A holistic approach to understand Earth formation

  grant N. 101019380


The first results of the project start to come in, revealing important constraints on the formation of Earth, but also new conundrums that we will have to address.

Burkhardt et al. Terrestrial planet formation from lost inner solar system material (Science advances, 2021; WP3analyzes the isotopic dichotomy of meteorites using the largest possible number of elements and shows that there is no common trend of non-carbonaceous (NC) meteorites towards carbonaceous (CC) meteorites, unlike what had been originally proposed (e.g. Schiller et al., 2018) by looking at a more restricted sample of isotopes, like Ca, Ti and Cr only. Also, the Earth does not appear intermediate between the NC and CC group. These measurements constrain the amount of CC material accreted by the Earth (and equivalently by Mars). This must be less than 10% by mass, with a more probable fraction of 4%.

Steller et al. Nucleosynthetic zinc isotope anomalies reveal a dual origin of terrestrial volatiles (Icarus, 2022; WP3) reports measurements of the zinc (Zn) isotope ratios 66Zn/64Zn and 68Zn/64Zn in meteorites and Earth.  It shows that CC and NC meteorites exhibit distinct isotopic ratios, which until now had only been shown for several non-volatile elements such as Ti, Cr, Ca, Mo, but never for a moderately volatile element such as Zn. This result is important because it shows that the NC-CC isotopic dichotomy is unlikely to have been caused by the condensation/evaporation of different chemical carriers, given that it holds for elements with vastly different condensation temperatures, ranging from ~700K (Zn) to ~1,600K (Ca, Ti, Mo). The other important result is that Earth, which is similar to NC meteorites for all non-volatile element isotopes, is found to be intermediate between NC and CC meteorites in Zn isotopes. This result demonstrates that 30% of terrestrial Zn was acquired from the accretion of CC material, the rest being acquired from NC materials. Because CC meteorites are richer in Zn and other volatile elements than NC meteorites, this implies that our planet accreted 5-6% of its bulk mass from CC material, which is consistent with the results of Burkhardt et al. (2021). The small amount of CC material accreted by Earth rules out the hypothesis that the terrestrial planets may have grown substantially by pebble accretion, because pebbles would have drifted from the outer disk, carrying a strong CC signature.

Intriguingly, the same analysis carried on martian meteorites shows no evidence for a CC contribution to the Zn budget of Mars (Kleine et al., An inner solar system origin of volatile elements in Mars, Icarus, 2023; WP3). This could reveal a complex dynamical history of CC planetesimals, so to deliver material to Earth but not to Mars. But this would be inconsistent with the evidence for CC-derived Mo in Mars. Alternatively, it may be possible that Zn, being more volatile, was poorly retained in CC impacts on Mars, unlike Mo which is far more refractory. We will explore this possibility in the future.

Hellmann et al. (Origin of Isotopic Diversity among Carbonaceous Chondrites, ApJ 2023; WP3) address the dispersion of isotopic values within the CC group. They show that this dispersion is the result of combination of different proportions of CC-chondrules, CAIs and CI-like matrix in the different CC meteorites. Schneider et al. (2020) had already shown that CC-chondrule precursors were the result of mixing of CAIs and AOAs with NC material. Instead, the origin of the dispersion of isotopic values within NC planetesimals and the characteristic linear correlation among all isotope anomalies remains elusive.

The inefficiency of pebble accretion in terrestrial planet formation is explained in Batygin and Morbidelli A Self-Consistent Model for Dust-Gas Coupling in Protoplanetary Disks (Astronomy & Astrophysics, 2022; WP1). This work shows that the small size of rocky grains and the high density of gas in the inner solar system result in pebbles having a very small Stokes number, which implies that the pebble layer is almost as vertically thick as the gas-disk. Pebble accretion is very sensitive on the thickness of the pebble layer. In particular, in the 3D regime, where the thickness of the layer is larger than the Bondi or Hill radius of the growing planet, pebble accretion becomes very slow. Collisions among local planetesimals thus become the dominant growth process for rocky planets (in contrast with the outer disk, beyond the snowline, where pebble accretion dominates and can produce the massive cores of giant planets). Terrestrial planet growth from local planetesimals is consistent with Earth having predominantly a NC composition, as revealed by the aforementioned isotopic analyses.

The motion of dust across the orbit of a giant planet and the efficiency of the so-called Jupiter-barrier against dust flow, usually invoked to preserve the NC-CC dichotomy in the solar system, has been discussed in details in Morbidelli, Batygin and Lega In situ enrichment in heavy elements of hot Jupiters (A&A, 2023; WP1), although the emphasis of the paper was put on hot Jupiters. This paper shows that a distat giant planet migrating towards the star -as it should have been the case for proto-Jupiter (when its mass was ~20 to 100 Earth masses)- creates a very efficient barrier against the drift of dust of any size across its orbit, because the gas flows through the planet-opened gap from the inside-out direction.  

