# Dynamical origin of Theia, the last giant impactor on Earth

Duarte Branco, Pedro Machado, Sean N. Raymond

► To cite this version:

Duarte Branco, Pedro Machado, Sean N. Raymond. Dynamical origin of Theia, the last giant impactor on Earth. Icarus, 2025, 441, pp.116724. 10.1016/j.icarus.2025.116724. hal-05353422

HAL Id: hal-05353422

https://hal.science/hal-05353422v1

Submitted on 8 Nov 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
<figure><img src="image_2.png" /></figure>

Research Paper

# Dynamical origin of Theia, the last giant impactor on Earth

Duarte Branco<sup>a,b ID</sup>, Pedro Machado<sup>a,b ID,*</sup>, Sean N. Raymond<sup>c ID</sup>

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

## ARTICLE INFO

### Keywords:

Solar system terrestrial planets

Planetary dynamics

Planet formation

Lunar origin

Earth (planet)

## ABSTRACT

Cosmochemical studies have proposed that Earth accreted roughly 5%–10% of its mass from carbonaceous (CC) material, with a large fraction delivered late via its final impactor, Theia (the Moon-forming impactor). Here, we evaluate this idea using dynamical simulations of terrestrial planet formation, starting from a standard setup with a population of planetary embryos and planetesimals laid out in a ring centered between Venus and Earth's orbits, and also including a population of CC planetesimals and planetary embryos scattered inward by Jupiter. We find that this scenario can match a large number of constraints, including (i) the terrestrial planets' masses and orbits; (ii) the CC mass fraction of Earth; (iii) the much lower CC mass fraction of Mars, as long as Mars only accreted CC planetesimals (but no CC embryos); (iv) the timing of the last giant (Moon-forming) impact; and (v) a late accretion phase dominated by non-carbonaceous (NC) bodies. For this scenario to work, the total mass in scattered CC objects must have been ~0.2–0.3*$M_{\oplus}$, with an embryo-to-planetesimal mass ratio of at least 8, and CC embryos in the ~0.01–0.05*$M_{\oplus}$ mass range. In that case, our simulations show there are roughly 50-50 odds of Earth's last giant impactor (Theia) having been a carbonaceous object — either a pure CC embryo or an NC embryo that previously accreted a CC embryo. Our simulations thus provide dynamical validation of cosmochemical studies.

## 1. Introduction

The standard scenario of terrestrial planet formation invokes several phases of growth (for a review, see Raymond and Morbidelli, 2022). First, planetesimals form from concentrations of pebbles or large dust particles that either drifted inward or condensed in preferential locations (e.g. Johansen et al., 2014; Birnstiel et al., 2016; Drażkowska et al., 2016). Current modeling favors condensation fronts as preferred locations for planetesimal formation, and infer that the Solar System likely formed an inner ring of planetesimals at ~1 au (Drażkowska and Dullemond, 2018; Lichtenberg et al., 2021; Morbidelli et al., 2022; Izidoro et al., 2022). Next, Moon-to-Mars-sized planetary embryos grow by accreting planetesimals (e.g. Kokubo and Ida, 1998; Kokubo and Ida, 2000; Leinhardt and Richardson, 2005; Wetherill and Stewart, 1993; Weidenschilling et al., 1997). After, there was a chaotic phase of giant impacts between planetary embryos, in the presence of a population of remaining planetesimals (e.g. Wetherill, 1990; Chambers and Wetherill, 1998; Raymond et al., 2006; O'Brien et al., 2006; Morbidelli et al., 2012; Raymond et al., 2014). The last giant impact on the proto-Earth was with an embryo commonly called 'Theia' – this impact caused the final differentiation event on the Earth and led to the formation of the Moon (Benz et al., 1986; Agnor et al., 1999; Canup and Asphaug,

2001; Canup, 2012; Ćuk and Stewart, 2012; Canup et al., 2021). Most studies invoke a timing of 30–100 Myr after CAIs for the Moon-forming impact (Kleine et al., 2009; Avice and Marty, 2014; Jacobson et al., 2014; Thiemens et al., 2019), although in principle it may have taken place as early as 10 Myr after CAIs (Fischer and Nimmo, 2018). Finally, during the 'late accretion' (or 'late veneer' as is more commonly used in cosmochemistry) phase, Earth and the other rocky planets underwent collisions with planetesimals, which delivered highly-siderophile elements to Earth's mantle and crust (Day et al., 2007; Walker, 2009; Bottke et al., 2010; Raymond et al., 2013; Zhu et al., 2021).

Meteorite measurements can constrain the building blocks of the terrestrial planets (e.g. Dauphas, 2017). Given the isotopic dichotomy measured in meteorites (Warren, 2011; Kruijer et al., 2020), there was likely a corresponding dichotomy in the Solar System's planetesimal populations, with non-carbonaceous (NC) material originating interior to Jupiter's orbit and carbonaceous (CC) material exterior (Kruijer et al., 2017). Based on the composition of the bulk silicate Earth, it has been inferred that Earth is composed of mostly NC material, with a ~4–10% CC contribution (e.g. Steller et al., 2022; Savage et al., 2022; Martins et al., 2023), although the exact fraction depends on whether a CI or CV endmember is used (Kleine et al., 2023; Nimmo et al., 2024b).

<footnote><sup>a</sup> Faculdade de Ciências da Universidade de Lisboa, Campo Grande 016, Lisbon, 1749-016, Portugal</footnote>

<footnote><sup>b</sup> Institute of Astrophysics and Space Sciences, Observatório Astronómico de Lisboa, Tapada da Ajuda, Edificio Leste - 2º, Piso, Lisbon, 1349-018, Portugal</footnote>

<footnote><sup>c</sup> Laboratoire d'Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, All. Geoffroy Saint-Hilaire, Bordeaux, 33600 Pessac, France</footnote>

<footnote>* Correspondence to: Faculdade de Ciências da Universidade de Lisboa, Campo Grande 016, 1349-016 Lisbon, Portugal. E-mail address: pmmachado@fc.ul.pt (P. Machado).</footnote>
In contrast, Mars appears to have had a smaller CC contribution of at most a few percent (Kleine et al., 2023). Measurements and modeling both suggest that the late accretion phase, which encompasses the final ~0.5% of material added to Earth, was dominated by NC material for both Earth and Venus (Gillmann et al., 2020; Worsham and Kleine, 2021).

Carbonaceous objects are thought to have accreted beyond Jupiter's orbit (Kruijer et al., 2017; Brasser and Mojzsis, 2020) and been scattered inward during Jupiter and Saturn's gas accretion (Raymond and Izidoro, 2017a) or migration (Walsh et al., 2011; Raymond and Izidoro, 2017a; Pirani et al., 2019). Some were trapped in the asteroid belt via aerodynamic gas drag, and other – in particular, larger bodies that felt weaker drag – were scattered all the way onto orbits that crossed the terrestrial planet region. Chemical modeling suggests that Earth acquired most of its carbonaceous material toward the later part of the main accretion phase (Rubie et al., 2015; Nimmo et al., 2024b; Dauphas et al., 2024). Nimmo et al. (2024b) proposed that the bulk of Earth's carbonaceous material was accreted in the form of a few large impactors rather than a sea of planetesimals (a conclusion also reached by Joiret et al., 2024). Budde et al. (2019) used Mo isotopes to propose the most extreme case, that the last giant impactor (Theia) was a carbonaceous planetary embryo. A top-heavy distribution of CC bodies in the inner Solar System has the advantage of making it easier to explain why Mars has a lower CC fraction than Earth (Kleine et al., 2023) and also why late accretion was dominated by NC material, considering that late accretion is assumed to include only planetesimal impacts (Bottke et al., 2010; Morbidelli and Wood, 2015).

In this paper, we dynamically test the idea that Theia was a carbonaceous object. We use N-body simulations to model the accretion of the terrestrial planets in conjunction with a tail of material scattered inward by Jupiter and Saturn's rapid gas accretion. We conclude that the scenario proposed by Budde et al. (2019) and Nimmo et al. (2024b) is dynamically plausible, and that Theia could have been either a CC planetary embryo or an embryo consisting of a mixture of NC and CC material.

## 2. Methodology

We performed a suite of N-body simulations of the accretion of the terrestrial planets. To start (Section 2.1), we replicate the 'annulus' or 'empty asteroid belt' scenario proposed by Hansen (2009) and tested by a number of subsequent studies (Kaib and Cowan, 2015; Raymond and Izidoro, 2017; Nesvorný et al., 2021; Woo et al., 2023; Joiret et al., 2024). We explain the initial conditions and integration method. Then (Section 2.2), we include a tail of carbonaceous material assumed to have been scattered inward by Jupiter (Raymond and Izidoro, 2017a). Finally (Section 2.3), we explain how we addressed the effect of the giant planet instability (Tsiganis et al., 2005; Nesvorný, 2018) in a subset of simulations.

