# Late accretion of Ceres-like asteroids and their implantation into the outer main belt

Driss Takir, Wladimir Neumann, Sean N. Raymond, Joshua Emery, Mario Trieloff

► To cite this version:

Driss Takir, Wladimir Neumann, Sean N. Raymond, Joshua Emery, Mario Trieloff. Late accretion of Ceres-like asteroids and their implantation into the outer main belt. Nature Astronomy, 2023, 7 (5), pp.524-533. 10.1038/s41550-023-01898-x. hal-04237079

HAL Id: hal-04237079

https://hal.science/hal-04237079v1

Submitted on 4 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Late accretion of Ceres-like asteroids and their implantation into the outer main belt

Received: 3 January 2022

Accepted: 18 January 2023

Published online: 20 February 2023

<figure><img src="image_2.png" /></figure>

Check for updates

Driss Takir Ⓓ1,7, Wladimir Neumann Ⓓ2,3,4, Sean N. Raymond Ⓓ5, Joshua P. Emery6 & Mario Trieloff Ⓓ3

Low-albedo asteroids preserve a record of the primordial Solar System planetesimals and the conditions in which the solar nebula was active. However, the origin and evolution of these asteroids are not well constrained. Here we measured visible and near-infrared (about 0.5–4.0 µm) spectra of low-albedo asteroids in the mid-outer main belt. We show that numerous large (diameter >100 km) and dark (geometric albedo <0.09) asteroids exterior to the dwarf planet Ceres’ orbit share the same spectral features, and presumably compositions, as Ceres. We also developed a thermal evolution model that demonstrates that these Ceres-like asteroids have highly porous interiors, accreted relatively late at 1.5–3.5 Myr after the formation of calcium–aluminium-rich inclusions, and experienced maximum interior temperatures of <900 K. Ceres-like asteroids are localized in a confined heliocentric region between about 3.0 au and 3.4 au, but were probably implanted from more distant regions of the Solar System during the giant planet’s dynamical instability.

Dark asteroids, most of which are located in the mid-outer main belt ($2.5 < a < 4.0$ au, where *a* is the semimajor axis)<fnref n="1" />, are thought to be leftovers 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 called primitive asteroids. Primitive asteroids have been studied using various observational techniques, including ground-based (for example, refs. ⁵,<fnref n="6" />) and space-based⁷ telescopes and spacecraft⁸. Using the NASA Infrared Telescope Facility (IRTF) telescope, Takir and Emery⁵ measured spectra (-1.9–4.1 µm) of low-albedo asteroids in the mid-outer main belt and identified four main spectral groups based on the 3 µm band shape:

(1) The sharp group has a 3 µm band consistent with CI or CM carbonaceous 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 absorption 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 example, 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 astronomical observations of these large dark asteroids in the context of the thermal evolution and dynamical models and provide interpretations for the origin and evolution of these asteroids.

<figure><img src="image_3.png" /></figure>

<footnote n="1">¹Jacobs, NASA Johnson Space Center, Houston, TX, USA. ²Institute of Geodesy and Geoinformation Science, Technische Universität Berlin, Berlin, Germany. ³Klaus-Tschira-Labor für Kosmochemie, Institut für Geowissenschaften, Universität Heidelberg, Heidelberg, Germany. ⁴Institute of Planetary Research, German Aerospace Center (DLR), Berlin, Germany. ⁵Laboratoire d'Astrophysique de Bordeaux Université de Bordeaux, Pessac, France.</footnote>

<footnote n="6">⁶Northern Arizona University, Flagstaff, AZ, USA. ⁷Present address: NASA Infrared Telescope Facility, University of Hawaii, Mauna Kea, HI, USA.</footnote>

<footnote>e-mail: driss.takir@nasa.gov</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1 | Orbital distribution of large dark asteroids.** The identified large dark asteroids (red squares) that were found to be spectrally similar to the dwarf planet Ceres are located in the -3.0–3.4 au heliocentric region (grey). The CM/CI-</figcaption></figure>

like and aqueously altered asteroids (sharp group; blue triangles) from ref. ⁵ are plotted at lower solar distances and unaltered asteroids (rounded group; black stars) at greater solar distances.

## Orbital distribution of Ceres-like asteroids

In this work, we are updating the classification of ref. ⁵ and combining Ceres- and Europa-like groups together in one group, a Ceres-like group. We identified nine additional asteroids (in addition to asteroid Europa) that are spectrally similar to Ceres have diameters greater than ~100 km with different spectral classes, including C, B, P, F and D, and geometric albedos of less than 0.09 (Supplementary Table 1). Spectra of Ceres-like asteroids exhibit a band centred around 3.05–3.15 µm (Supplementary Table 2, column 2) mainly superimposed on a much broader absorption feature from ~2.8 µm to 3.7 µm and a broad feature centred at ~1–1.5 µm that generally has a concave-up shape at shorter wavelengths (~0.6–2.0 µm) (Supplementary Fig. 1). The absorption band intensities 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 visible spectra (0.4–0.93 µm; https://sbnapps PSI.edu/ferret/) are also included in this study to provide a deeper understanding of the surface composition of these asteroids. Supplementary Fig. 2 shows processed spectra of all the identified large dark asteroids that are found to be consistent with those of the dwarf planet Ceres.

Figure 1 illustrates that all identified Ceres-like asteroids are concentrated between -3.0 au and 3.4 au. Two asteroids, (24) Themis and (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 spectral 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 spectral shape in the -0.5–2.5 µm region, characterized by a steep slope with a slight upwards curvature around 1.5 µm, further suggests the classification of Bamberga in the sharp group. Bamberga may have a heterogeneous surface representing both groups, Ceres-like and sharp.

Except for asteroid Cybele located at 3.4 au, all Ceres-like asteroids are located in a narrow heliocentric region between -3.0 au and -3.2 au, beyond Ceres' orbit at -2.8 au. Figure 1 also shows bodies located closer to the Sun whose ice melted, leading to aqueous alteration (sharp group), and those farther from the Sun that contain unmelted ice (rounded group)⁵.

