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Early terrestrial planet formation by torque-driven convergent migration of planetary embryos


The massive cores of the giant planets are thought to have formed in a gas disk by the accretion of pebble-sized particles whose accretional cross-section was enhanced by aerodynamic gas drag1,2. A commonly held view is that the terrestrial planet system formed later (30–200 Myr after the dispersal of the gas disk) by giant collisions of tens of lunar- to Mars-sized protoplanets3,4. Here we propose, instead, that the terrestrial planets of the Solar System formed earlier by the gas-driven convergent migration of protoplanets towards ~1 au. To investigate situations in which convergent migration occurs and determine the thermal structure of the gas and pebble disks in the terrestrial planet zone, we developed a radiation–hydrodynamic model with realistic opacities5,6. We find that protoplanets grow in the first 10 Myr by mutual collisions and pebble accretion, and gain orbital eccentricities by gravitational scattering and the hot-trail effect7,8. The orbital structure of the inner Solar System is well reproduced in our simulations, including its tight mass concentration at 0.7–1 au and the small sizes of Mercury and Mars. The early-stage protosolar disk temperature exceeds 1,500 K inside 0.4 au, implying that Mercury grew in a highly reducing environment next to the evaporation lines of iron and silicates, influencing Mercury’s bulk composition9. A dissipating gas disk, however, is cold, and pebbles drifting from larger heliocentric distances would deliver volatile elements.

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Fig. 1: Radiation–hydrodynamic model of the terrestrial planet zone with Mercury- to Mars-sized protoplanets migrating in a gas disk.
Fig. 2: Convergent migration towards ~1 au is illustrated for Mercury- to Earth-mass protoplanets.
Fig. 3: Convergent migration leads to a compact configuration of orbits that matches the orbital architecture of the terrestrial planet system.
Fig. 4: The temperature profile of the protoplanetary disk determines the local chemical composition of solids, whereas temperature perturbations affect the orbital evolution of protoplanets.

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Data availability

The initial conditions of all simulations, as well as selected snapshots of hydrodynamical simulations and data used to produce the respective figures, are available at

Code availability

Thorin is publicly available at (and its specific version used in this study at the previous URL). SyMBA, used in simulations, is proprietary, but its specific part implementing additional accelerations is available.


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The work of M.B. and O.C. was supported by the Grant Agency of the Czech Republic (grant number 18-06083S). The work of O.C. was supported by Charles University (research programme number UNCE/SCI/023). The work of D.N. work was supported by the NASA SSERVI and XRP programmes. Computational resources were supplied by the project ‘e-Infrastruktura CZ’ (e-INFRA LM2018140) provided within the programme Projects of Large Research, Development and Innovations Infrastructures. We are grateful to W. F. Bottke and A. Morbidelli for valuable discussions. We thank R. Fischer for sharing her geochemical computations with us.

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Authors and Affiliations



All authors conceived and designed the numerical experiments. O.C. and D.N. contributed analysis tools and performed some of the experiments. M.B. and N.D. analysed the data. M.B. and D.N. wrote the paper.

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Correspondence to M. Brož.

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Peer review information Nature Astronomy thanks Elena Lega and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Information and Figs. 1–17.

Supplementary Video 1

Radiation–hydrodynamic model of the terrestrial planet zone with Mercury- to Mars-size protoplanets migrating in a gas disk.

Supplementary Video 2

Convergent migration leads to a compact configuration of orbits that matches the orbital architecture of the terrestrial planet system.

Supplementary Video 3

Temperature perturbations induced by hot accreting protoplanets affect their orbital eccentricity.

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Brož, M., Chrenko, O., Nesvorný, D. et al. Early terrestrial planet formation by torque-driven convergent migration of planetary embryos. Nat Astron 5, 898–902 (2021).

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