### 2.1. Simulations to match the terrestrial planets

Our simulations start in the late phase of terrestrial accretion, after dispersion of the gaseous disk. We make the assumption that the solid mass is divided between planetesimals and planetary embryos, and that they are initial distributed in a narrow ring, following the annulus model (Hansen, 2009; Kaib and Cowan, 2015; Nesvorný et al., 2021) and consistent with recent models of planetesimal formation (e.g. Drążkowska and Alibert, 2017; Morbidelli et al., 2022; Izidoro et al., 2022). As in previous studies (e.g. Chambers and Wetherill, 1998; Raymond et al., 2009), we assume that embryos are spaced in units of mutual Hill radii, defined as (Chambers et al., 1996):

$$R_{Hm_{i,l+1}} = \left[ \frac{M_i + M_{i+1}}{3M_{\odot}} \right]^{1/3} \frac{(a_i + a_{i+1})}{2}, \quad (1)$$

where *M* and *a* are the mass and semi-major axis of the two planets and *M*<sub>☉</sub> is the stellar mass. We assume a surface density profile that

<caption>Table 1</caption>

Initial positions for Jupiter and Saturn in simulations. Symbols represent: Semi-major axis (a), eccentricity (e), inclination (i), argument of pericenter (g), longitude of ascending node (n) and mean anomaly (M).

<table><thead><tr><th>Planet</th><th>a (AU)</th><th>e × 10<sup>-2</sup></th><th>i (deg)</th><th>g (deg)</th><th>n (deg)</th><th>M (deg)</th></tr></thead><tbody><tr><td>Jupiter</td><td>5.4297</td><td>0.490</td><td>0.1</td><td>0</td><td>113.2953</td><td>6.9170</td></tr><tr><td>Saturn</td><td>7.2987</td><td>0.995</td><td>0.2</td><td>10</td><td>276.4414</td><td>191.6128</td></tr></tbody></table>

scales with orbital radius *r* as $\Sigma(r) = \Sigma_1 r^{-3/2}$ (note that, for broad disks, the exponent has important consequences for accretion; see Raymond et al., 2005; Izidoro et al., 2015). The planetesimal number and mass is the same within every set of simulations, with only their distribution changing.

We varied a few parameters to achieve a good replica of the Solar System, including the position and width of the annulus, the inter-embryo spacing (measured in units of mutual Hill radii), and the total masses of embryos and planetesimals within the annulus. The orbital eccentricities of planetesimals and embryos were initially set to zero, and the inclination was randomly chosen between zero and 0.5°, following Hansen (2009). The other orbital angles were drawn at random. We assumed that Jupiter and Saturn were already present, and trapped in a mutual 3:2 mean motion resonance (configuration in Table 1), consistent with simulations of their migration within the Sun's gaseous disk (Morbidelli et al., 2007; Pierens and Nelson, 2008). Of course, our simulations start after dispersal of the disk so gas drag and migration are not accounted for.

#### 2.1.1. Integration method

Our simulations used the hybrid integrator in the Mercury6 N-Body code (Chambers, 1999), which uses the mapping of Wisdom and Holman (1992) when objects are well-separated and switches to a Bulirsch–Stoer integrator for close encounters. Our simulations were carried out for 200 Myr using a time step of 6 days. The size of the Sun was inflated to 0.15 au, to avoid numerical errors during perihe- lion passages (Rauch and Holman, 1999). The Bulirsch–Stoer accuracy parameter was set to $10^{-11}$. Collisions were treated as inelastic mergers.

Embryos interacted gravitationally with all other massive objects in the simulation, but planetesimal particles did not interact gravitation- ally with other planetesimals (but did feel the gravity of the embryos and planets).

#### 2.1.2. Simulation outcomes

To evaluate the success of simulations, we compared the orbits of the planets to the real ones', and also relied on two system-wide quantities: the terrestrial planets' radial mass concentration (RMC) and the normalized angular momentum deficit (AMD) (Chambers, 2001; Laskar, 1997). These are defined as:

$$AMD = \frac{\Sigma_j m_j \sqrt{a_j} [1 - \sqrt{(1 - e_j^2) \cos i_j}]}{\Sigma_j m_j \sqrt{a_j}} \quad (2)$$

$$RMC = \max \left( \frac{\Sigma_j m_j}{\Sigma_j m_j [\log_{10}(a_j/a_{j+1})]^2} \right) \quad (3)$$

The terrestrial planets' real values are AMD = 0.0018 and RMC = 89.9 (Chambers, 2001).

Table 2 lists the parameters that we found provided the best match to the terrestrial planets. Fig. 1 shows the outcome of 7 simulations with this setup, in terms of the planets' orbits and the system-wide RMC and AMD values.
<table><caption>**Table 2**

Parameters chosen to replicate the terrestrial planets.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>Annulus radius</td><td>0.7 to 1.2 AU</td><td>Mutual hill radii spacing (Δ)</td><td>2 to 4</td></tr><tr><td>Σ<sub>1</sub></td><td>20.48 g cm<sup>-2</sup></td><td>Number of planetesimals</td><td>900</td></tr><tr><td>Total embryo mass target</td><td>2 M<sub>⊕</sub></td><td>Total planetesimal mass</td><td>0.25 M<sub>⊕</sub></td></tr><tr><td>Embryo mass range</td><td>0.03 M<sub>⊕</sub> to 0.07 M<sub>⊕</sub></td><td>Range of embryo number</td><td>34 to 43</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Comparisons of 7 simulations with no CC objects from Section 2.1 with the real solar system. Left: Mass and semi-major axis are compared. Right: RMC and AMD are compared.</figcaption></figure>

## 2.2. Simulations including carbonaceous (CC) planetesimals

Our next step was to introduce a population of CC objects that were scattered inwards and into intersecting orbits with the terrestrial planets during Jupiter and Saturn's rapid gas accretion. Raymond and Izidoro (2017a) showed that gas drag plays a central role in size-sorting objects scattered inward by the gas giants. Smaller planetesimals feel stronger gas and are trapped on wider orbits, strictly in the outer parts of the asteroid belt, whereas larger ones (typically $D \sim 1000$ km) may be scattered onto more eccentric orbits that cross within the terrestrial planet realm. If we consider an embryo/planetesimal size dichotomy, it is natural that scattered embryos would have a much higher probability of interacting with the terrestrial planets and potentially delivering CC material. Nonetheless, given our ignorance of the mass distribution of objects scattered by Jupiter, and the fact that Jupiter's migration can also scatter planetesimals in a less size-dependent manner (Walsh et al., 2011), we tested three different scenarios:

* Only small CC objects – that is, planetesimals. We call this scenario *small only*.

* Only large CC objects – planetary embryos. We call this scenario *large only*.

* Both CC planetesimals and embryos. This is the *mixed* scenario.

These simulations started from the same setup described in Section 2.1, but with an additional CC component. Carbonaceous planetesimals and embryos were distributed in a similar fashion to the setup in O'Brien et al. (2014), with perihelia $q$ uniformly drawn between 0.7 AU$\le$ $q$ $\le$1.5 AU, inclinations following a Rayleigh distribution with $\sigma = 2.5$, and aphelia ($Q$) less than or equal to 5.5 AU. As above, CC embryos gravitationally interact with all massive objects in the simulation, whereas CC planetesimals do not self-interact (or interact with non-carbonaceous planetesimals).

In the *small only* scenario, 1050 CC planetesimals were included with a total mass of 0.2 $M_{\oplus}$ (following Joiret et al., 2024). In the *large only* simulations, 25 CC embryos were included with masses between 1%–2% of Earth's mass. The number of CC embryos is somewhat higher than one would expect if the typical CC embryo mass were the same

as the often-assumed ~Mars-mass, but having a significant number of particles helps in determining the odds of a collision with Earth.

In the *mixed* scenario, we made use of the collision probabilities for CC objects with the growing rocky planets from the *small only* and *large only* scenarios. We adjusted the mass of CC objects to try to keep the mass of the terrestrial planets close to their actual values. As such, the *mixed* simulations each started with 15 CC embryos with masses between 1%–2% of the Earth's mass and 500 planetesimals carrying a total mass of 0.04 $M_{\oplus}$, for a total mass range in CCs between 0.19 $M_{\oplus}$–0.34 $M_{\oplus}$.