## Ceres-like asteroids' thermal evolution

Primitive asteroids are thought to be composed initially of mixtures of anhydrous materials and water ice that was later melted by heat sources such as the decay of ²⁶Al, reacting with anhydrous materials to form H₂O/OH-rich minerals¹⁵, and a carbonaceous chondritic CM- or CI-like composition. The temperature and bulk density evolution of initially water-rich small bodies were calculated using a one-dimensional (1D) finite differences thermal evolution model¹⁶,¹⁷ for planetesimals heated by ²⁶Al, ⁶⁰Fe and long-lived radionuclides. An ice-rich initial composition that leads to a material dominated by phyllosilicates after aqueous 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.

In particular, thermally activated compaction due to hot pressing of asteroids from an initially low density (that is, highly unconsolidated porous structure) and a bigger size to a higher density and a smaller size was modelled to fit the bulk densities and sizes of the studied large dark asteroids. To this end, a typical initial porosity of 50% (ref. ¹⁷) was reduced following the change of the strain rate calculated as Voigt approximation from the strain rates of components¹⁷. Material properties (thermal conductivity, density, heat capacity and so on) corresponded to the composition assumed and were adjusted with temperature and porosity. For illustration and comparability, we associate bodies of an equal mass but different porosities (that is, different bulk densities and sizes obtained after a model calculation) 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 relative 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 masses and bulk densities obtained from compaction were searched for matches with the masses and bulk densities of observed asteroids. From those matches, accretion times were derived. Figure 2 shows the maximum temperature and the average density calculated as
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 2** | Maximum temperature and average density for initially water-rich planetesimals as a function of the accretion time relative to CAIs and the reference mass. **a**, Maximum temperature. **b**, Average density. The squares show fitted asteroids centred at their reference masses and accretion times and the vertical error bars show the mass uncertainty. The studied asteroids' numbers are also included in the plots. See Methods for more details about thermal evolution modelling. Supplementary Table 3 summarizes key observed properties of asteroids fitted with thermal evolution models, their initial and intermediate properties involved in the modelling procedure and the final calculated properties of asteroid fits and resulting accretion times derived. The error bars plotted show the mass uncertainties of the fits (Methods) that result from the mass estimate observation uncertainties. For the accretion time estimate uncertainty, see Supplementary Table 3.</figcaption></figure>

functions of reference masses and accretion time, where the mass and the accretion time $t_0$ were varied as stated above. Furthermore, the accretion times for several of the asteroids studied that result from the bulk density and mass fits are shown. See Methods for more information about the fitting procedure of bulk densities for the studied large dark asteroids and their corresponding accretion times and uncertainties.

The availability of $^{26}$Al determines the heating and compaction of planetesimals, that is, by the accretion time $t_0$, such that maximum temperatures and structures vary enormously for $t_0 < 3$ Myr relative to CAIs. However, for a later accretion, only the mass (more precisely, the surface-to-volume ratio, that is, the size that corresponds to this mass at a given grain density and bulk porosity) of the body determines its maximum temperature and density due to nearly constant heating by long-lived radionuclides. The models fit the asteroid bulk densities

as an observational parameter and calculate bulk porosities consistent with these densities. We find that most highly porous interiors characterize the large and dark asteroids (Fig. 3) and, consequently, accreted relatively late, that is, at 1.5–3.5 Myr relative to the formation of CAIs with a maximum temperature of <900 K (Fig. 2). Lower bounds on the maximum temperatures can be provided by comparing masses with maximum central temperatures in Fig. 2a for those five asteroids for which observational constraints (that is, the density) do not suffice for producing accretion time fits. These lower bounds are 300 K, 450 K, 550 K, 620 K and 650 K for (762) Pulcova, (31) Euphrosyne, (360) Carlova, (165) Loreley and (241) Germania, respectively. The range of maximum temperatures agrees with the hydration of dry silicates and is insufficient for dehydration, in agreement with the spectra of large dark asteroids.

Contrary to what was assumed by ref. $^{15}$, state-of-the-art accretion models do not produce a correlation between accretion times and heliocentric distance. The current semimajor axes should not be used to derive such objects' accretion times. However, this includes such a correlation at the original accretion location of these asteroids that might have differed considerably from the present ones according to our dynamical models.

## Dynamics of Ceres-like asteroids' orbital implantation

The planets' growth and dynamical evolution caused widespread radial mixing of small bodies$^2$. Volatile-rich asteroids were implanted from more distant orbits by being scattered inwards by the giant planets and then trapped on stable orbits within the belt. This probably happened 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 drag$^{18}$.

(2) The giant planets' orbital migration acted to scatter and shepherd planetesimals. In the Grand Tack model context, the giant planets' late outwards migration scattered volatile-rich planetesimals inwards and implanted a fraction into the belt$^{19}$. Other migration pathways—such as those dominated by the inwards migration of the giant planets—would also have led to implantation$^{18,20}$.

(3) The ice giants' accretion—from the inwards migration and collisional growth of a population of about five Earth-mass cores$^{21}$—scattered planetesimals inwards, implanting a fraction in the asteroid belt due to gas drag$^{22}$.

(4) The giant planet dynamical instability scattered the bulk of the primordial outer planetesimal disk through the inner Solar System to be ejected by Jupiter$^{23}$. A small fraction of these very volatile-rich objects were captured onto stable orbits in the inner Solar System: Jupiter's co-orbital region$^{24,25}$ and the asteroid belt$^{26,27}$.

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 different mechanisms simply because planetesimals must have formed before being implanted. The feeding zones of the other mechanisms also form a rough radial progression. Jupiter and Saturn's in situ growth (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 objects originating between ~5 au and 10 au (refs. $^{18,20,28}$). The ice giants' growth implanted planetesimals from ~10 au to at least 20–30 au (ref. $^{22}$). Finally, the dynamical instability implanted planetesimals that accreted at ~20–40 au (ref. $^{25}$).

