperatureTS.
Compositionandmaterialproperties
We assume properties similar to CM chondrites based on spectral
similaritiesoflargedarkasteroidswithwater-richcarbonaceouschon-
drites.Theinitialcompositionisconsideredtobemainlyamixtureof
anhydrousmaterialsandwatericethatwaslatermeltedbyheatsources
such as the decay of 26
Al, reacting with anhydrous materials to form
H2O/OH-rich minerals15
. An ice-rich initial composition that leads to
a material dominated by phyllosilicates after aqueous alteration was
assumed as suggested by the water content and modal mineralogy
of CM chondrites51
, that is, ~13 wt% or ~33 vol% H2O ice initially that is
entirelyconsumedfortheaqueousalterationleadingtoacomposition
with~60 vol%hydratedsilicatesand~40 vol%anhydroussilicates,that
is,~50 wt%foreither.Inthefollowing,notationsxice = 0.13,xdust = 0.87,
vice = 0.33, vdust = 0.67, xhyd = 0.5, xanh = 0.5, vhyd = 0.6 and vanh = 0.4 are
used.Thisagreeswithanaveragegraindensityof~2,460 kg m−3
calcu-
lated for a mix of water ice and olivine initially and a mix of antigorite
and olivine after water consumption. This initial composition is an
idealized approximation that provides material properties, such as
graindensity,thermalconductivityandheatcapacity,neededforthe
numerical procedure. This approximation does not include minor
phasesandtraceelements.Minorphasessuchasammoniawouldinflu-
ence material properties to an amount that would lead to negligible
differencesinthethermalevolutionmodellingoutcomes.Therefore,
they are neglected, but this neglection does not contradict the pres-
enceofammoniaintheinitialcomposition.Thegraindensityisatthe
lower end of known CM grain densities. An average grain density of
2,700 kg m−3
appliedtotheasteroidsconsideredwouldimplycurrent
porositiesofupto50%.However,theprocessofcoldpressingthatacts

7. Nature Astronomy
Article https://doi.org/10.1038/s41550-023-01898-x
during the accretion in the absence of notable heating (for example,
ref.52
)alreadyreducestheporosityinplanetesimalsto~43%.Thus,we
chose a grain density corresponding to no more than 43% of current
porosities. The initial water content could have varied according to
the range derived for CM chondrites. In general, a different water
fraction would influence the energy balance in the models only via
small changes in the latent heat consumption during the melting of
ice. A reasonable variation in the water content would, thus, lead to
negligiblevariationsinthemodellingoutcome.Thus,thecomposition
used here is reasonably representative in terms of thermal evolution
andcompactionbehaviour.
Atypicalinitialporosityof50%wasreducedfollowingthechange
of the strain rate that is calculated as Voigt approximation from the
strain rates of components53
. While a variation of the initial porosity
within a few per cent appears to be reasonable, we believe that we
already considered a reasonable value. Porous non-lithified material
canbeapproximatedbypackingsofspheres.Theloosestclosepacking
thatisjuststableundertheapplicationofexternalforceshasaporosity
of ~44% (refs. 54,55
). While planetesimals accrete from very fluffy dust
aggregateswithporositiesofupto90%,collisionsoftheseaggregates
lead to compaction of the material, and experiments show that such
repeated micro-impacts can reduce the porosity to less than ~60%
(refs. 56,57
) before the accretion of these aggregates to a planetesimal.
The value of 50% used is smaller than 60% and larger than that of the
random loose packing and is, further, typically used for planetesimal
thermalevolutionmodels(forexample,ref.52
andfollow-uppapers).
Material properties (thermal conductivity, density, heat capac-
ity and so on) corresponded to the composition assumed and were
adjusted with temperature, porosity and composition. The melting
of water ice is considered in a temperature interval of two degrees
between Ts = 272 K and Tl = 274 K to avoid numerical issues with too
sharp a phase transition at 273 K. We include the consumption of the
latent heat L = 3.34 × 105
J K−1
kg−1
during the melting of the ice via a
Stefan number (equation (1) and ref. 43
) using for its calculation the
heatcapacityof4,200 J K−1
kg−1
ofliquidwater.Theaqueousalteration
and,therefore,theformationofhydratedsilicatesisassumedtooccur
quasi-instantaneouslyafterreachingTl.