## 2.3. The giant planet dynamical instability

In a subset of simulations, we very simply mimicked the effect of the giant planet dynamical instability (Tsiganis et al. (2005), Morbidelli et al. (2007), see Nesvorný (2018) for a review). We chose 10 simulations from each of our three sets (9 from the small one) and instantaneously ‘jumped’ the orbits of Jupiter and Saturn to their present-day ones. This was done at a simulation time of 20 Myr. It is important to keep in mind that the exact timing of the instability is uncertain. A variety of cosmochemical and dynamical constraints suggest that it must have taken place within the first 100 Myr after CAIs (Morbidelli et al., 2018; Nesvorný et al., 2018; Mojzsis et al., 2019), and some hint that it may have taken place within a few million years of the dispersal of the gaseous disk (Hunt et al., 2022; Edwards et al., 2024). From a dynamical point of view, the instability timing depends on the trigger, which is itself uncertain Gomes et al. (although several mechanisms have been proposed; see 2005), Levison et al. (although several mechanisms have been proposed; see 2011), Ribeiro et al. (although several mechanisms have been proposed; see 2020), Liu et al. (although several mechanisms have been proposed; see 2022). Our choice of 20 Myr for the instability timing is intermediate – early enough to potentially affect Mars' accretion (Clement et al., 2018), but late enough not to assume the earliest possible trigger.
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Left: Mass and orbital radii of surviving large NC bodies after 200 Myr in all 60 simulations of the *mixed* scenario. Constraints for planet selection are visualized with the boxes, and the real solar system planets are shown for comparison. Right: The final configuration in the 10 *mixed* simulations that also included the giant planet instability.</figcaption></figure>

### 3. Simulation outcomes

In this section, we first (Section 3.1) describe the constraints we use to determine whether a simulation should be considered a viable analog to the Solar System. Next (Section 3.2), we present the detailed dynamical and collisional evolution of one simulation from the *mixed* scenario is shown, both with and without the giant planet instability. In Section 3.3, we explore the amount of CC mass accreted by terrestrial planet analogs all of the sets of simulations. Then, we determine the CC mass fraction within the late accretion of these planets. Finally (Section 3.4), we determine the compositions of the last giant impacts (Theia analogs) in all viable simulations, in the context of cosmochemical and dynamical constraints.

Our inventory of simulations is as follows. We ran 60 simulations of the *mixed* scenario, 10 of the *large only* and 9 of the *small only* scenarios. We ran an additional 10 simulations (9 for the *small only* set) also including the giant planet dynamical instability.

Fig. 2 shows the masses and orbital radii of the planets that formed in the *mixed* scenario. The boxes present the contours of our criteria for choosing analogs to each terrestrial planet. They were chosen to be within ~ a factor of 1.5 of the current values, with less strict constraints around Mars and Mercury analogs. Among simulations without the giant planet dynamical instability (left panel of Fig. 2), the most common final arrangement was the formation of 3 to 4 terrestrial planets and in some rare occurrences 2 or 5 remained at the end. The formation of 4 terrestrial planets did not always mean that a Mercury analog formed, but rather that another, typically Mars-sized, planet formed between the Earth and Venus analogs or the Earth and Mars analogs. Indeed, such low-mass planets are common in the distribution from Fig. 2 (left panel). Including the giant planet instability helps remove those remaining Mars sized bodies, by forcing them to collide with the Earth or Venus analogs (see right panel of Fig. 2). Most other remaining NC and CC bodies, that were not the planet analogs, were also cleared out by the giant planet instability. In most cases all CC embryos were accreted or ejected from the solar system. However, a rare occurrence for both the *large only* and *mixed* scenarios was the survival of one CC embryo beyond the orbit of Mars.

Fig. 3 compares the radial mass concentration *RMC* and normalized angular momentum deficit *AMD* of the terrestrial planets in the *mixed* scenario with and without the giant planet instability with the actual terrestrial planets. The instability seems to increase the angular momentum deficit of the simulations, while keeping the radial mass concentration similar.

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Normalized angular momentum deficit *AMD* and radial mass concentration *RMC* for the 60 simulations in using the *mixed* scenario (black) and the 10 giant planet instability ones (blue), as well as a comparison with the real solar system value (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

#### 3.1. Evolution of an individual simulation

In this subsection we present the evolution of a promising Solar System analog simulation from the *mixed* scenario. We then present how the evolution changed when the giant planet instability was included.

Fig. 4 shows the evolution of the simulation, without including the giant planet dynamical instability. At early times, the scattered CC objects mix with the NC bodies in the terrestrial planet-forming region, while leaving some large CCs orbiting in between planets or still too far to collide. The simulation ended with 4 terrestrial planets, including a reasonable Earth analog with 1 $M_⊕$ and Mars analog with 0.1 $M_⊕$. The *RMC* and *AMD* for this simulation are 66 and $2.27 \times 10^{-3}$ respectively. The final giant impact on the Earth analog happened with a CC embryo at 97 Myr. Fig. 5 shows the growth curve of the Earth analog separated into the NC and CC contributions. The final giant
<figure><img src="image_7.png" /></figure>

**Fig. 4.** Eccentricity and position snapshots over time of a simulation using the *mixed* scenario where all 4 terrestrial planets fit constraints and the Earth analog had a final CC embryo impact. Snapshots are shown over time, including the moment after the final giant impact. The initial NC embryos and planetesimals are shown with the embryos in black and the planetesimals in orange, as well as the CC embryos and planetesimals in blue with Jupiter and Saturn in black on the far right. The final snapshot is the real solar system. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

<figure><img src="image_8.png" /></figure>

**Fig. 5.** Growth curve of Earth analog in the simulation from Fig. 4. Total mass is separated into contribution from NC and CC bodies.

impactor's contribution can be seen in the sudden late and large gain of CC mass before 100 Myr.

**Fig. 6** shows the evolution of the exact same simulation when the giant planet instability is taken into account, as Jupiter and Saturn's orbits are instantaneously moved to their present-day ones at 20 Myr. The giant planet instability dramatically changed the evolution of the system causing a strong pulse of eccentricity excitement, which lead to a wave of collisions and ejections. The final state of the system is only modestly-changed from the instability-free case from Fig. 4 – there are still four terrestrial planets with the Earth analog having 1 $M_⊕$ and the Mars analog having 0.1 $M_⊕$. The *RMC* and *AMD* for this simulation are 63.9 and $2.81×10^{-3}$, respectively. However, the final giant impact on the Earth analog was quite different, happening at 10 Myr with a dry, NC embryo.

<figure><img src="image_9.png" /></figure>

**Fig. 6.** Eccentricity and position snapshots over time of the simulation in Fig. 4 now with the giant planet instability at 20 Myr. The initial NC embryos and planetesimals are shown with the embryos in black and the planetesimals in orange, as well as the CC embryos and planetesimals in blue with Jupiter and Saturn in black on the far right. The final snapshot is the real solar system. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

## 3.2. The CC mass fraction

A key constraint on our simulated planets is the fraction of their mass that was accreted from carbonaceous material, as well as the timing of its accretion. Cosmochemical studies indicate that the CC fraction for Earth is a few to 10–15% (e.g. Dauphas, 2017; Martins et al., 2023; Kleine et al., 2023; Dauphas et al., 2024; Nimmo et al., 2024b). Nimmo et al. (2024b) and Dauphas et al. (2024) argued that at least some of this CC material was delivered during the last ~10% of our planet's accretion. For Mars, the CC fraction is lower, between almost zero and 2–3% (Kleine et al., 2023). There are no direct measurements of the other terrestrial planets due to the lack of samples.

**Fig. 7** shows the orbits and CC mass fractions of Venus, Earth and Mars analogs and their masses for the *mixed* simulations. The Earth analogs are a good match, with a median [mean] of 6.4% [6.8%] in *mixed* simulations with no instability, and 5.1% [5.3%] in simulations with a giant planet dynamical instability. Venus analogs tend to have a similar CC mass fraction as Earth analogs, with typical values of ~5%.

In the *small only* simulations, the typical CC fraction of Earth is somewhat lower, with a median [mean] of 4.1% [4%] in *mixed* simulations with no instability, and 3.6% [3.6%] in simulations with a giant planet dynamical instability. Venus analogs in the *small only* simulations have typical CC mass fractions of ~3–4%. In contrast, the CC mass fractions are higher in the *big only* simulations. The median [mean] CC mass fraction of Earth analogs is 8.8% [8.4%] in simulations with no giant instability, and 8.1% [8.9%] in simulations with a giant planet instability. Venus had a somewhat higher CC mass fraction than Earth in the *big only* simulations, with a median [mean] of 8.7% [12.1%] in *mixed* simulations with no instability, and 8% [9.4%] in simulations with a giant planet dynamical instability. The giant planet instability did not seem to affect the CC mass provided by the final impactor in the simulations.

Within the *small only* scenario, Mars and Earth analogs each accreted with a similar CC mass fraction, typically around 4%. This was likewise found in the simulations of Joiret et al. (2024). This served as motivation for the idea presented by Nimmo et al. (2024b) and Joiret et al. (2024) that CC objects in the terrestrial realm must have included larger objects (planetary embryos).