Although the exact timing of giant planet growth, migration and instability remain uncertain, we expect later asteroid accretion times to
<figure><img src="image_7.png" /><figcaption>**Fig. 3 |** Evolution of the asteroid interior structure from left to right, as well as final structures obtained. **a,** Asteroids form as loose agglomerates of dry dust and ice particles. **b,** Heating of the interior triggers hydration and progressive compaction. **c,** Grazing impacts then remove the remaining loose surficial layer exposing a hydrated surface. **d,** Some asteroids evolve to a stage that is characterized by fully compacted central regions. Final structures range from structures that are porous throughout (though partially compacted to a varying degree for different asteroids) with a high central porosity of $\phi_c \approx 25\%$ (c), to structures with strongly reduced central porosities of down to 3% (c), to fully compacted interiors overlain by highly porous outer layers (d).</figcaption></figure>

correlate with a more distant origin and implantation by a later-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 outermost parts of the main belt, mostly between 3.0 au and 3.2 au (Fig. 1). Gas-driven capture (mechanisms 1, 2 and 3) produces a broader distribution of implanted asteroids in which it is statistically unlikely not to have captured any objects interior to Ceres' present-day orbit<sup>18,19,22</sup>. For both mechanisms 1 and 3, the peak in the distribution of implanted Ceres-sized planetesimals is close to Ceres' actual orbit<sup>18,22</sup>. However, suppose we assume that Ceres and the large dark asteroids are part of the same population and that no large dark asteroids exist closer to the Sun than Ceres. In that case, it becomes apparent that these mechanisms cannot explain the implantation of the large dark asteroids. In contrast, implantation 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 planets during the dynamical instability<sup>26,27</sup>). This implies that the large dark asteroids originated in the 20–40 au region<sup>26,27</sup>. The outstanding question is why the dwarf planet Ceres should be the innermost.

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 System<sup>2,29</sup>. The carbonaceous/non-carbonaceous isotopic dichotomy measured in meteorites<sup>30</sup> suggests that their parent bodies formed concurrently but not nearby<sup>31</sup>. Instead, the disk of planetesimal-forming solids was divided in two, perhaps by Jupiter's growing core, a non-planet-related pressure bump in the disk or other processes related to the planetesimal formation<sup>32</sup>. Dark primitive asteroids probably represent planetary building blocks in the outermost parts of the disk.

## Surface and interior composition of large dark asteroids

The nature of the surface compositions of Ceres, and also Ceres-like asteroids, is still under debate, and different interpretations have been put forth to explain the absorption features in these objects<sup>33–35</sup>. Laboratory and spectroscopic experiments on meteorites representing all nine carbonaceous chondrite types found no spectral matches for

these large asteroids<sup>36</sup>. Previous studies of Ceres have been conducted to constrain and estimate its surface composition. Using linear mixing, ref. 35 found hydroxide brucite, serpentine and carbonates consistent with Ceres' ground-based spectra. Another study<sup>33</sup> estimated the surface composition of Ceres and found evidence of widespread NH₃-phylosilicates across its surface using best-fit solutions to Dawn's NIR spectra. The presence of NH₃-phylosilicates implies that material from the outer Solar System was incorporated into large dark asteroids, either during their formation at a great heliocentric distance or incorporating material transported into the main belt region<sup>13</sup>.

Spectra of large dark asteroids are similar to the spectra of Himalaya<sup>37</sup>, the largest irregular satellite of Jupiter at 5.2 au. The irregular satellite's spectra exhibit 1 µm and 3 µm bands consistent with those found in Ceres-like asteroids. In addition, NIR spectroscopic measurements of comet 67P/Churyumov–Gerasimenko by the Rosetta spacecraft<sup>38</sup> 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 µm feature in comet 67P was attributed to ammonium salts<sup>38</sup>. Another study<sup>39</sup> also suggested that icy ammonia, condensed in the outer Solar System beyond 5 au, could have migrated inwards and incorporated into Ceres and presumably other large dark asteroids in the main belt.

Ceres has a specific composition that appears to differ from most other large dark asteroids in the main belt<sup>40</sup>. 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 differentiation<sup>41</sup> and might have experienced a loss of a past water ocean<sup>42</sup>. Both modelling and observations suggest a small porosity for Ceres<sup>40,43</sup>, in agreement with more vital compaction due to its larger size and more energetic thermal evolution<sup>44</sup>. In contrast, current observations indicate no free water and higher porosity, and lower metamorphic temperatures for the other large dark asteroids, supported by our modelling thermal evolution section. Being much more evolved, Ceres owes its impressive geological evolution and past to its dwarf planet size and a much more extensive water action.

Is asteroid Hygiea, the fourth largest main belt asteroid, the second dwarf planet in the main belt? The Dawn mission revealed that Ceres is geologically evolved, with evidence of tectonic and cryovolcanic activities and a heavily cratered surface<sup>8</sup>. Previous observational results showed that the dwarf planet Ceres and asteroid Hygiea are spectrally similar in that they both have a 3 µm band centred at ~3.05 µm (ref. 7), unlike most of the studied large dark asteroids that have a 3 µm feature centred at ~3.15 µm. In addition, Hygiea was found to have a basin-free spherical shape comparable to Ceres<sup>44</sup>. The accretion time of 2.65 Myr after CAIs derived for Hygiea is earlier than the accretion times of ≥5 Myr after CAIs suggested for Ceres by different studies (for example, ref. 16 and references therein). This is consistent with less efficient cooling of Ceres through the surface than for Hygiea. If Ceres had accreted 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 asteroids addressed here, it was explicitly not fitted. However, models with a Ceres-like water fraction would necessitate a lower grain density, shifting the density isolines in Fig. 2b to more enormous reference masses and to later accretion times since the water fraction would not contain radioactive heat sources. The shapes of the density isolines in Fig. 2b imply an accretion time close to or later than ~5 Myr after CAIs. Suppose Ceres and Hygiea have a similar surface composition and are of a similar origin. In that case, the accretion of planetesimals must have occurred over an extended time interval of more than 2.5 Myr in the region of the Solar System where both objects formed. The discovery of large dark asteroids smaller than Ceres near its orbital vicinity suggests that this dwarf planet is possibly not unique in the main belt and its surface composition is not driven by its vast size.
<figure><img src="image_8.png" /></figure>

**Fig. 4 | Implantation of planetesimals into the asteroid belt during the planets' growth and dynamical evolution.** The disk's temperature profile established a gradient in the composition of small bodies during planetesimal formation (for example, ref. ¹⁵). The presence of ammoniated phyllosilicates³³ indicates that Ceres (and presumably also the large dark planetesimals) probably originated beyond Saturn's orbit and perhaps much farther out. Planetesimals from the Jupiter-Saturn region were implanted during the gas giants' rapid gas accretion¹⁸. The migration of the gas and ice giants caused the source region

of implanted planetesimals to expand outwards¹⁸,¹⁹. The ice giants' growth implanted additional planetesimals²². The giant planet's instability then implanted some asteroids from the outer planetesimal disk²⁵,²⁶—this is the likely source of the large dark asteroids. The instability may have been triggered by the dispersal of the gaseous disk⁶⁸, such that these implantation mechanisms were separated in time by only a few to ten million years. Many volatile-poor asteroids were probably implanted from the terrestrial planet-forming region²⁹.

