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

Nature Astronomy volume 5, pages 898–902 (2021)Cite this article

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Abstract

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 http://sirrah.troja.mff.cuni.cz/~mira/fargo_terrestrial/.

Code availability

Thorin is publicly available at http://sirrah.troja.mff.cuni.cz/~chrenko/ (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.

References

  1. Lambrechts, M. & Johansen, A. Rapid growth of gas-giant cores by pebble accretion. Astron. Astrophys. 544, A32 (2012).

    Article  ADS  Google Scholar 

  2. Levison, H. F., Kretke, K. A. & Duncan, M. J. Growing the gas-giant planets by the gradual accumulation of pebbles. Nature 524, 322–324 (2015).

    Article  ADS  Google Scholar 

  3. Wetherill, G. W. Formation of the earth. Annu. Rev. Earth Planet. Sci. 18, 205–256 (1990).

    Article  ADS  Google Scholar 

  4. Chambers, J. E. & Wetherill, G. W. Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions. Icarus 136, 304–327 (1998).

    Article  ADS  Google Scholar 

  5. Zhu, Z., Hartmann, L., Nelson, R. P. & Gammie, C. F. Challenges in forming planets by gravitational instability: disk irradiation and clump migration, accretion, and tidal destruction. Astrophys. J. 746, 110 (2012).

    Article  ADS  Google Scholar 

  6. Semenov, D., Henning, T., Helling, C., Ilgner, M. & Sedlmayr, E. Rosseland and Planck mean opacities for protoplanetary discs. Astron. Astrophys. 410, 611–621 (2003).

    Article  ADS  Google Scholar 

  7. Chrenko, O., Brož, M. & Lambrechts, M. Eccentricity excitation and merging of planetary embryos heated by pebble accretion. Astron. Astrophys. 606, A114 (2017).

    Article  ADS  Google Scholar 

  8. Eklund, H. & Masset, F. S. Evolution of eccentricity and inclination of hot protoplanets embedded in radiative discs. Mon. Not. R. Astron. Soc. 469, 206–217 (2017).

    Article  ADS  Google Scholar 

  9. Hauck, S. A. et al. The curious case of Mercury’s internal structure. J. Geophys. Res. Planets 118, 1204–1220 (2013).

    Article  ADS  Google Scholar 

  10. Morbidelli, A., Lunine, J. I., O’Brien, D. P., Raymond, S. N. & Walsh, K. J. Building terrestrial planets. Annu. Rev. Earth Planet. Sci. 40, 251–275 (2012).

    Article  ADS  Google Scholar 

  11. Hansen, B. M. S. Formation of the terrestrial planets from a narrow annulus. Astrophys. J. 703, 1131–1140 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Ogihara, M., Kokubo, E., Suzuki, T. K. & Morbidelli, A. Formation of the terrestrial planets in the solar system around 1 au via radial concentration of planetesimals. Astron. Astrophys. 612, L5 (2018).

    Article  ADS  Google Scholar 

  14. Raymond, S. N., Izidoro, A., Bitsch, B. & Jacobson, S. A. Did Jupiter’s core form in the innermost parts of the Sun’s protoplanetary disc? Mon. Not. R. Astron. Soc. 458, 2962–2972 (2016).

    Article  ADS  Google Scholar 

  15. Deienno, R., Walsh, K. J., Kretke, K. A. & Levison, H. F. Energy dissipation in large collisions—no change in planet formation outcomes. Astrophys. J. 876, 103 (2019).

    Article  ADS  Google Scholar 

  16. Dauphas, N. & Pourmand, A. Hf–W–Th evidence for rapid growth of Mars and its status as a planetary embryo. Nature 473, 489–492 (2011).

    Article  ADS  Google Scholar 

  17. Levison, H. F., Kretke, K. A., Walsh, K. J. & Bottke, W. F. Growing the terrestrial planets from the gradual accumulation of sub-meter sized objects. Proc. Natl Acad. Sci. USA 112, 14180–14185 (2015).

    Article  ADS  Google Scholar 

  18. Johansen, A., Mac Low, M.-M., Lacerda, P. & Bizzarro, M. Growth of asteroids, planetary embryos, and Kuiper belt objects by chondrule accretion. Sci. Adv. 1, 1500109 (2015).

    Article  ADS  Google Scholar 

  19. Tanaka, H. & Ward, W. R. Three-dimensional interaction between a planet and an isothermal gaseous disk. II. Eccentricity waves and bending waves. Astrophys. J. 602, 388–395 (2004).

    Article  ADS  Google Scholar 

  20. Benítez-Llambay, P., Masset, F., Koenigsberger, G. & Szulágyi, J. Planet heating prevents inward migration of planetary cores. Nature 520, 63–65 (2015).

    Article  ADS  Google Scholar 

  21. Kretke, K. A. & Lin, D. N. C. The importance of disk structure in stalling type I migration. Astrophys. J. 755, 74 (2012).