Let us now focus on the *mixed* scenario simulations, specifically on simulations in which the Earth/Mars mass ratio was within a factor
<figure><img src="image_10.png" /><figcaption>Fig. 7. Orbital and CC mass distribution of Earth, Venus and Mars analogs in the mixed sets with CC mass fractions under 14%. Colors represent the mass of the analog in Earth masses. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

of two of its current value. Mars analogs followed one of two paths: they were either hit by a CC embryo or not. In 62.5% of simulations, the Mars analog was hit by a CC embryo, and due to its size, the CC mass fraction of the analog jumped above 10%. When the analog was not hit, its CC mass fraction was between 0.5% and 1%. In these simulations Earth analogs had an average CC mass fraction of ~6%, consistent with cosmochemical constraints for Earth and Mars (Kleine et al., 2023; Nimmo et al., 2024b). These are simulations with no giant planet instability. If we include the instability, Mars systematically receives less CC material. In the mixed scenario, the Mars analog is hit 75% of the time leading still to a CC mass fraction above 10% and when not hit the fraction is under 0.5% instead. In the small only scenario, both Mars and Earth analogs again finish with about a 3.6% CC mass fraction.

### 3.3. The last giant impact

We now address the details of the last giant impacts in our simulations, which are the potential Moon-forming collisions (e.g. Canup and Asphaug, 2001). We focus specifically on the origin of the impactor – Theia – in these last collisions, as Budde et al. (2019) claimed that it may have been a carbonaceous object.

In the mixed scenario with no giant planet instability, Earth's final impactor included a CC component in more than half of all simulations. In 38.5% of simulations, the final impactor was a pure CC embryo, and in another 13.5%, the impactor was an NC embryo that had previously accreted a CC embryo. Fig. 8 (left panel) shows the distribution of the impact timing for last giant impacts, broken down by the composition of the impactor. Fig. 8 (right panel) shows the distribution of all giant impacts with Earth analogs that contained a CC component. The mixed fraction decays much faster than the CC embryo fraction with most impacts happening before 10 Myr. This is because, once a CC embryo has collided with an NC embryo, the new larger embryo is by default more centrally located, likely within the heart of the annulus, and likely to undergo additional collisions on a short timescale.

Fig. 9 shows the relative timing of the last giant impact for the ten simulations from the mixed set that were run both with and without the giant planet dynamical instability. The punchline is simply, once again, that including the giant planet dynamical instability leads to earlier last

giant impacts on Earth analogs. This is because the instability tends to excite terrestrial embryos and stimulate giant impacts. Our results are consistent with those of DeSouza et al. (2021), who found a typical delay of ~20 Myr between the time of the instability and the last giant impact.

### 3.4. Late accretion

We now turn our attention to the CC mass fraction of the late accretion phase. Recall that late accretion represents planetesimal impacts after the last giant (embryo) impact (see, e.g. Jacobson et al., 2014; Morbidelli and Wood, 2015). There is cosmochemical evidence that late accretion was dominated by dry (NC) material (Gillmann et al., 2020; Worsham and Kleine, 2021).

Fig. 11 shows the carbonaceous (CC) mass fraction of late accretion for Earth, Venus and Mars analogs as a function of the time of the last giant impact (i.e., the start time of late accretion). It is immediately clear that simulated planets in the small only scenario have a much higher CC fraction of late accretion than in the mixed scenario. This appears to be a simple consequence of the fact that the small only simulations have far more total mass in CC planetesimals, and enough CC planetesimals survive to provide a significant amount of late accretion (this was also found by Joiret et al., 2024).

The mixed scenario has a much more NC-rich late accretion phase in general (Fig. 11). The majority of CC material is delivered to each of the terrestrial planets during the main phase of accretion. In most cases, Venus has a late accretion with only a small fraction of CC material, broadly consistent with the results of Gillmann et al. (2020). It is noticeable that the CC fraction rises modestly when the last giant impact happens late. This is a byproduct of the fact that a later last giant impact correlates with less late accretion (Jacobson et al., 2014) – since CC planetesimals are modestly farther from the Sun than NC ones on average, their collision rates are lower and a higher fraction survive to late times.

The effect of the giant planet dynamical instability timing is also evident in Fig. 11. None of the simulations with the giant planet instability has a last giant impact later than ~40 Myr on Earth. This is a simple byproduct of the eccentricity excitation induced by the instability, which led to a rapid clearing of stray embryos by collisions.
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Left: Distribution of 41 final giant impacts with Earth analogs. The blue bars represent the CC embryo final impactor fraction, the green bars are the mixed NC+CC embryo (second order) fraction, while the gray bars represent dry NC embryo fraction. Right: Distribution in time of 155 giant impacts with CC components with Earth analogs. Blue bars represent the CC embryo impactor fraction and the green bars are the mixed NC+CC embryos (second order) fraction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** A comparison between the timing of the last giant impacts in 10 mixed simulations that were run both with and without the giant planet instability. The black line represents the point where both values are equal. Each point has two halves with the left half representing the impactor type in the simulation without the giant planet instability and the right half representing the simulation with the giant planet instability. Dry NC impactors are black, CC embryos are blue and CC+NC mixed embryos are green. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Top: Mass distribution of CC impactors on Earth analogs in the mixed sets, in relation to the analog's mass at time of impact relative to its final mass. Diamonds are pure CC impactors, while circles are mixed CC+NC impactors with their color representing their CC mass fraction. Bottom: Distribution of 155 CC bearing impacts in relation to the analog's mass at time of impact relative to its final mass. Green fraction represents mixed NC+CC impactors while blue represents the pure CC fraction. In red is the fraction of pure CC objects with masses between 1% to 1.5% of the Earth's mass which impacted in the final 5% of accretion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

In a handful of cases, the dynamical instability also resulted in an elevated CC fraction for late accretion in Earth and Mars analogs.

## 4. Summary and discussion

Our primary result is to show that it is plausible that the last giant impactor on Earth (Theia) was a carbonaceous (CC) object, in the context of a full dynamical scenario for the accretion and early evolution of the terrestrial planets. The basic idea that Theia may have been carbonaceous was proposed by Budde et al. (2019), and the idea that carbonaceous material in the inner Solar System included embryos was proposed by Nimmo et al. (2024b) and Joiret et al. (2024).

The scenario is illustrated in our mixed simulations and proceeds as follows. First, planetesimal formation started quickly in the Sun's protoplanetary disk, likely at locations associated with condensation fronts (Armitage et al., 2016; Dążkowska and Dullemond, 2018). This
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** CC mass fraction of late accretion for Earth, Venus and Mars analogs, as a function of the time of the last giant impact (which marks the start of late accretion). The circles and triangles are from the *mixed* scenario. Squares and diamonds mark the *small only* simulations. The colors indicate the total mass fraction accreted during late accretion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

led to two or more rings of planetesimals — the inner one was rocky, non-carbonaceous (NC), and centered around 1 au, containing a total of ~2–2.5*M<sub>⊕</sub>* (Morbidelli et al., 2022; Izidoro et al., 2022). The giant planets' cores grew from a more distant ring at ~5–10 au. The rapid gas accretion phase of the gas giants, as well as the migration of the ice giants, scattered CC material inward. Some planetesimals were trapped in the asteroid belt (as the C-types) and, given their weaker gas drag, preferentially larger bodies were scattered onto terrestrial planet-crossing orbits (Raymond and Izidoro, 2017a). The late-stage accretion of the terrestrial planets involved a series of giant impacts between NC embryos and planetesimals, with occasional impacts of CC objects. The last giant impact on the proto-Earth produced the Moon (e.g. Canup and Asphaug, 2001) and marked the start of late accretion phase of planetesimal impacts. The giant planet dynamical instability took place during the main phase of terrestrial accretion (Morbidelli et al., 2018; Nesvorný et al., 2018; Mojzsis et al., 2019), likely within ~20 Myr of gas disk dispersal (Ribeiro et al., 2020; Liu et al., 2022; Hunt et al., 2022; Edwards et al., 2024), although the exact timing remains a matter of debate.

This scenario can explain a number of Solar System constraints. First, the general setup can adequately match the masses and orbits of the terrestrial planets, including the large Earth/Mars mass ratio (as shown by Hansen, 2009). Our simulations also provide a decent match to the Solar System's normalized Angular Momentum Deficit *AMD* and Radial Mass Concentration *RMC*. Second, the scenario can match the orbital distribution of the asteroids, as NC planetesimals (largely S-types) were scattered outward from the terrestrial planet-forming region (Raymond and Izidoro, 2017b; Izidoro et al., 2024) and C-types were scattered inward from the giant planet region (Raymond and Izidoro, 2017a). Our simulations do not model this phase.