# 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) to reduce the data⁴⁶.

For asteroids' LXD and Prism observations, we followed the same 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 spectral 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

frames at beam B of the telescope. After this subtraction, the residual 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 measured close in airmass to remove telluric absorptions (mostly water vapour at these wavelengths). Wavelength calibration was conducted at $\lambda < 2.5$ µm using argon lines measured with the internal calibration box and at $\lambda > 2.5$ µm using telluric absorption lines.

## Thermal flux modelling and correction

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 spectra is essential for adequately characterizing mineral absorptions in asteroids. We used the Near-Earth Asteroid Thermal Model (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
measured thermal excess was fitted with a model excess (Supplementary Fig. 3) that was then subtracted from the measured thermal flux relative spectra of the asteroids (Supplementary Fig. 4).

In the thermal model, we used parameters that include heliocentric 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. The beaming parameter was incorporated in the NEATM model to account for differences in surface roughness. To minimize a chi-squared fit to asteroids' observational data and find the surface temperature that best matches the measured thermal flux, the NEATM model iterates through several approximations of the beaming and geometric albedo. We assumed both bolometric and spectral emissivity to be 0.9 and the night sides of the asteroids to emit no thermal energy in the model.

## Calculation of the 3 µm band parameters

The absorption feature at ~3 µm in the studied asteroids was isolated and divided by a straight-line continuum in wavelength space following 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, $D_\lambda$, at a given wavelength, was calculated relative to the continuum using the following equation:

$$D_\lambda = \frac{R_c - R_\lambda}{R_c}, \qquad (1)$$

where $R_\lambda$ is the reflectance at a given wavelength $\lambda$, and $R_c$ is the reflectance of the continuum at the same wavelength as $R_\lambda$. Band depth uncertainty was calculated using the following equation:

$$\delta D_\lambda = D_\lambda \times \sqrt{\left(\frac{\delta R_1}{R_1}\right)^2 + \left(\frac{\delta R_c}{R_c}\right)^2}, \qquad (2)$$

where

$$R_1 = R_c - R_\lambda, \qquad (3)$$

and

$$\delta R_1 = \sqrt{(\delta R_c)^2 + (\delta R_\lambda)^2}, \qquad (4)$$

$\delta R_c$ and $\delta R_\lambda$ were derived using each wavelength's uncertainty calculated during the data reduction process.

The 3 µm band area was calculated by integrating the spectral curve below the continuum of the absorption feature. The band centre was computed by applying a sixth-order polynomial fit to the central part of the absorption feature. An average of at least five measurements made by varying the positions of band maxima was used for the band area and band centre calculations. Uncertainties for the band area and centre were calculated by the 2σ standard deviation representing variability from the average.

## Thermal evolution model description

The temperature and bulk density evolution of initially water-rich small bodies were calculated using a 1D finite differences thermal evolution model¹⁶,¹⁷ for planetesimals heated by ²⁶Al, ⁶⁰Fe and long-lived radionuclides. In particular, thermally activated compaction due to the hot pressing of bodies with an initially unconsolidated porous structure was modelled to fit the bulk densities of large low-albedo asteroids under consideration and, therefore, constrain their accretion time.

## Energy balance

A 1D finite differences thermal evolution model for planetesimals heated mainly by ²⁶Al presented in refs. ¹⁶,¹⁷ was adapted for the current study. It calculates the heating of small porous bodies, their thermal evolution, and the compaction of a mixture of dry and hydrated material from an initially unconsolidated state due to hot pressing by solving 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 and solved for the temperature:

$$\rho c_p (1 + x_{\text{ice}} S_{\text{ice}}) \frac{\partial T}{\partial t} = \frac{1}{r^2} \frac{\partial}{\partial r} (kr^2 \frac{\partial T}{\partial r}) + Q(r, t), \qquad (5)$$

with the bulk density $\rho$, the heat capacity $c_p$, the initial fraction $x_{\text{ice}}$ and the Stefan number $S_{\text{ice}}$ 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 ²⁶Al and ⁶⁰Fe and long-lived ⁴⁰K, ²³²Th, ²³⁵U and ²³⁸U:

$$Q(r, t) = (1 - v_{\text{ice}}) \rho \sum_i f_i Z_i \frac{E_i}{\tau_i} \exp\left(-\frac{t - t_0}{\tau_i}\right), \qquad (6)$$

with the initial water ice volume fraction $v_{\text{ice}}$, the porosity-dependent bulk density $\rho$, the number of atoms of a stable isotope per 1 kg of the primordial material $f$, the initial ratio of radioactive and stable isotope $Z$, the decay energy $E$, the mean life $\tau = \lambda/\log(2)$, the half-life $\lambda$ and the accretion time $t_0$ of the planetesimal. See Supplementary Table 6 for the associated parameter values. A homogeneous heat source distribution within the material is assumed, while the heat source density scales further with the porosity $\phi$. The porosity is initially constant throughout 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 $T_s = 230$ K throughout the planetesimal with a constant surface temperature $T_s$.

## Composition and material properties

We assume properties similar to CM chondrites based on spectral similarities of large dark asteroids with water-rich carbonaceous chondrites. The initial composition is considered to be mainly a mixture of anhydrous materials and water ice that was later melted by heat sources such as the decay of ²⁶Al, 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 entirely consumed for the aqueous alteration leading to a composition with ~60 vol% hydrated silicates and ~40 vol% anhydrous silicates, that is, ~50 wt% for either. In the following, notations $x_{\text{ice}} = 0.13$, $x_{\text{dust}} = 0.87$, $v_{\text{ice}} = 0.33$, $v_{\text{dust}} = 0.67$, $v_{\text{hyd}} = 0.5$, $x_{\text{anh}} = 0.5$, $v_{\text{hyd}} = 0.6$ and $v_{\text{anh}} = 0.4$ are used. This agrees with an average grain density of ~2,460 kg m⁻³ calculated 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 grain density, thermal conductivity and heat capacity, needed for the numerical procedure. This approximation does not include minor phases and trace elements. Minor phases such as ammonia would influence material properties to an amount that would lead to negligible differences in the thermal evolution modelling outcomes. Therefore, they are neglected, but this neglection does not contradict the presence of ammonia in the initial composition. The grain density is at the lower end of known CM grain densities. An average grain density of 2,700 kg m⁻³ applied to the asteroids considered would imply current porosities of up to 50%. However, the process of cold pressing that acts
during the accretion in the absence of notable heating (for example, ref. 52) already reduces the porosity in planetesimals to ~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 negligible variations in the modelling outcome. Thus, the composition used here is reasonably representative in terms of thermal evolution and compaction behaviour.