The local bulk density ρ is derived from the grain density ρg by
scaling it with the local volume filling factor (1 − ϕ): ρ = (1 − ϕ)ρg. The
equations for the heat capacity cp and the thermal conductivity k are
averages of the water ice and anhydrous silicates (T < Tl) or hydrated
andanhydroussilicates(T ≥ Tl)contributions.Thethermalconductiv-
ity k is calculated as a volume-fraction-weighted geometric mean of
thethermalconductivitiesofwatericeandanhydroussilicatedust:
k (ϕ, T) = (
567
T
)
vice
4.3vdust [exp (−
4
0.08
ϕ) − exp (−4.4 −
4
0.17
ϕ)]
1/4
(7)
for T < Tl,orofhydratedandanhydroussilicates
k (ϕ, T) = (
1
0.404+0.000246T
)
vhyd
4.3vanh
[(max (1 − 2.216ϕ, 0))
4
− exp (−4.8 −
4
0.167
ϕ)]
1/4
(8)
for T ≥ Tl.
Similarly, the heat capacity is calculated as a mass fraction-
weightedarithmeticmean
cp (T) = xice (185 + 7.037T) + xdust (800 + 0.25T − 1.5 × 107
T−2
) (9)
for T < Tl,and
cp (T) = xhyd (0.9 − 6.3T−0.5
− 14, 600T−2
+ 1.91 × 106
T−3
)
+xanh (800 + 0.25T − 1.5 × 107
T−2
)
(10)
for T ≥ Tl, where the olivine heat capacity is approximated with a
H-chondriticcp.
Forthethermalconductivitiesandheatcapacitiesofthespecies,
seeref.16
andreferencestherein.
Porosity
Theevolutionofthevolumefractionofbulkporespace,thatis,poros-
ityϕiscalculatedforT ≥ Tl byconsideringthecreepofdryolivineand
wet olivine as an approximation of the bulk material. It is described
by non-stationary differential equations for a strain rate–stress rela-
tion. The bulk strain rate is calculated as a volume-fraction-averaged
expressionintheVoigtapproximation53
:
∂ log (1 − ϕ)
∂t
= ̇
ε = vhyd ̇
ε1 + vanh ̇
ε2, (11)
with a diffusion creep equation for the deformation of wet olivine
derivedbyref.58
:
̇
ε2 = 1.2 × 10−26
σ1.1
b−3
exp (−
295, 000 + P × 20 × 10−6
8.314T
) , (12)
and a diffusion creep equation for the deformation of dry olivine
derivedbyref.59
:
̇
ε2 = 1.26 × 10−18
σ1.5
b−3
exp (−
355, 640
8.314T
) , (13)
withtheeffectivestressσ,thegrainsizeb = 10−5
m,thelithostaticpres-
sure P and the temperature T in kelvin. An initial porosity of ϕ0 = 0.5
used is a typical value based on the porosities of the random loose
and random close packings43,52
). The effective stress σ is calculated
as in ref. 17
for the simple cubic packing of equally sized spheres59
that
has a porosity of ~50%. With ϕ0 = 0.5 and ρg = 2,460 kg m−3
, the initial
densityis1,230 kg m−3
.
Radiusandresolution
TheradiusR(t)oftheobjectconsideredchangeswiththebulkporosity
ϕbulk(t)atthetimet,obtainedbyintegratingthelocalporosityoverthe
radius r,accordingto
R (t) = (1 − ϕbulk)
−1/3
R, (14)
whereRisthereferenceradius,thatis,theradiusatzeroporosity.The
referenceradiusisusedfortheanalysisoftheresultsasitisrepresenta-
tive for sets of bodies with equal mass and grain density but different
porosity.Allequationsinvolvedaresolvedonthespatialradiusdomain
ranging from the centre of the planetesimal up to its surface. The
spatial grid is transformed from 0 ≤ r ≤ R, with the distance from the
centre r in metres, to 0 ≤ η ≤ 1 using the transformation η = r/R(t). The
timeandspacederivativesarealsotransformedandthetransformed
expressionsareappliedtoallequationsinvolved,suchthatfeatureslike
Lagrangian transport of porosity and other quantities are accounted
for. While the positions of the grid points between 0 and 1 are fixed,
the variable values at the grid points are updated at every time step
accordingtotheabovetransformations.Non-stationaryequationsare
alsodiscretizedwithrespecttothetimevariabletandsolvedusingthe
implicitfinite-differencemethod.