    Article  ADS  Google Scholar 

  22. Flock, M., Fromang, S., Turner, N. J. & Benisty, M. 3D radiation nonideal magnetohydrodynamical simulations of the inner rim in protoplanetary disks. Astrophys. J. 835, 230 (2017).

    Article  ADS  Google Scholar 

  23. Rafikov, R. R. Protoplanetary disks as (possibly) viscous disks. Astrophys. J. 837, 163 (2017).

    Article  ADS  Google Scholar 

  24. Paardekooper, S.-J., Baruteau, C. & Kley, W. A torque formula for non-isothermal type I planetary migration—II. Effects of diffusion. Mon. Not. R. Astron. Soc. 410, 293–303 (2011).

    Article  ADS  Google Scholar 

  25. Duncan, M. J., Levison, H. F. & Lee, M. H. A multiple time step symplectic algorithm for integrating close encounters. Astron. J. 116, 2067–2077 (1998).

    Article  ADS  Google Scholar 

  26. Canup, R. M. et al. in New Views of the Moon II (Mineralogical Society of America, in the press).

  27. Lambrechts, M. et al. Formation of planetary systems by pebble accretion and migration. How the radial pebble flux determines a terrestrial-planet or super-Earth growth mode. Astron. Astrophys. 627, A83 (2019).

    Article  Google Scholar 

  28. Bitsch, B., Johansen, A., Lambrechts, M. & Morbidelli, A. The structure of protoplanetary discs around evolving young stars. Astron. Astrophys. 575, A28 (2015).

    Article  ADS  Google Scholar 

  29. Brasser, R., Morbidelli, A., Gomes, R., Tsiganis, K. & Levison, H. F. Constructing the secular architecture of the Solar System II: the terrestrial planets. Astron. Astrophys. 507, 1053–1065 (2009).

    Article  ADS  Google Scholar 

  30. Clement, M. S., Kaib, N. A., Raymond, S. N. & Walsh, K. J. Mars’ growth stunted by an early giant planet instability. Icarus 311, 340–356 (2018).

    Article  ADS  Google Scholar 

  31. Elkins-Tanton, L. T. Magma oceans in the inner Solar System. Annu. Rev. Earth Planet. Sci. 40, 113–139 (2012).

    Article  ADS  Google Scholar 

  32. Fischer, R. A. & Nimmo, F. 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 (2018).

    Article  ADS  Google Scholar 

  33. Thiemens, M. M., Sprung, P., Fonseca, R. O. C., Leitzke, F. P. & Münker, C. Early Moon formation inferred from hafnium–tungsten systematics. Nat. Geosci. 12, 696–700 (2019).

    Article  ADS  Google Scholar 

  34. Roig, F., Nesvorný, D. & DeSouza, S. R. Jumping Jupiter can explain Mercury’s orbit. Astrophys. J. 820, L30 (2016).

    Article  ADS  Google Scholar 

  35. Asphaug, E. & Reufer, A. Mercury and other iron-rich planetary bodies as relics of inefficient accretion. Nat. Geosci. 7, 564–568 (2014).

    Article  ADS  Google Scholar 

  36. Nittler, L. R., Chabot, N. L., Grove, T. L. & Peplowski, P. N. The Chemical Composition of Mercury 30–51 (Cambridge Univ. Press, 2018).

  37. Lyra, W., Paardekooper, S.-J. & Mac Low, M.-M. Orbital migration of low-mass planets in evolutionary radiative models: avoiding catastrophic infall. Astrophys. J. Lett. 715, L68–L73 (2010).

    Article  ADS  Google Scholar 

  38. Morbidelli, A. et al. Fossilized condensation lines in the Solar System protoplanetary disk. Icarus 267, 368–376 (2016).

    Article  ADS  Google Scholar 

  39. Raymond, S. N. & Izidoro, A. Origin of water in the inner solar system: planetesimals scattered inward during Jupiter and Saturn’s rapid gas accretion. Icarus 297, 134–148 (2017).

    Article  ADS  Google Scholar 

  40. Peslier, A. H., Schönbächler, M., Busemann, H. & Karato, S.-I. Water in the Earth’s interior: distribution and origin. Space Sci. Rev. 212, 743–810 (2017).

    Article  ADS  Google Scholar 

  41. Masset, F. FARGO: a fast eulerian transport algorithm for differentially rotating disks. Astron. Astrophys. Suppl. Ser. 141, 165–173 (2000).

    Article  ADS  Google Scholar 

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Acknowledgements

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.

Author information

Authors and Affiliations

  1. Institute of Astronomy, Charles University, Prague, Czech Republic

    M. Brož & O. Chrenko

  2. Department of Space Studies, Southwest Research Institute, Boulder, CO, USA

    D. Nesvorný

  3. Origins Laboratory, Department of the Geophysical Sciences and Enrico Fermi Institute, The University of Chicago, Chicago, IL, USA

    N. Dauphas

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  1. M. Brož
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  4. N. Dauphas
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Contributions

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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The authors declare no competing interests.

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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). https://doi.org/10.1038/s41550-021-01383-3

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