A typical initial porosity of 50% was reduced following the change of the strain rate that is calculated as Voigt approximation from the strain rates of components 53. 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 can be approximated by packings of spheres. The loosest close packing that is just stable under the application of external forces has a porosity of ~44% (refs. 54,55). While planetesimals accrete from very fluffy dust aggregates with porosities of up to 90%, collisions of these aggregates 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 thermal evolution models (for example, ref. 52 and follow-up papers).

Material properties (thermal conductivity, density, heat capacity 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 $T_s = 272$ K and $T_i = 274$ K to avoid numerical issues with too sharp a phase transition at 273 K. We include the consumption of the latent heat $L = 3.34 \times 10^5$ 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 heat capacity of 4,200 J K$^{-1}$ kg$^{-1}$ of liquid water. The aqueous alteration and, therefore, the formation of hydrated silicates is assumed to occur quasi-instantaneously after reaching $T_i$.

The local bulk density $\rho$ is derived from the grain density $\rho_g$ by scaling it with the local volume filling factor $(1-\phi): \rho = (1-\phi)\rho_g$. The equations for the heat capacity $c_p$ and the thermal conductivity $k$ are averages of the water ice and anhydrous silicates ($T < T_i$) or hydrated and anhydrous silicates ($T \ge T_i$) contributions. The thermal conductivity $k$ is calculated as a volume-fraction-weighted geometric mean of the thermal conductivities of water ice and anhydrous silicate dust:

$$k(\phi, T) = \left(\frac{567}{T}\right)^{\nu_{\text{ice}}} 4.3^{\nu_{\text{dust}}} \left[\exp\left(-\frac{4}{0.08}\phi\right) - \exp\left(-4.4 - \frac{4}{0.17}\phi\right)\right]^{1/4} \quad (7)$$

for $T < T_i$, or of hydrated and anhydrous silicates

$$k(\phi, T) = \left(\frac{1}{0.404+0.000246T}\right)^{\nu_{\text{hyd}}} 4.3^{\nu_{\text{anh}}} \left[ (\max(1-2.216\phi, 0))^4 - \exp\left(-4.8 - \frac{4}{0.167}\phi\right) \right]^{1/4} \quad (8)$$

for $T \ge T_i$.

Similarly, the heat capacity is calculated as a mass fraction-weighted arithmetic mean

$$c_p(T) = x_{\text{ice}}(185 + 7.037T) + x_{\text{dust}}(800 + 0.25T - 1.5 \times 10^7 T^{-2}) \quad (9)$$

for $T < T_i$, and

$$c_p(T) = x_{\text{hyd}}(0.9 - 6.3T^{-0.5} - 14,600T^{-2} + 1.91 \times 10^6 T^{-3}) + x_{\text{anh}}(800 + 0.25T - 1.5 \times 10^7 T^{-2}) \quad (10)$$

for $T \ge T_i$, where the olivine heat capacity is approximated with a H-chondritic $c_p$.

For the thermal conductivities and heat capacities of the species, see ref. 16 and references therein.

## Porosity

The evolution of the volume fraction of bulk pore space, that is, porosity $\phi$ is calculated for $T \ge T_i$ by considering the creep of dry olivine and wet olivine as an approximation of the bulk material. It is described by non-stationary differential equations for a strain rate-stress relation. The bulk strain rate is calculated as a volume-fraction-averaged expression in the Voigt approximation 53:

$$\frac{\partial \log(1-\phi)}{\partial t} = \dot{\epsilon} = \nu_{\text{hyd}}\dot{\epsilon}_1 + \nu_{\text{anh}}\dot{\epsilon}_2, \quad (11)$$

with a diffusion creep equation for the deformation of wet olivine derived by ref. 58:

$$\dot{\epsilon}_2 = 1.2 \times 10^{-26} \sigma^{1.1} b^{-3} \exp\left(-\frac{295,000 + P \times 20 \times 10^{-6}}{8.314T}\right), \quad (12)$$

and a diffusion creep equation for the deformation of dry olivine derived by ref. 59:

$$\dot{\epsilon}_2 = 1.26 \times 10^{-18} \sigma^{1.5} b^{-3} \exp\left(-\frac{355,640}{8.314T}\right), \quad (13)$$

with the effective stress $\sigma$, the grain size $b = 10^{-5}$ m, the lithostatic pressure $P$ and the temperature $T$ in kelvin. An initial porosity of $\phi_0 = 0.5$ used is a typical value based on the porosities of the random loose and random close packings 43,52). The effective stress $\sigma$ is calculated as in ref. 17 for the simple cubic packing of equally sized spheres 59 that has a porosity of ~50%. With $\phi_0 = 0.5$ and $\rho_g = 2,460$ kg m$^{-3}$, the initial density is 1,230 kg m$^{-3}$.

## Radius and resolution

The radius $R(t)$ of the object considered changes with the bulk porosity $\phi_{\text{bulk}}(t)$ at the time $t$, obtained by integrating the local porosity over the radius $r$, according to

$$R(t) = (1 - \phi_{\text{bulk}})^{-1/3} R, \quad (14)$$

where $R$ is the reference radius, that is, the radius at zero porosity. The reference radius is used for the analysis of the results as it is representative for sets of bodies with equal mass and grain density but different porosity. All equations involved are solved on the spatial radius domain ranging from the centre of the planetesimal up to its surface. The spatial grid is transformed from $0 \le r \le R$, with the distance from the centre $r$ in metres, to $0 \le \eta \le 1$ using the transformation $\eta = r/R(t)$. The time and space derivatives are also transformed and the transformed expressions are applied to all equations involved, such that features like 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 according to the above transformations. Non-stationary equations are also discretized with respect to the time variable $t$ and solved using the implicit finite-difference method.