Morbidelli et al. Contemporary formation of early solar system planetesimals at two distinct radial locations (Nature Astronomy, 2022; WP2) shows that the first planetesimals, related to the iron meteorite parent bodies, may have formed at the sites of the snowline and the silicate sublimation line, at about 5 and 1 au respectively. Assuming that the disk exhibits an isotopic radial gradient due to the accretion of distinct materials at different times (as proposed by Nanne et al., 2019), the formation of early planetesimals at two distinct sites explains the isotopic dichotomy of iron meteorites, revealed in Kruijer et al. (2017). The formation of one of the two groups of planetesimals at the snowline also explains why the cores of the iron meteorite parent bodies isotopically related to carbonaceous chondrites (CC) had a smaller core than those related to non-carbonaceous chondrites (NC), which suggest that the former were more oxidized (i.e. contained more water).This work has been significantly extended in Marschall and Morbidelli An inflationary disk phase to explain extended protoplanetary dust disks (A&A, 2023; WP2), which investigated the conditions that allow dust disks to become wider than 50 au in radius, showing that a very fast initial radial expansion is needed. Having such rapid radial expansion requires a rapid accretion of material into the inner part of the disk, triggering temporarily large Raynolds stresses, as well as a small fragmentation velocity for cold ice particle, inhibiting dust growth. The latter has been demonstrated in recent laboratory experiments.

The formation of early planetesimals in a ring around the silicate sublimation line gives strong support to the idea that terrestrial planets fromed from a ring of small objects (Hansen, 2009; Nesvorny et al., 2021). Thus, we focus on this model in our dynamical approach to terrestrial planet formation.

We decided to revisit this model from the very beginning: the growth of the first planetary embryos from a ring of planetesimals. Previous work on this model (Hansen, 2009; Nesvorny et al., 2021; Izidoro et al., 2022) assumed the exitence of a confined ring of planetesimals AND embryos at the disappearance of the gas from the protoplanetary disk. But the formation of embryos from planetesimals during the gas-disk phase should be modeled self-consistently and can have profpund effects on the ring structure.

In Woo et al. Terrestrial planet formation from a ring (Icarus, 2023; WP1) focuses precisely on this step. We use the code GENGA, which allows simulating the mutual interactions and collisions among the planetesimals. We account for gas drag and migration forces acting on planetesimals and growing embryos. We find that, while they form, the planetary embryos spread radially under the effect of mutual scattering, dynamical friction and eccentricity damping from the disk of gas. At the end of the gas-disk lifetime we obtain a large number of embryos whose orbits are so radially separated from each other that no further collisions occur, even during the giant planet instability. Thus, these simulations fail forming Earth and Venus but lead to a spread-out systems of multiple small planets. Planetesimal formation in a ring is therefore not a sufficient condition for the successful formation of the terrestrial solar system planets. We show that the formation of Earth and Venus analogues can be obtained if the gas surface density distribution is sufficiently peaked near 1 au, causing convergent migration of the embryos. Convergent migration has been already invoked to explain terrestrial planet formation starting from a radially extended disk of planetesimals or embryos (Ogihara et al., 2018; Broz et al.). In Woo et al. we show that it is also needed in the planetesimal-ring hypothesis. Convergent migration needs to be not too strong, otherwise Earth forms within the lifetime of the disk, which is inconsistent with isotope chronology that indicated a minimal formation age of 40 My for our planet.

In Woo et al. Terrestrial planet formation from a ring. Long term simulations accounting for a giant planet instability (Icarus 2024, WP1) we continue the most promising simulations obtained in the previous paper for 200 My after gas removal. These simulations account for a phase of giant planet instability, that we enact at different times (15, 60 and 100 My), given that the exact chronology of this instability is not well known. We find terrestrial planet systems that correctly reproduce the mass-distant distribution of the real planets. Only systems for which the last giant impact on Earth occurs between 40 and 80 My can have a final dynamical excitation consistent with the real one and the material accreted by Earth after the last giant impact can match the real Late Veneer mass. The timing of the giant planet instability affects the statiistical distribution of the timing of the last giant impact, but not so sharply to be able to constrain the former from the latter.