Third, this scenario can match the CC mass fraction of Earth and Mars. Earth's CC mass fraction is constrained by measurements to be a few to 10–15%, with typically inferred values of ~6% (Kleine et al., 2023; Dauphas et al., 2024; Nimmo et al., 2024b). In contrast, Mars' CC mass fraction is much lower, at most a few percent (Kleine et al., 2023). Our simulations tend to form Earth analogs with CC mass fractions of a few to ten percent, in agreement with this constraint. If the CC material was entirely in the form of planetesimals (the *small only* simulations), the mass fraction of Earth and Mars would be roughly the same (as also shown by Joiret et al., 2024). However, if the mass in CCs is predominantly in embryos, our simulations can explain Earth's much larger CC mass fraction as long as Mars was not hit by a CC embryo (as proposed by Nimmo et al., 2024b). In 62.5% of simulations, the Mars analog is indeed hit by a CC embryo, causing its CC mass fraction to jump above 10%. Such outcomes are not consistent with cosmochemical measurements (Kleine et al., 2023). In simulations where Mars analogs are not hit by a CC embryo, their CC mass fraction is typically ~0.5–1% and Earth's is ~5–7%, both of which match constraints.

Fourth, this scenario can match the approximate timing of the Moon-forming impact. The last embryo impact took place in our simulations after 5–150 Myr, with a large fraction of last giant impacts at 20–70 Myr. Given the uncertainties in interpreting the timing of Moon formation (e.g. Fischer and Ciesla, 2014; Nimmo et al., 2024a), our simulations produce viable realizations.

Finally, this scenario can produce a volatile-poor, NC-dominated late accretion phase. Late accretion is constrained by models and cosmochemical measurements to have been NC-dominated (Gillmann et al., 2020; Worsham and Kleine, 2021). The late accretion phase in our *mixed* simulations is indeed NC-dominated, for the simple reason that only a small fraction of the CC mass was in planetesimals. Mars analogs also had a higher median of CC/NC mass fraction accreted during late accretion than Earth and Venus analogs, with Venus having the lowest.

Within the context of this scenario, the last giant impactor on Earth contained a CC component in roughly half of all of the *mixed* simulations. In the majority of these (38% of simulations), Theia was a pristine CC embryo, and in the remainder of cases Theia was an NC embryo that had previously accreted a CC embryo. This offers credence to the idea of Budde et al. (2019). As modeled by Nimmo et al. (2024b), CC embryos and planetesimals can be accreted throughout Earth's growth, but they are concentrated toward the later phases. Fig. 10 supports this with most impacts from embryos with CC components happening after the Earth analog has accreted 80% of its final mass, with a considerable fraction of lower mass pure CC embryos impacting after 95% of accretion.

It is worth keeping in mind that Bermingham et al. (2025) came to the opposite conclusion: that the last 10%–20% of Earth's accretion was likely NC-rich. In this scenario, Earth's CC budget must have been accreted in the first 80%–90% of accretion. This is also entirely plausible within the context of our simulations (see Fig. 10), as many CC-rich embryo impacts take place in that window. Evaluating the exact timing of CC accretion appears to require cosmochemical analysis, as our simulations cannot distinguish between the scenarios of Nimmo et al. (2024b) and that of Bermingham et al. (2025).
Using our results as a guide, we can estimate the initial mass in CC planetesimals relative to CC embryos as follows. In the small only simulations, Earth and Mars tended to have the same CC mass fraction of ~4% (as did Venus). Let us assume that Earth and Mars generally accrete the same fraction of the planetesimal mass, as normalized by their mass ratio (of ~9). Let us also take the results of Kleine et al. (2023) at face value, and adopt a Mars total CC mass fraction of ~0.5% and a value of ~6% for Earth. This means that ~0.5% of Earth's mass was delivered by CC planetesimals, and the remaining ~5.5% by CC embryos. From the mixed set of simulations, Earth analogs accreted a median of 5.7% of CC material from embryos and 0.7% from planetesimals. Mars analogs also accreted a median of 0.7% CC mass from CC planetesimals, which follows the logic of the approximation made before. There must therefore have been ~8 times more mass in CC embryos than in CC planetesimals.

We can also use simple arguments to evaluate the typical CC embryo mass. If there were too many embryos, it would be extremely unlikely that Mars could have avoided a CC impact. The number of embryos for which the odds of Earth accreting embryos but Mars not accreting any should be roughly the same as the their accretion ratio, which is simply their mass ratio of ~9 (because they accreted the same mass fraction in CC planetesimals). Indeed, in our mixed simulations with 15 embryos, Mars accreted a CC embryo in more than half (62.5%) of simulations. To avoid dropping the odds of success any further, we do not expect CC embryos to have been less massive than the 1%–2% of an Earth-mass assumed here. On the other hand, the most massive CC embryo cannot have been more massive than the ~5.5% of Earth's mass that was accreted in the form of CC embryos. From Budde et al. (2019), we also have a prediction of the CI material provided by the final impactor – 2%±1%. Depending on the nature of the CC embryos, this can further limit the mass of the final impactor. A reasonable mass range for CC embryos is therefore ~1–5% of Earth's mass. This is below the mass range for Theia in the canonical Moon-forming impact (Canup and Asphaug, 2001), but could represent a plausible Moon-forming impact as long as the proto-Earth was spinning fast (Čuk and Stewart, 2012). If a larger Theia mass were needed to match the Earth–Moon system (Canup et al., 2021), then the most viable option is an NC embryo that previously accreted a CC embryo – a scenario that happened for 13.5% of our Earth analogs in the mixed set.

Put together, this reasoning implies that the total mass in CC material injected into the inner Solar System was ~0.2–0.3*$M_⊕$, with a ~8:1 mass division between embryos and planetesimals. The total mass ensures a match to Earth's CC mass fraction, whereas the embryo/planetary mass balance ensures that Mars did not accrete a CC embryo. An even higher embryo-to-planetesimal CC mass ratio may be needed, to ensure that the late accretion phase was NC-dominated.

If ~0.2–0.3*$M_⊕$ of CC material was injected into the inner Solar System, it implies the existence of a much larger primordial reservoir in the outer Solar System. The efficiency of implantation depends on the relative importance of giant planet growth and migration (Walsh et al., 2011; Raymond and Izidoro, 2017a), as well as the strength of gas drag (connected with the object size). The implantation efficiency is far higher for objects originating in the Jupiter–Saturn region (interior to ~10 au) than in the ice giant realm (out to ≥20 au; Raymond and Izidoro, 2017a; Nesvorný et al., 2024). Assuming an implantation efficiency of 1%–10%, this implies that 2–30*$M_⊕$ in unaccreted CC embryos existed in the Jupiter–Saturn region. If the gas giants' cores were ~10*$M_⊕$ each, this suggests that the accretion efficiency of CC embryos was at most ~90% and perhaps as low as 50% (or less). This fits with the well-established paradigm that the growth of the giant planets' cores requires accretion of strongly damped objects (pebbles) (Ormel and Klahr, 2010; Lambrechts and Johansen, 2012), as large planetesimals and embryos tend to gravitationally scatter each other rather than accrete (e.g. Thommes et al., 2003).

Our exploration of this scenario admittedly includes some uncertainties and limitations. As our simulations started after gas disk dispersal, we did not model the injection of carbonaceous objects into

the inner Solar System in a self-consistent fashion. In addition, we made the assumption that an annulus of planetary embryos and planetesimals could be maintained to the end of the gas disk phase, even though migration and drag might make that impossible unless there was a convergent migration zone (Woo et al., 2023). Finally, our implementation of the giant planet dynamical instability was highly simplified, although we note that it did broadly match the outcomes seen by DeSouza et al. (2021).

### CRediT authorship contribution statement

**Duarte Branco:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis.

**Pedro Machado:** Supervision, Resources, Project administration, Funding acquisition. **Sean N. Raymond:** Writing – review & editing, Supervision, Project administration, Methodology, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

We thank the anonymous referees for their constructive reports, and acknowledge helpful discussions with Katherine Bermingham. We would like to thank the Faculdade de Ciências da Universidade de Lisboa for providing us with access to the cluster used for the simulations in this paper. We would also like to thank the Laboratoire d'Astrophysique de Bordeaux, the Université de Bordeaux and Erasmus for enabling the partnership between authors. S. N. R acknowledges funding from the Programme Nationale de Planetologie (PNP) of the INSU (CNRS), and in the framework of the Investments for the Future programme IdEx, Université de Bordeaux/RRI ORIGINS. This work was supported by Fundacao para a Ciencia e a Tecnologia (FCT) through the research grant UID/04434/2025. We thank the Institute of Astrophysics and Space Sciences, Portugal, for all the support.

### Data availability

No data was used for the research described in the article.

### References

* Agnor, C.B., Canup, R.M., Levison, H.F., 1999. On the character and consequences of large impacts in the late stage of terrestrial planet formation. Icarus 142 (1), 219–237. http://dx.doi.org/10.1006/icar.1999.6201.

* Armitage, P.J., Eisner, J.A., Simon, J.B., 2016. Prompt planetesimal formation beyond the Snow line. Astrophys. J. Lett. 828 (1), L2. http://dx.doi.org/10.3847/2041-8205/828/1/L2, arXiv:1608.03592.