## Fitting procedure

We used asteroid bulk densities and sizes from ref. 60 for most asteroids, 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 macroporosities assumed to be representative of all asteroids presented in ref. 60
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 km objects surpassing the age of the Solar System⁶³, and on the sizes of the asteroids we consider in the present study being >90 km, all these asteroids are probably not rubble piles and should have nearly zero macroporosity. A new macroporosity result of ~16% for the sub-kilometre rubble pile Ryugu indicates, further, that even for tiny rubble piles, macroporosities may have been systematically overestimated in the past⁶⁴. Therefore, we consider that the porosity is microporosity by its nature and calculate it from the asteroid bulk densities and the meteorite analogue grain density:

$$ \phi = \phi_{\text{micro}} = 1 - \frac{\rho_{\text{asteroid,bulk}}}{\rho_{\text{meteorite,grain}}}, \quad (15) $$

where $\rho_{\text{meteorite,grain}}$ is the grain density of the meteorite analogue. As a meteorite analogue we used CM chondrites, as suggested by refs.⁶⁰,⁶⁵, and very similar spectral properties that indicate a similar composition. Previous studies⁵,¹⁰,¹² found that the 3 µm reflectance spectra of Ceres and the largest ($d > 200$ km) dark asteroids have similar spectral properties and presumably compositions. We extend this statement to the asteroids investigated in the current study. Therefore, it is reasonable to assume a similar composition for the modelling. A CV analogue suggested for Aletheia and Palma and a mesosiderite analogue suggested for Cybele by ref.⁶⁰ would contradict asteroids' hydrated surfaces actually observed, as CV chondrites experienced very little to no aqueous alteration and have less than ~4 vol% phyllosilicates⁵¹,⁶⁶,⁶⁷ and mesosiderites are similar to igneous eucrites and diogenites in their silicate composition.

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 $t_0$ values that result in bulk density and diameter values that match the bulk densities and diameters of the large primitive asteroids considered. For illustration and comparability, we associate bodies of an equal mass but different porosities (that is, also different bulk densities and sizes obtained after a model calculation) with a 'reference' diameter, that is, a theoretical diameter at zero porosity. Note that for illustration and comparability, we associated such bodies with a reference mass in the main paper as the reference diameter scale is effectively equivalent to a mass scale at a uniform grain density. The reference diameter and accretion time intervals covered by our calculations are 10 km to 1,000 km and 1 Myr to 5 Myr relative to the formation of CAIs, respectively. Unlike previous thermal modelling investigations that assumed a correlation 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 current semimajor axes should not be used for deriving accretion times 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 the end time of planetesimal accretion. Thermal evolution and compaction models with a low initial density (that is, a high initial porosity) and bigger initial diameters than reference diameters (as prescribed by the initial porosity) were calculated for all resulting pairs of parameters.

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 diameter becomes smaller, the porosity becomes smaller, the bulk density becomes higher and all values are calculated consistently. Due to the boundary condition of $T_s = 230$ K for the planetesimal surface, a relatively thin superficial regolith layer is retained, where water ice does not melt at any time during the evolution and where the initial composition of water ice and dry silicates does not change. This does not agree with the spectral observations of asteroids in the present study. In particular,

the structure of this layer is that of an unsintered low-strength loose particle agglomerate. Therefore, such layers must have been ablated by impacts, such that hydrated and higher-strength partially sintered material was exposed. Removing thin upper layers by impacts is also reasonable as asteroid families are observed, and they probably formed in a similar way. Assuming that those impacts that occur after the cessation 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 of the interior. The average density is a value that is bounded above by 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 their bulk densities were then searched for matches with the asteroids' sizes and bulk densities. Such matches already have the bulk densities and sizes of the asteroids. For a given asteroid, a match can occur only 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 layer is typically a few 100 m thick at most.

## Accretion time and reference diameter (or mass) uncertainties

Our analysis is concentrated on the size and density values currently provided within the margin of error⁶⁰. While the size uncertainties are 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, as the thermal evolution of planetesimals that accrete after the extinction of ²⁶Al (a few half-lives) and are heated only by long-lived radionuclides is very similar regardless of the accretion time, the bulk density isolines reach plateaus (Fig. 2) where both peak temperature and bulk density isolines become nearly horizontal). Therefore, if plotted, some error bars for the accretion time would extend infinitely in time towards the present day. This is not reasonable since accretion times are limited by the time when the accretion of planetesimals ended. The results of our modelling inherit the shortcomings of the available data. The resulting uncertainties in the accretion times derived can be constrained only for a few cases. For (259) Aletheia, an uncertainty of +0.1/-0.6 Myr can be determined for $t_0$. In other cases, an estimate only towards either an earlier or a later formation time can be provided (or even none): (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 Myr relative to CAIs.

The maximally possible uncertainties for the reference diameters, thus, masses, arise from the mass estimate uncertainties. They were obtained using the equation:

$$ D = 2 \left( \frac{3}{4\pi} \frac{M}{\rho_{\text{meteorite,grain}}} \right)^{1/3} \text{metres} \quad (16) $$

and vary from <7 km (Aletheia) to 69 km (Patientia), corresponding to 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 slight tendencies towards the upper bounds.

## Data availability

All data are available in the paper or its Supplementary Information.

## References

1. DeMeo, F. E. & Carry, B. Solar System evolution from the compositional mapping of the asteroid belt. Nature 505, 629-634 (2014).
2. Raymond, S. N. & Nesvorny, D. in *Vesta and Ceres: Insights from the Dawn Mission for the Origin of the Solar System* (eds Marchi, S. et al.) 227–249 (Cambridge Univ. Press, 2022).

3. Cuzzi, J. N., Hogan, R. C. & Bottke, W. F. Towards initial mass functions for asteroids and Kuiper belt objects. *Icarus* **208**, 518–538 (2010).

4. Gaffey, M. F., Burbine, T. H. & Binzel, R. P. Asteroid spectroscopy: progress and perspective. *Meteoritics* **28**, 161–187 (1993).

5. Takir, D. & Emery, J. P. Outer main belt asteroids: Identification and distribution of four 3-µm spectral groups. *Icarus* **219**, 641–654 (2012).