A potential problem of the ring model for the formation of the terrestrial planet is heterogenous accretion to explain the chemistry of our planet. Already Rubie et al. (2011, 2015) had pointed out that Earth has to accrete a variety of materials, from more reduced to more oxidized. We emphasized the need for heterogenous accretion by looking at the volatile depletion pattern of the bulk silicate Earth (BSE). In Sossi et al. Stochastic accretion of the Earth (Nature Astronomy, 2022; WP1) we show that Earth should have accreted a variety of planetesimals, formed at different temperatures in the protoplanetary disk. These planetesimals should have had a step-like volatile depletion pattern, like asteroid Vesta, i.e. they should have been strongly depleted in all elements that are gaseous at the temperature at which they formed. The combination of objects depleted of volatiles at different temperatures produced the smooth volatile depletion pattern characteristic of our planet. This result suggests that Earth accreted planetesimals from a wide range of heliocentric distances, so to probe a variety of formation temperatures, in contrast with the idea that it formed from a narrow ring. A potential solution of this conundrum is that the temperature characterizing the volatile depletion pattern of each planetesimal was determined by its internal thermal evolution and not by its radial location in the disk where it formed. In this case, even a planetesimal population formed in a narrow ring could exhibit a variety of volatile-depletion temperatures and produce a planet with a smooth volatile depletion pattern as Earth. However, volatile-rich and volatile-poor planetesimals would be accreted at random times, in contrast with the constraint coming from the Pd-Ag radiogenic system indicating that volatile-rich bodies have been accreted towards the end of Earth's growth history (Schönbächler et al., 2010).

These results show that a more specific modeling of the chemical evolution of the bulk silicate Earth as our planet accretes in various dynamical models is needed, A first step has been to improve the code originally developed by Rubie et al. (2015), in order to reduce the number of free parameters and use information from laboratory experiments and SPH simulations on the volume of magma generated in impacts and the fraction of it that equilibrates with the impactor's metal. This has been the object of the work by Dale et al. An improved model of metal/silicate differentiation during Earth's accretion (Icarus, 2023; WP1), which also relaxed the assumption that all planetesimals are differentiated. Armed with this code we can now investigate the chemical properties of a planet formed from a planetesimal ring and constrain the amount of "exotic" oxidized material (chondrites of both the NC and CC groups) needed to reproduce the observed properties of the bulk silicate Earth. This is the object of ongoing work.

In conlusion, at the current state of our project, the ring model seems to be the most promising one to explain the formation of the terrestrial planets and the general structure of the inner Solar system. However, a number of problems remain to be investigated, particularly concerning the compatibility of this model with chemical and chronological constraints.

Other results related to the HolyEarth project

Nesvorny et al. Formation of Lunar Basins from Impacts of Leftover Planetesimals (ApJ, 2022) and Early bombardment of the moon: Connecting the lunar crater record to the terrestrial planet formation (Icarus, 2023) close the problem of understanding how terrestrial planet accretion ended. Previous work (Morbidelli et al., 2018; Zhu et al. 2019, 2021) showed that the most likely scenario is that the planets accreted the population of planetesimals that had formed originally in the same region (the terrestrial planet formation ring), as the latter gradually decayed in time. Indeed this scenario explains the masses accreted as a "late veneer" by Earth, Moon, Mars and even the asteroid Vesta, as well as the lunar crater record. The Nesvorny et al. papers demonstrate for the first time that this scenario also explains the timeline of formation of lunar impact basins, including the formation of late and large basins like Imbrium and Orientale. Few doubts therefore remain on the tail-end accretion of the terrestrial planets. The putative "terminal lunar cataclysm" did not occur. Nevertheless, the Icarus paper shows that the giant planet instability could not have occurred earlier than 20 - 60 My before the Moon-forming event, otherwise the cometary post-lunar-formation bombardment of the Earth would have been too weak to explain the abundance of atmospheric Xe and Kr of cometary origin, as constrained by isotopic data (Marty et al., 2017,  Rubin et al., 2018).

Batygin and Morbidelli Formation of rocky super-earths from a narrow ring of planetesimals (Nature Astronomy, 2023) extends the planetesimal ring model originally developed for the formation of the terrestrial planets to explain the formation of rocky super-Earths, with a great similarity in masses within each given system. The idea is that if the rocky planetesimal ring contains multiple Earth masses of solid material, planets can form faster and more massive than our terrestrial planet precursors. Then, they can migrate towards the central star by tidal gravitational interaction with the disk of gas. Once they exit the planetesimal ring, their accretion stops and their mass remains frozen. A sequence of planets of similar masses can grow, then migrate out, of a single rocky planetesimal ring. The final masses are dictated by the original mass in the ring and, for the planets that grew early and massive enough to migrate so close to the star to be detectable by transit observations, they are all similar in the end. This explains the peas-in-the-pot observed pattern for super-Earths. 


Please visit the publication page to access the papers from our group described here.