* Avice, G., Marty, B., 2014. The iodine-plutonium-xenon age of the Moon-Earth system revisited. Philos. Trans. R. Soc. Lond. Ser. A 372 (2024), http://dx.doi.org/10.1098/rsta.2013.0260, 20130260–20130260.

* Benz, W., Slattery, W.L., Cameron, A.G.W., 1986. The origin of the moon and the single-impact hypothesis I. Icarus 66 (3), 515–535. http://dx.doi.org/10.1016/0019-1035(86)90088-6.

* Bermingham, K.R., Tornabene, H.A., Walker, R.J., Godfrey, L.V., Meyer, B.S., Piccoli, P., Mojzsis, S.J., 2025. The non-carbonaceous nature of Earth's late-stage accretion. Geochim. Cosmochim. Acta 392, 38–51. http://dx.doi.org/10.1016/j.gca.2024.11.005.

* Birnstiel, T., Fang, M., Johansen, A., 2016. Dust evolution and the formation of planetesimals. Space Sci. Rev. 205 (1–4), 41–75. http://dx.doi.org/10.1007/s11214-016-0256-1, arXiv:1604.02952.

* Bottke, W.F., Walker, R.J., Day, J.M.D., Nesvorny, D., Elkins-Tanton, L., 2010. Stochastic late accretion to Earth, the Moon, and Mars. Science 330 (6010), 1527. http://dx.doi.org/10.1126/science.1196874.

* Brasser, R., Mojzsis, S.J., 2020. The partitioning of the inner and outer solar system by a structured protoplanetary disk. Nat. Astron. 4, 492–499. http://dx.doi.org/10.1038/s41550-019-0978-6.
Budde, G., Burkhardt, C., Kleine, T., 2019. Molybdenum isotopic evidence for the late accretion of outer Solar system material to earth. Nat. Astron. 3 (8), 736-741. http://dx.doi.org/10.1038/s41550-019-0779-y.

Canup, R.M., 2012. Forming a Moon with an Earth-like composition via a Giant impact. Science 338 (6110), 1052. http://dx.doi.org/10.1126/science.1226073.

Canup, R.M., Asphaug, E., 2001. Origin of the moon in a giant impact near the end of the earth's formation. Nature 412 (6848), 708-712. http://dx.doi.org/10.1038/35089010.

Canup, K., Dauphas, N., Pahlevan, K., Ćuk, M., Lock, S.J., Stewart, S.T., Salmon, J., Rufu, R., Nakajima, M., Magna, T., 2021. Origin of the moon. ArXiv E-Prints arXiv:2103.02045.

Chambers, J., 1999. A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304 (4), 793-799. http://dx.doi.org/10.1046/j.1365-8711.1999.02379.x.

Chambers, J.E., 2001. Making more terrestrial planets. Icarus 152 (2), 205-224. http://dx.doi.org/10.1006/icar.2001.6639.

Chambers, J., Wetherill, G., 1998. Making the terrestrial planets: N-Body integrations of planetary embryos in three dimensions. Icarus 136 (2), 304-327. http://dx.doi.org/10.1006/icar.1998.6007, URL: https://www.sciencedirect.com/science/article/pii/S0019103598960079.

Chambers, J.E., Wetherill, G.W., Boss, A.P., 1996. The stability of multi-planet systems. Icarus 119 (2), 261-268. http://dx.doi.org/10.1006/icar.1996.0019.

Clement, M.S., Kaib, N.A., Raymond, S.N., Walsh, K.J., 2018. Mars' growth stunted by an early giant planet instability. Icarus 311, 340-356. http://dx.doi.org/10.1016/j.icarus.2018.04.008, arXiv:1804.04233.

Ćuk, M., Stewart, S.T., 2012. Making the moon from a fast-spinning earth: A giant impact followed by resonant despinning. Science 338 (6110), 1047. http://dx.doi.org/10.1126/science.1225542.

Dauphas, N., 2017. The isotopic nature of the earth's accreting material through time. Nature 541 (7638), 521-524. http://dx.doi.org/10.1038/nature20830.

Dauphas, N., Hopp, T., Nesvorný, D., 2024. Bayesian inference on the isotopic building blocks of Mars and earth. Icarus 408, 115805. http://dx.doi.org/10.1016/j.icarus.2023.115805, arXiv:2309.15290.

Day, J.M.D., Pearson, D.G., Taylor, L.A., 2007. Highly siderophile element constraints on accretion and differentiation of the earth-moon system. Science 315 (5809), 217. http://dx.doi.org/10.1126/science.1133355.

DeSouza, S.R., Roig, F., Nesvorný, D., 2021. Can a jumping-Jupiter trigger the Moon's formation impact? Mon. Not. R. Astron. Soc. 507 (1), 539-547. http://dx.doi.org/10.1093/mnras/stab2188, arXiv:2107.04181.

Dražkowska, J., Alibert, Y., 2017. Planetesimal formation starts at the snow line. Astron. Astrophys. 608, A92. http://dx.doi.org/10.1051/0004-6361/201731491, arXiv:1710.00009.

Dražkowska, J., Alibert, Y., Moore, B., 2016. Close-in planetesimal formation by pile-up of drifting pebbles. Astron. Astrophys. 594, A105. http://dx.doi.org/10.1051/0004-6361/201628983, arXiv:1607.05734.

Dražkowska, J., Dullemond, C.P., 2018. Planetesimal formation during protoplanetary disk buildup. Astron. Astrophys. 614, A62. http://dx.doi.org/10.1051/0004-6361/201732221, arXiv:1803.00575.

Edwards, G.H., Keller, C.B., Newton, E.R., Stewart, C.W., 2024. An early giant planet instability recorded in asteroidal meteorites. Nat. Astron. 8 (10), 1264-1276. http://dx.doi.org/10.1038/s41550-024-02340-6, arXiv:2309.10906.

Fischer, R.A., Giesla, F.J., 2014. Dynamics of the terrestrial planets from a large number of N-body simulations. Earth Planet. Sci. Lett. 392, 28-38. http://dx.doi.org/10.1016/j.epsl.2014.02.011.

Fischer, R.A., Nimmo, F., 2018. Effects of core formation on the hf-w isotopic composition of the earth and dating of the moon-forming impact. Earth Planet. Sci. Lett. 499, 257-265. http://dx.doi.org/10.1016/j.epsl.2018.07.030, URL: https://www.sciencedirect.com/science/article/pii/S0012821X18304369.

Gillmann, C., Golabek, G.J., Raymond, S.N., Schönbächler, M., Tackley, P.J., Dehant, V., Debaille, V., 2020. Dry late accretion inferred from Venus's coupled atmosphere and internal evolution. Nat. Geosci. 13 (4), 265-269. http://dx.doi.org/10.1038/s41561-020-0561-x, arXiv:2010.07132.

Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Origin of the cataclysmic late heavy bombardment period of the terrestrial planets. Nature 435 (7041), 466-469. http://dx.doi.org/10.1038/nature03676.

Hansen, B.M.S., 2009. Formation of the terrestrial planets from a narrow annulus. Astrophys. J. 703 (1), 1131-1140. http://dx.doi.org/10.1088/0004-637X/703/1/1131, URL: http://dx.doi.org/10.1088/0004-637X/703/1/1131.

Hansen, B.M.S., 2009. Formation of the terrestrial planets from a narrow annulus. Astrophys. J. 703 (1), 1131-1140. http://dx.doi.org/10.1088/0004-637X/703/1/1131, arXiv:0908.0743.

Hunt, A.C., Theis, K.J., Rehkämper, M., Benedix, G.K., Andreasen, R., Schönbächler, M., 2022. The dissipation of the solar nebula constrained by impacts and core cooling in planetesimals. Nat. Astron. 6, 812-818. http://dx.doi.org/10.1038/s41550-022-01675-2, arXiv:2211.08306.

Izidoro, A., Dasgupta, R., Raymond, S.N., Deienno, R., Bitsch, B., Isella, A., 2022. Planetesimal rings as the cause of the solar system's planetary architecture. Nat. Astron. 6, 357-366. http://dx.doi.org/10.1038/s41550-021-01557-z, arXiv:2112.15558.

Izidoro, A., Deienno, R., Raymond, S.N., Clement, M.S., 2024. Implantation of asteroids from the terrestrial planet region: The effect of the timing of the giant planet instability. http://dx.doi.org/10.48550/arXiv:2404.10831, ArXiv E-Prints arXiv:2404.10831, arXiv:2404.10831.

Izidoro, A., Raymond, S.N., Morbidelli, A., Winter, O.C., 2015. Terrestrial planet formation constrained by Mars and the structure of the asteroid belt. Mon. Not. R. Astron. Soc. 453 (4), 3619-3634. http://dx.doi.org/10.1093/mnras/stv1835, arXiv:1508.01365.