6. Rivkin, A. S., Thomas, C. A., Howell, E. S. & Emery, J. P. The Ch-class asteroids: connecting a visible taxonomic class to a 3-µm band shape. *Astron. J.* **150**, 198 (2015).

7. Usui, F., Hasegawa, S., Ootsubo, T. & Onaka, T. AKARI/IRC Near-infrared Asteroid Spectroscopic Survey: AcuA-spec. *Publ. Astron. Soc. Jpn* **71**, 1 (2019).

8. Russell, C. T. et al. Dawn arrives at Ceres: exploration of a small, volatile-rich world. *Science* **353**, 1008–1010 (2016).

9. Takir, D. et al. Constraints and nature and the degree of aqueous alteration in CM and carbonaceous chondrites. *Meteorit. Planet. Sci.* **48**, 1618–1637 (2013).

10. Takir, D., Emery, J. P. & McSween, H. Y. Toward an understanding of phyllosilicate mineralogy in the outer main asteroid belt. *Icarus* **257**, 185–193 (2015).

11. Rivkin, A. S. & Emery, J. P. Detection of ice and organics on an asteroidal surface. *Nature* **64**, 1322–1323 (2010).

12. Rivkin, A. S., Howell, E. S. & Emery, J. P. Infrared spectroscopy of large, low-albedo asteroids: are Ceres and Themis archetypes or outliers? *J. Geophys. Res. Planets* **124**, 1393–1409 (2019).

13. Rivkin, A. S. et al. The nature of low-albedo small bodies from 3 µm spectroscopy: one group that formed within the ammonia snow line and one that formed beyond It. *Planet. Sci. J.* **3**, 153 (2022).

14. Takir, D. & Emery, J. P. A large 3-micron spectroscopic survey of mid-outer main belt asteroids. In *53rd Lunar and Planetary Science Conference abstr. 1481* (2022).

15. Grimm, R. E. & McSween, H. Y. Heliocentric zoning of the asteroid belt by aluminum-26 heating. *Science* **259**, 653–655 (1993).

16. Neumann, W., Jaumann, R., Castillo-Rogez, J. C., Raymond, C. A. & Russell, C. T. Ceres' partial differentiation: undifferentiated crust mixing with a water-rich mantle. *Astron. Astrophys.* **633**, A117 (2020).

17. Neumann, W. et al. Microporosity and parent body of the rubble-pile NEA (162173) Ryugu. *Icarus* **358**, 114–166 (2021).

18. Raymond, R. N. & Izidoro, A. Origin of water in the inner Solar System: planetesimals scattered inward during Jupiter and Saturn's rapid gas accretion. *Icarus* **297**, 134–148 (2017).

19. Walsh, K. J., Morbidelli, A., Raymond, S. N., O'Brien, D. P. & Mandell, A. M. A low mass for Mars from Jupiter's early gas-driven migration. *Nature* **475**, 206–209 (2011).

20. Pirani, S., Johansen, A., Bitsch, B., Mustill, A. J. & Turrini, D. Consequences of planetary migration on the minor bodies of the early Solar System. *Astron. Astrophys.* **623**, A169 (2019).

21. Izidoro, A., Morbidelli, A., Raymond, S. N., Hersant, F. & Pierens, A. Accretion of Uranus and Neptune from inward-migrating planetary embryos blocked by Jupiter and Saturn. *Astron. Astrophys.* **582**, A99 (2015).

22. Ribeiro de Sousa, R. et al. Dynamical origin of the dwarf planet Ceres. *Icarus* **379**, 114933 (2022).

23. Tsiganis, K., Gomes, R., Morbidelli, A. & Levison, H. F. Origin of the orbital architecture of the giant planets of the Solar System. *Nature* **435**, 459–461 (2005).

24. Morbidelli, A., Levison, H. F., Tsiganis, K. & Gomes, R. Chaotic capture of Jupiter's Trojan asteroids in the early Solar System. *Nature* **435**, 462–465 (2005).

25. Nesvorný, D., Vokrouhlicky, D. D. & Morbidelli, A. A. Capture of Trojans by jumping Jupiter. *Astrophys. J.* **768**, 45 (2013).

26. Levison, H. F., Morbidelli, A., Tsiganis, K., Nesvorný & Gomes, R. Late orbital instabilities in the outer planets are induced by interaction with a self-gravitating planetesimal disk. *Astron. J.* **142**, 5 (2009).

27. Vokrouhlicky, D., Bottke, W. F. & Nesvorny, D. Capture of trans-Neptunian planetesimals in the main asteroid belt. *Astron. J.* **152**, 39 (2016).

28. O'Brien, D. P., Walsh, K. J., Morbidelli, A., Raymond, S. N. & Mandell, A. M. Water delivery and giant impacts in the Grand Tack scenario. *Icarus* **239**, 74–84 (2014).

29. Raymond, S. & Izidoro, A. The empty primordial asteroid belt. *Sci. Adv.* **3**, e1701138 (2017).

30. Warren, P. H. Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: a subordinate role for carbonaceous chondrites. *Earth Planet. Sci. Lett.* **311**, 93–100 (2011).

31. Kruijer, T. S., Kleine, T. & Borg, L. E. The great isotopic dichotomy of the early Solar System. *Nat. Astron.* **4**, 32–40 (2020).

32. Izidoro, A. et al. Planetesimal rings as the cause of the Solar System's planetary architecture. *Nat. Astron.* **6**, 357–366 (2022).

33. De Sanctis, M. C. et al. Ammoniated phyllosilicates with a likely outer Solar System origin on (1) Ceres. *Nature* **528**, 241–244 (2015).

34. King, T. V. V., Clark, R. N., Calvin, W. M., Sherman, D. M. & Brown, R. H. Evidence for ammonium-bearing minerals on Ceres. *Science* **255**, 1551–1553 (1992).

35. Miliken, R. E. & Rivkin, A. S. Brucite and carbonate assemblages from altered olivine-rich materials on Ceres. *Nat. Geosci.* **2**, 258–261 (2009).

36. Takir, D., Stockstill-Cahill, K. R., Hibbitts, C. A. & Nakauchi, Y. 3-µm reflectance spectroscopy of carbonaceous chondrites under asteroid-like conditions. *Icarus* **333**, 243–251 (2019).