Fittingprocedure
We used asteroid bulk densities and sizes from ref. 60
for most aster-
oids, ref. 44
for Hygiea and ref. 61
for Nephele. The total porosities of
the asteroids were calculated from the densities and sizes. Note that
ref. 60
also presented porosities. However, those were macroporosi-
ties assumed to be representative of all asteroids presented in ref. 60

8. Nature Astronomy
Article https://doi.org/10.1038/s41550-023-01898-x
for which they assumed rubble pile structure. However, based on the
sizes of known rubble piles of <10 km in size62
, on collisional lifetimes
of≥10 kmobjectssurpassingtheageoftheSolarSystem63
,andonthe
sizes of the asteroids we consider in the present study being >90 km,
alltheseasteroidsareprobablynotrubblepilesandshouldhavenearly
zero macroporosity. A new macroporosity result of ~16% for the sub-
kilometrerubblepileRyuguindicates,further,thatevenfortinyrubble
piles,macroporositiesmayhavebeensystematicallyoverestimatedin
the past64
. Therefore, we consider that the porosity is microporosity
by its nature and calculate it from the asteroid bulk densities and the
meteoriteanaloguegraindensity:
ϕ = ϕmicro = 1 −
ρasteroid,bulk
ρmeteorite,grain
, (15)
where ρmeteorite,grain is the grain density of the meteorite analogue. As a
meteoriteanalogueweusedCMchondrites,assuggestedbyrefs.60,65
,
and very similar spectral properties that indicate a similar composi-
tion. Previous studies5,10,12
found that the 3 μm reflectance spectra of
Ceresandthelargest(d > 200 km)darkasteroidshavesimilarspectral
properties and presumably compositions. We extend this statement
to the asteroids investigated in the current study. Therefore, it is rea-
sonabletoassumeasimilarcompositionforthemodelling.ACVana-
logue suggested for Aletheia and Palma and a mesosiderite analogue
suggested for Cybele by ref. 60
would contradict asteroids’ hydrated
surfacesactuallyobserved,asCVchondritesexperiencedverylittleto
no aqueous alteration and have less than ~4 vol% phyllosilicates51,66,67
,
and mesosiderites are similar to igneous eucrites and diogenites in
theirsilicatecomposition.
For deriving the accretion times of the asteroids, we use an
approach similar to that in ref. 17
, where the bulk porosity calculated
for planetesimals was compared with the porosity of Ryugu’s surface
boulders. The goal of the fitting procedure is to find accretion time t0
values that result in bulk density and diameter values that match the
bulkdensitiesanddiametersofthelargeprimitiveasteroidsconsidered.
Forillustrationandcomparability,weassociatebodiesofanequalmass
but different porosities (that is, also different bulk densities and sizes
obtainedafteramodelcalculation)witha‘reference’diameter,thatis,
a theoretical diameter at zero porosity. Note that for illustration and
comparability, we associated such bodies with a reference mass in the
mainpaperasthereferencediameterscaleiseffectivelyequivalenttoa
massscaleatauniformgraindensity.Thereferencediameterandaccre-
tion time intervals covered by our calculations are 10 km to 1,000 km
and1 Myrto5 MyrrelativetotheformationofCAIs,respectively.Unlike
previousthermalmodellinginvestigationsthatassumedacorrelation
of the accretion times with heliocentric distance15
, this work showed
that the accretion times of large dark asteroids derived are not found
to correlate in any way with their current semimajor axes and that the
currentsemimajoraxesshouldnotbeusedforderivingaccretiontimes
of such objects. Therefore, the accretion time is a free parameter, its
earliest value being limited by the formation of CAIs and the latest by
theendtimeofplanetesimalaccretion.Thermalevolutionandcompac-
tionmodelswithalowinitialdensity(thatis,ahighinitialporosity)and
biggerinitialdiametersthanreferencediameters(asprescribedbythe
initialporosity)werecalculatedforallresultingpairsofparameters.
Within the compaction procedure, a body of a given mass and
porosity (that is, bulk density) becomes less porous (that is, denser)
due to compaction via creep. The mass remains constant, the diam-
eterbecomessmaller,theporositybecomessmaller,thebulkdensity
becomes higher and all values are calculated consistently. Due to the
boundary condition of TS = 230 K for the planetesimal surface, a rela-
tivelythinsuperficialregolithlayerisretained,wherewatericedoesnot
meltatanytimeduringtheevolutionandwheretheinitialcomposition
ofwatericeanddrysilicatesdoesnotchange.Thisdoesnotagreewith
thespectralobservationsofasteroidsinthepresentstudy.Inparticular,
the structure of this layer is that of an unsintered low-strength loose
particle agglomerate. Therefore, such layers must have been ablated
byimpacts,suchthathydratedandhigher-strengthpartiallysintered
material was exposed. Removing thin upper layers by impacts is also
reasonableasasteroidfamiliesareobserved,andtheyprobablyformed
inasimilarway.Assumingthatthoseimpactsthatoccuraftertheces-
sation of the compaction remove the primordial low-strength layer
that would partly evaporate and partly disperse, we consider only
the interior of planetesimals where hydrated and at least partially
lithified material was able to form and calculate the average density
oftheinterior.Theaveragedensityisavaluethatisboundedaboveby
the grain density (approached only for nearly complete compaction)
and below by the initial density (retained if no compaction occurs at
all), and its value depends on the thermal evolution experienced by
a planetesimal. The sizes of the hydrated parts of planetesimals and
theirbulkdensitieswerethensearchedformatcheswiththeasteroids’
sizesandbulkdensities.Suchmatchesalreadyhavethebulkdensities
andsizesoftheasteroids.Foragivenasteroid,amatchcanoccuronly
for some unique accretion time, such that an accretion time can be
assigned to this asteroid. For the cases shown in Fig. 2, the primordial
layeristypicallyafew100 mthickatmost.