Jacobson, S.A., Morbidelli, A., Raymond, S.N., O'Brien, D.P., Walsh, K.J., Rubie, D.C., 2014. Highly siderophile elements in earth's mantle as a clock for the moon-forming impact. Nature 508 (7494), 84-87. http://dx.doi.org/10.1038/nature13172, URL: https://doi.org/10.1038/nature13172.

Johansen, A., Blum, J., Tanaka, H., Ormel, C., Bizzarro, M., Rickman, H., 2014. The multifaceted planetesimal formation process. In: Beuther, H., Klessen, R.S., Dullemond, C.P., Henning, T. (Eds.), Protostars and Planets VI. pp. 547-570. http://dx.doi.org/10.2458/azu_uapress_9780816531240-ch024, arXiv:1402.1344.

Joiret, S., Raymond, S.N., Avice, G., Clement, M.S., 2024. Crash chronicles: Relative contribution from comets and carbonaceous asteroids to earth's volatile budget in the context of an early instability. Icarus 414, 116032. http://dx.doi.org/10.1016/j.icarus.2024.116032, URL: https://www.sciencedirect.com/science/article/pii/S0019103524000915.

Kaib, N.A., Cowan, N.B., 2015. The feeding zones of terrestrial planets and insights into moon formation. Icarus 252, 161-174. http://dx.doi.org/10.1016/j.icarus.2015.01.013, URL: http://dx.doi.org/10.1016/j.icarus.2015.01.013.

Kleine, T., Steller, T., Burkhardt, C., Nimmo, F., 2023. An inner solar system origin of volatile elements in mars. Icarus 397, 115519. http://dx.doi.org/10.1016/j.icarus.2023.115519, URL: https://www.sciencedirect.com/science/article/pii/S0019103523000969.

Kleine, T., Touboul, M., Bourdon, B., Nimmo, F., Mezger, K., Palme, H., Jacobsen, S.B., Yin, Q.-Z., Halliday, A.N., 2009. Hf-w chronology of the accretion and early evolution of asteroids and terrestrial planets. Geochim. Cosmochim. Acta 73 (17), 5150-5188. http://dx.doi.org/10.1016/j.gca.2008.11.047.

Kokubo, E., Ida, S., 1998. Oligarchic growth of protoplanets. Icarus 131 (1), 171-178. http://dx.doi.org/10.1006/icar.1997.5840, URL: https://www.sciencedirect.com/science/article/pii/S0019103597958401.

Kokubo, E., Ida, S., 2000. Formation of protoplanets from planetesimals in the solar Nebula. Icarus 143 (1), 15-27. http://dx.doi.org/10.1006/icar.1999.6237.

Kruijer, T.S., Burkhardt, C., Budde, G., Kleine, T., 2017. Age of jupiter inferred from the distinct genetics and formation times of meteorites. Proc. Natl. Acad. Sci. 114 (26), 6712-6716. http://dx.doi.org/10.1073/pnas.1704461114, arXiv:https://www.pnas.org/doi/pdf/10.1073/pnas.1704461114, URL: https://www.pnas.org/doi/abs/10.1073/pnas.1704461114.

Kruijer, T.S., Kleine, T., Borg, L.E., 2020. The great isotopic dichotomy of the early solar system. Nat. Astron. 4, 32-40. http://dx.doi.org/10.1038/s41550-019-0959-9.

Lambrechts, M., Johansen, A., 2012. Rapid growth of gas-giant cores by pebble accretion. Astron. Astrophys. 544, A32. http://dx.doi.org/10.1051/0004-6361/201219127, arXiv:1205.3030.

Laskar, J., 1997. Large scale chaos and the spacing of the inner planets. Astron. Astrophys. 317, L75-L78.

Leinhardt, Z.M., Richardson, D.C., 2005. Planetesimals to protoplanets. I. Effect of fragmentation on terrestrial planet formation. Astrophys. J. 625 (1), 427-440. http://dx.doi.org/10.1086/429402.

Levison, H.F., Morbidelli, A., Tsiganis, K., Nesvorný, D., Gomes, R., 2011. Late orbital instabilities in the outer planets induced by interaction with a self-gravitating planetesimal disk. Astron. J. 142 (5), 152. http://dx.doi.org/10.1088/0004-6256/142/5/152.

Lichtenberg, T., Dražkowska, J., Schönbächler, M., Golabek, G.J., Hands, T.O., 2021. Bifurcation of planetary building blocks during solar system formation. Science 371 (6527), 365-370. http://dx.doi.org/10.1126/science.abb3091, arXiv:2101.08571.

Liu, B., Raymond, S.N., Jacobson, S.A., 2022. Early solar system instability triggered by dispersal of the gaseous disk. Nature 604 (7907), 643-646. http://dx.doi.org/10.1038/s41586-022-04535-1.

Martins, R., Kuthning, S., Coles, B.J., Kreissig, K., Rehkämper, M., 2023. Nucleosynthetic isotope anomalies of zinc in meteorites constrain the origin of earth's volatiles. Science 379 (6630), 369-372. http://dx.doi.org/10.1126/science.abn1021.

Mojzsis, S.J., Brasser, R., Kelly, N.M., Abramov, O., Werner, S.C., 2019. Onset of giant planet migration before 4480 million years ago. Astrophys. J. 881 (1), 44. http://dx.doi.org/10.3847/1538-4357/ab2c03, arXiv:1903.08825.

Morbidelli, A., Baillié, K., Batygin, K., Charnoz, S., Guillot, T., Rubie, D.C., Kleine, T., 2022. Contemporary formation of early solar system planetesimals at two distinct radial locations. Nat. Astron. 6, 72-79. http://dx.doi.org/10.1038/s41550-021-01517-7, arXiv:2112.15413.

Morbidelli, A., Lunine, J.I., O'Brien, D.P., Raymond, S.N., Walsh, K.J., 2012. Building terrestrial planets. Annu. Rev. Earth Planet. Sci. 40 (1), 251-275. http://dx.doi.org/10.1146/annurev-earth-042711-105319, arXiv:1208.4694.

Morbidelli, A., Nesvorny, D., Laurenz, V., Marchi, S., Rubie, D.C., Elkins-Tanton, L., Wieczorek, M., Jacobson, S., 2018. The timeline of the lunar bombardment: Revisited. Icarus 305, 262-276. http://dx.doi.org/10.1016/j.icarus.2017.12.046, arXiv:1801.03756.
Morbidelli, A., Tsiganis, K., Crida, A., Levison, H.F., Gomes, R., 2007. Dynamics of the giant planets of the solar system in the gaseous protoplanetary disk and their relationship to the current orbital architecture. Astron. J. 134 (5), 1790–1798. http://dx.doi.org/10.1086/521705, arXiv:0706.1713.

Morbidelli, A., Wood, B.J., 2015. Late accretion and the late veneer. Geophys. Monogr. Ser. 212, 71–82. http://dx.doi.org/10.1002/9781118860359.ch4, arXiv:1411.4563.

Nesvorný, D., 2018. Dynamical evolution of the early solar system. Annu. Rev. Astron. Astrophys. 56 (1), 137–174. http://dx.doi.org/10.1146/annurev-astro-081817-052028.

Nesvorný, D., Dauphas, N., Vokrouhlický, D., Deienno, R., Hopp, T., 2024. Isotopic trichotomy of main belt asteroids from implantation of outer solar system planets. Earth Planet. Sci. Lett. 626, 118521. http://dx.doi.org/10.1016/j.epsl.2023.118521, arXiv:2311.16053.

Nesvorný, D., Roig, F.V., Deienno, R., 2021. The role of early giant-planet instability in terrestrial planet formation. Astron. J. 161 (2), 50. http://dx.doi.org/10.3847/1538-3881/abc8ef.

Nesvorný, D., Vokrouhlický, D., Bottke, W.F., Levison, H.F., 2018. Evidence for very early migration of the solar system planets from the patroclus-menoetius binary jupiter trojan. Nat. Astron. 2, 878–882. http://dx.doi.org/10.1038/s41550-018-0564-3, arXiv:1809.04007.

Nimmo, F., Kleine, T., Morbidelli, A., 2024a. Tidally driven remelting around 4.35 billion years ago indicates the moon is old. Nature 636 (8043), 598–602. http://dx.doi.org/10.1038/s41586-024-08231-0.

Nimmo, F., Kleine, T., Morbidelli, A., Nesvorny, D., 2024b. Mechanisms and timing of carbonaceous chondrite delivery to the earth. Earth Planet. Sci. Lett. 648, 119112. http://dx.doi.org/10.1016/j.epsl.2024.119112, arXiv:2411.04889.

O'Brien, D.P., Morbidelli, A., Levison, H.F., 2006. Terrestrial planet formation with strong dynamical friction. Icarus 184 (1), 39–58. http://dx.doi.org/10.1016/j.icarus.2006.04.005.