37. Brown, M. E. & Rhoden, R. A. The 3 mm spectrum of Jupiter's irregular satellite Himalia. *Astrophys. J.* **793**, L44 (2014).

38. Poch, O. Ammonium salts are a reservoir of nitrogen on a cometary nucleus and possibly on some asteroids. *Science* **367**, eaaw7462 (2020).

39. Mousis, O. & Alibert, Y. On the composition of ices incorporated in Ceres. *Mon. Not. R. Astron. Soc.* **353**, 188–192 (2005).

40. Castillo-Rogez, J. C. et al. Ceres: astrobiological target and possible ocean world. *Astrobiology* **20**, 269–291 (2020).

41. McCord, T. B. & Castillo-Rogez, J. B. Ceres's internal evolution: the view after Dawn. *Meteorit. Planet. Sci.* **53**, 1778–1792 (2018).

42. Fu, R. et al. The interior structure of Ceres as revealed by surface topography. *Earth Planet. Sci. Lett.* **47**, 153–164 (2017).

43. Neumann, W., Breuer, D. & Spohn, T. Modeling the internal structure of Ceres: coupling of accretion with compaction by creep and implications for the water-rock differentiation. *Astron. Astrophys.* **584**, A117 (2015).

44. Vernazza, P. et al. A basin-free spherical shape as an outcome of a giant impact on asteroid Hygiea. *Nat. Astron.* **4**, 136–141 (2020).

45. Rayner, J. T. et al. SpeX: a medium-resolution 0.8–5.5 micron spectrograph and imager for the NASA Infrared Telescope Facility. *Publ. Astron. Soc. Pac.* **115**, 362–382 (2003).

46. Cushing, M. Spectral extraction package for SpeX, a 0.8–5.5 micron cross-dispersed spectrograph. *Publ. Astron. Soc. Pac.* **166**, 362–376 (2004).

47. Harris, A. A thermal model for near-Earth asteroids. *Icarus* **131**, 291–30 (1998).

48. Lebofsky, L. A. A refined 'standard' thermal model for asteroids based on observations of 1 Ceres and 2 Pallas. *Icarus* **68**, 239–251 (1986).
49. Bowell, E. et al. in *Asteroids II* (eds Binzel, R. P. et al.) (Univ. Arizona Press, 1989).

50. Cloutis, E. A., Gaffey, M. J., Jackowski, T. L. & Reed, K. L. Calibrations of phase abundance, composition, and particle size distribution for olivine-orthopyroxene mixtures from reflectance spectra. *J. Geophys. Res.* **91**, 11641–11653 (1986).

51. O'D. Alexander, C., Howard, K. T., Bowden, R. & Fogel, M. L. The classification of CM and CR chondrites using bulk H, C and N abundances and isotopic compositions. *Geochim. Cosmochim. Acta* **123**, 244–260 (2013).

52. Henke, H. P., Gail, H., Trieloff, M., Schwarz, W. H. & Kleine, T. Thermal evolution and sintering of chondritic planetesimals. *Astron. Astrophys.* **537**, A45 (2012).

53. Dygert, N., Hirth, G. & Liang, Y. A flow law for ilmenite in dislocation creep: implications for lunar cumulate mantle overturn. *Geophys. Res. Lett.* **43**, 532–540 (2016).

54. Onoda, G. Y. & Liniger, E. G. Random loose packings of uniform spheres and the dilatancy onset. *Phys. Rev. Lett.* **64**, 2727 (1990).

55. Jaeger, H. M. & Nagel, S. Physics of the granular state. *Science* **255**, 1523–1531 (1992).

56. Weidling, R., Guttler, C., Blum, J. & Brauer, F. The physics of protoplanetary dust agglomerates. III. Compaction in multiple. *Astrophys. J.* **696**, 2036–2043 (2009).

57. Kothe, S., Güttler, S. C. & Blum, J. The physics of protoplanetary dust agglomerates. V. Multiple impacts of dusty agglomerates at velocities above the fragmentation threshold. *Astrophys. J.* **725**, 1242–1251 (2010).

58. Mei, S. & Kohlstedt, D. L. Influence of water on plastic deformation of olivine aggregates: 1. Diffusion creep regime. *J. Geophys. Res.* **105**, 21457–21469 (2000).

59. Schwenn, M. B. & Goetze, C. Creep of olivine during hot-pressing. *Tectonophysics* **48**, 41–60 (1978).

60. Carry, B. Density of asteroids. *Planet. Space Sci.* **73**, 98–118 (2012).

61. Fienga, A., Avdellidou, C. & Hanuš, J. Asteroid masses obtained with INPOP planetary ephemerides. *Mon. Not. R. Astron. Soc.* **492**, 589–602 (2020).

62. Walsh, K. J. Rubble pile asteroids. *Annu. Rev. Astron. Astrophys.* **56**, 593–624 (2018).

63. Bottke, W. et al. The fossilized size distribution of the main asteroid belt. *Icarus* **175**, 111–140 (2005).

64. Grott, M. et al. Macroporosity and grain density of rubble pile asteroid (162173) Ryugu. *J. Geophys. Res. Planets* **125**, e2020JE006519 (2020).

65. Clark, E. B. et al. Spectroscopy of B-type asteroids: subgroups and meteorite analogs. *J. Geophys. Res. Planets* **115**, E06005 (2010).

66. Howard, K. T., Benedix, G. K., Bland, P. A. & Cressey, G. Modal mineralogy of CV3 chondrites by X-ray diffraction (PSD-XRD). *Geochim. Cosmochim. Acta* **74**, 5084–5097 (2010).

67. Marrocchi, Y., Bekaert, D. & Piani, L. Origin and abundance of water in carbonaceous asteroids. *Earth Planet. Sci. Lett.* **482**, 23–32 (2018).

68. Liu, B., Raymond, S. N. & Jacobson, S. A. The dispersal of the gaseous disk triggers early Solar System instability. *Nature* **604**, 643–646 (2022).

## 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.

## Author contributions

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.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41550-023-01898-x.

**Correspondence and requests for materials** should be addressed to Driss Takir.

**Peer review information** *Nature Astronomy* thanks Andrew Rivkin, Henry Hsieh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

**Reprints and permissions information** is available at www.nature.com/reprints.

**Publisher's note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

© The Author(s), under exclusive licence to Springer Nature Limited 2023