Accretiontimeandreferencediameter(ormass)uncertainties
Our analysis is concentrated on the size and density values currently
providedwithinthemarginoferror60
.Whilethesizeuncertaintiesare
rather negligible, the density values have, in most cases, significant
uncertainties of up to 60%. In some cases, one or both of the lowest
and the highest density values available are outside of the interval
spanned by the initial density of 1,230 kg m−3
and the grain density of
2,460 kg m−3
.Furthermore,asthethermalevolutionofplanetesimals
thataccreteaftertheextinctionof26
Al(afewhalf-lives)andareheated
onlybylong-livedradionuclidesisverysimilarregardlessoftheaccre-
tion time, the bulk density isolines reach plateaus (Fig. 2) where both
peaktemperatureandbulkdensityisolinesbecomenearlyhorizontal).
Therefore, if plotted, some error bars for the accretion time would
extendinfinitelyintimetowardsthepresentday.Thisisnotreasonable
sinceaccretiontimesarelimitedbythetimewhentheaccretionofplan-
etesimalsended.Theresultsofourmodellinginherittheshortcomings
oftheavailabledata.Theresultinguncertaintiesintheaccretiontimes
derived can be constrained only for a few cases. For (259) Aletheia, an
uncertaintyof+0.1/−0.6 Myrcanbedeterminedfort0.Inothercases,
an estimate only towards either an earlier or a later formation time
canbeprovided(orevennone):(423)Diotima,−0.6 Myr;(52)Europa,
−1.5 Myr;(372)Palma,−0.1 Myr;(451)Patientia,−0.9 Myr;(10)Hygiea,
−0.7 Myr;(65)Cybele,−0.4 MyrrelativetoCAIs.
Themaximallypossibleuncertaintiesforthereferencediameters,
thus, masses, arise from the mass estimate uncertainties. They were
obtainedusingtheequation:
D = 2 (
3
4𝜋𝜋
M
ρmeteorite,grain
)
1/3
metres (16)
andvaryfrom<7 km(Aletheia)to69 km(Patientia),correspondingto
radius differences of ~3 km to ~35 km. The reference diameter spread
for each asteroid is shown in Fig. 2 with vertical error bars. Our fitted
reference diameters are nearly centred within these intervals, with
slighttendenciestowardstheupperbounds.
Dataavailability
AlldataareavailableinthepaperoritsSupplementaryInformation.
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Acknowledgements
D.T. acknowledges support by NASA’s Solar System Observations
grant NNX17AJ24G. S.N.R. thanks the CNRS’ PNP and MITI programmes
for their support. W.N. acknowledges support by the Deutsche
Forschungsgemeinschaft (DFG), project number 434933764. W.N. and
M.T. acknowledge support by Klaus Tschira Foundation. We thank B.
Carry for providing the unpublished density values of some large dark
asteroids used in this study. We also thank the NASA IRTF staff for their
assistance with asteroid observations. Spextool software is written
and maintained by M. Cushing at the University of Toledo, B. Vacca
at SOFIA and A. Boogert at NASA InfraRed Telescope Facility (IRTF),
Institute for Astronomy, University of Hawai’i. NASA IRTF is operated
by the University of Hawai’i under contract NNH14CK55B with NASA.
D.T. is a visiting astronomer at the Infrared Telescope Facility under
contract from the National Aeronautics and Space Administration,
which is operated by the University of Hawaii.
Authorcontributions
D.T. measured, analysed and interpreted asteroid data. W.N. developed
thermal evolution models for the observed asteroids. S.N.R. helped
place asteroid observations in terms of the dynamics of the solar
system. D.T., W.N. and S.N.R. wrote the first draft of the paper. J.P.E.
and M.T. edited the paper and assisted with the data analysis and
interpretation. All authors contributed to the revision of the paper.
Competinginterests
The authors declare no competing interests.
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