O'Brien, D.P., Walsh, K.J., Morbidelli, A., Raymond, S.N., Mandell, A.M., 2014. Water delivery and giant impacts in the "grand tack" scenario. Icarus 239, 74–84. http://dx.doi.org/10.1016/j.icarus.2014.05.009, URL: https://www.sciencedirect.com/science/article/pii/S001903514002620.

Ormel, C.W., Klahr, H.H., 2010. The effect of gas drag on the growth of protoplanets. Analytical expressions for the accretion of small bodies in laminar disks. Astron. Astrophys. 520, A43. http://dx.doi.org/10.1051/0004-6361/201014903, arXiv:1007.0916.

Pierens, A., Nelson, R.P., 2008. Constraints on resonant-trapping for two planets embedded in a protoplanetary disc. Astron. Astrophys. 482 (1), 333–340. http://dx.doi.org/10.1051/0004-6361:20079062, arXiv:0802.2033.

Pirani, S., Johansen, A., Bitsch, B., Mustill, A.J., Turrini, D., 2019. Consequences of planetary migration on the minor bodies of the early solar system. Astron. Astrophys. 623, A169. http://dx.doi.org/10.1051/0004-6361/201833713, arXiv:1902.04591.

Rauch, K.P., Holman, M., 1999. Dynamical chaos in the Wisdom-Holman integrator: Origins and solutions. Astron. J. 117 (2), 1087–1102. http://dx.doi.org/10.1086/300720, arXiv:astro-ph/9803340.

Raymond, S.N., Izidoro, A., 2017. The empty primordial asteroid belt. Sci. Adv. 3 (9), e1701138. http://dx.doi.org/10.1126/sciadv.1701138, arXiv:https://www.science.org/doi/pdf/10.1126/sciadv.1701138, URL: https://www.science.org/doi/abs/10.1126/sciadv.1701138.

Raymond, S.N., Izidoro, A., 2017a. Origin of water in the inner solar system: Planetesimals scattered inward during Jupiter and Saturn's rapid gas accretion. Icarus 297, 134–148. http://dx.doi.org/10.1016/j.icarus.2017.06.030, arXiv:1707.01234.

Raymond, S.N., Izidoro, A., 2017b. The empty primordial asteroid belt. Sci. Adv. 3 (9), e1701138. http://dx.doi.org/10.1126/sciadv.1701138, arXiv:1709.04242.

Raymond, S.N., Kokubo, E., Morbidelli, A., Morishima, R., Walsh, K.J., 2014. Terrestrial planet formation at home and abroad. In: Protostars and Planets VI. University of Arizona Press, http://dx.doi.org/10.2458/azu_uapress_9780816531240-ch026.

Raymond, S.N., Morbidelli, A., 2022. Planet formation: Key mechanisms and global models. In: Biazzo, K., Bozza, V., Mancini, L., Sozzetti, A. (Eds.), Demographics of Exoplanetary Systems, Lecture Notes of the 3rd Advanced School on Exoplanetary Science. In: Astrophysics and Space Science Library, 466, pp. 3–82. http://dx.doi.org/10.1007/978-3-030-88124-5_1, arXiv:2002.05756.

Raymond, S.N., O'Brien, D.P., Morbidelli, A., Kaib, N.A., 2009. Building the terrestrial planets: Constrained accretion in the inner solar system. Icarus 203 (2), 644–662. http://dx.doi.org/10.1016/j.icarus.2009.05.016, arXiv:0905.3750.

Raymond, S.N., Quinn, T., Lunine, J.I., 2005. Terrestrial planet formation in disks with varying surface density profiles. Astrophys. J. 632 (1), 670–676. http://dx.doi.org/10.1086/433179.

Raymond, S.N., Quinn, T., Lunine, J.I., 2006. High-resolution simulations of the final assembly of earth-like planets I. Terrestrial accretion and dynamics. Icarus 183 (2), 265–282. http://dx.doi.org/10.1016/j.icarus.2006.03.011, arXiv:astro-ph/0510284.

Raymond, S.N., Schlichting, H.E., Hersant, F., Selsis, F., 2013. Dynamical and collisional constraints on a stochastic late veneer on the terrestrial planets. Icarus 226 (1), 671–681. http://dx.doi.org/10.1016/j.icarus.2013.06.019, arXiv:1306.4325.

Ribeiro, R.d., Morbidelli, A., Raymond, S.N., Izidoro, A., Gomes, R., Vieira Neto, E., 2020. Dynamical evidence for an early giant planet instability. Icarus 339, 113605. http://dx.doi.org/10.1016/j.icarus.2019.113605, URL: https://www.sciencedirect.com/science/article/pii/S001903519301332.

Rubie, D.C., Jacobson, S.A., Morbidelli, A., O'Brien, D.P., Young, E.D., de Vries, J., Nimmo, F., Palme, H., Frost, D.J., 2015. Accretion and differentiation of the terrestrial planets with implications for the compositions of early-formed solar system bodies and accretion of water. Icarus 248, 89–108. http://dx.doi.org/10.1016/j.icarus.2014.10.015, arXiv:1410.3509.

Savage, P.S., Moynier, F., Boyet, M., 2022. Zinc isotope anomalies in primitive meteorites identify the outer solar system as an important source of earth's volatile inventory. Icarus 386, 115172. http://dx.doi.org/10.1016/j.icarus.2022.115172.

Steller, T., Burkhardt, C., Yang, C., Kleine, T., 2022. Nucleosynthetic zinc isotope anomalies reveal a dual origin of terrestrial volatiles. Icarus 386, 115171. http://dx.doi.org/10.1016/j.icarus.2022.115171.

Thiemens, M.M., Sprung, P., Fonseca, R.O.C., Leitzke, F.P., Münker, C., 2019. Early moon formation inferred from hafnium-tungsten systematics. Nat. Geosci. 12 (9), 696–700. http://dx.doi.org/10.1038/s41561-019-0398-3.

Thommes, E.W., Duncan, M.J., Levison, H.F., 2003. Oligarchic growth of giant planets. Icarus 161 (2), 431–455. http://dx.doi.org/10.1016/S0019-1035(02)00043-X, arXiv:astro-ph/0303269.

Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Origin of the orbital architecture of the giant planets of the solar system. Nature 435 (7041), 459–461.

Walker, R.J., 2009. Highly siderophile elements in the earth, moon and mars: Update and implications for planetary accretion and differentiation. Chem. Erde / Geochem. 69 (2), 101–125. http://dx.doi.org/10.1016/j.chemer.2008.10.001.

Walsh, K.J., Morbidelli, A., Raymond, S.N., O'Brien, D.P., Mandell, A.M., 2011. A low mass for mars from Jupiter's early gas-driven migration. Nature 475 (7355), 206–209. http://dx.doi.org/10.1038/nature10201, arXiv:1201.5177.

Warren, P.H., 2011. Stable-isotopic anomalies and the accretionary assemblage of the earth and mars: A subordinate role for carbonaceous chondrites. Earth Planet. Sci. Lett. 311 (1), 93–100. http://dx.doi.org/10.1016/j.epsl.2011.08.047, URL: https://www.sciencedirect.com/science/article/pii/S0012821X11005115.

Weidenschilling, S.J., Spaute, D., Davis, D.R., Marzari, F., Ohtsuki, K., 1997. Accretional evolution of a planetesimal swarm. Icarus 128 (2), 429–455. http://dx.doi.org/10.1006/icar.1997.5747.

Wetherill, G.W., 1990. Formation of the earth. Annu. Rev. Earth Planet. Sci. 18, 205–256. http://dx.doi.org/10.1146/annurev.ea.18.050190.001225.

Wetherill, G.W., Stewart, G.R., 1993. Formation of planetary embryos: Effects of fragmentation, low relative velocity, and independent variation of eccentricity and inclination. Icarus 106 (1), 190–209. http://dx.doi.org/10.1006/icar.1993.1166.

Wisdom, J., Holman, M., 1992. Symplectic maps for the n-body problem: Stability analysis. Astron. J. 104, 2022. http://dx.doi.org/10.1086/116378.

Woo, J., Morbidelli, A., Grimm, S., Stadel, J., Brasser, R., 2023. Terrestrial planet formation from a ring. Icarus 396, 115497. http://dx.doi.org/10.1016/j.icarus.2023.115497.

Worsham, E.A., Kleine, T., 2021. Late accretionary history of earth and moon preserved in lunar impactites. Sci. Adv. 7 (44), eabh2837. http://dx.doi.org/10.1126/sciadv.abh2837.

Zhu, M.-H., Morbidelli, A., Neumann, W., Yin, Q.-Z., Day, J.M.D., Rubie, D.C., Archer, G.J., Artemieva, N., Becker, H., Wünnemann, K., 2021. Common feedstocks of late accretion for the terrestrial planets. Nat. Astron. 5, 1286–1296. http://dx.doi.org/10.1038/s41550-021-01475-0.