Letter | Published:

Growing the gas-giant planets by the gradual accumulation of pebbles

Nature volume 524, pages 322324 (20 August 2015) | Download Citation


It is widely held that the first step in forming gas-giant planets, such as Jupiter and Saturn, was the production of solid ‘cores’ each with a mass roughly ten times that of the Earth1,2. Getting the cores to form before the solar nebula dissipates (in about one to ten million years; ref. 3) has been a major challenge for planet formation models4,5. Recently models have emerged in which ‘pebbles’ (centimetre-to-metre-sized objects) are first concentrated by aerodynamic drag and then gravitationally collapse to form objects 100 to 1,000 kilometres in size6,7,8,9. These ‘planetesimals’ can then efficiently accrete left-over pebbles10 and directly form the cores of giant planets11,12. This model is known as ‘pebble accretion’; theoretically, it can produce cores of ten Earth masses in only a few thousand years11,13. Unfortunately, full simulations of this process13 show that, rather than creating a few such cores, it produces a population of hundreds of Earth-mass objects that are inconsistent with the structure of the Solar System. Here we report that this difficulty can be overcome if pebbles form slowly enough to allow the planetesimals to gravitationally interact with one another. In this situation, the largest planetesimals have time to scatter their smaller siblings out of the disk of pebbles, thereby stifling their growth. Our models show that, for a large and physically reasonable region of parameter space, this typically leads to the formation of one to four gas giants between 5 and 15 astronomical units from the Sun, in agreement with the observed structure of the Solar System.

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  1. 1.

    , & Instability of a gaseous envelope surrounding a planetary core and formation of giant planets. Prog. Theor. Phys. 60, 699–710 (1978)

  2. 2.

    et al. Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124, 62–85 (1996)

  3. 3.

    , & Disk frequencies and lifetimes in young clusters. Astrophys. J. 553, L153–L156 (2001)

  4. 4.

    , & Final stages of planet formation. Astrophys. J. 614, 497–507 (2004)

  5. 5.

    , & Modeling the formation of giant planet cores. I. Evaluating key processes. Astron. J. 139, 1297–1314 (2010)

  6. 6.

    , , & Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence. Astrophys. J. 546, 496–508 (2001)

  7. 7.

    & Streaming instabilities in protoplanetary disks. Astrophys. J. 620, 459–469 (2005)

  8. 8.

    et al. Rapid planetesimal formation in turbulent circumstellar disks. Nature 448, 1022–1025 (2007)

  9. 9.

    On the formation of planetesimals via secular gravitational instabilities with turbulent stirring. Astrophys. J. 731, 99 (2011)

  10. 10.

    & 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 (2010)

  11. 11.

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

  12. 12.

    & Forming the cores of giant planets from the radial pebble flux in protoplanetary discs. Astron. Astrophys. 572, A107 (2014)

  13. 13.

    & Challenges in forming the Solar System’s giant planet cores via pebble accretion. Astron. J. 148, 109 (2014)

  14. 14.

    et al. Dust properties of protoplanetary disks in the Taurus-Auriga star forming region from millimeter wavelengths. Astron. Astrophys. 512, A15 (2010)

  15. 15.

    , & A simple model for the evolution of the dust population in protoplanetary disks. Astron. Astrophys. 539, A148 (2012)

  16. 16.

    & Evolution of planetesimal velocities. Icarus 74, 542–553 (1988)

  17. 17.

    Stirring and dynamical friction rates of planetesimals in the solar gravitational field. Icarus 88, 129–145 (1990)

  18. 18.

    Protoplanet migration by nebula tides. Icarus 126, 261–281 (1997)

  19. 19.

    & Some dynamical aspects of the accretion of Uranus and Neptune — the exchange of orbital angular momentum with planetesimals. Icarus 58, 109–120 (1984)

  20. 20.

    The origin of Pluto’s orbit: implications for the Solar System beyond Neptune. Astron. J. 110, 420–429 (1995)

  21. 21.

    , , & Origin of the orbital architecture of the giant planets of the Solar System. Nature 435, 459–461 (2005)

  22. 22.

    , & A Lagrangian integrator for planetary accretion and dynamics (LIPAD). Astron. J. 144, 119–138 (2012)

  23. 23.

    , & A multiple time step symplectic algorithm for integrating close encounters. Astron. J. 116, 2067–2077 (1998)

  24. 24.

    & Catastrophic disruptions revisited. Icarus 142, 5–20 (1999)

  25. 25.

    & On the orbital evolution and growth of proto-planets embedded in a gaseous disc. Astronomy 315, 823–833 (2000)

  26. 26.

    , & The gas drag effect on the elliptical motion of a solid body in the primordial solar nebula. Prog. Theor. Phys. 56, 1756–1771 (1976)

  27. 27.

    Atmospheres of protoplanetary cores: critical mass for nucleated instability. Astrophys. J. 648, 666–682 (2006)

  28. 28.

    & Toward a deterministic model of planetary formation. IV. Effects of type I migration. Astrophys. J. 673, 487–501 (2008)

  29. 29.

    , & Tidal barrier and the asymptotic mass of proto-gas giant planets. Astrophys. J. 660, 791–806 (2007)

  30. 30.

    , & Separating gas-giant and ice-giant planets by halting pebble accretion. Astron. Astrophys. 572, A35 (2014)

  31. 31.

    Giant planet formation with pebble accretion. Icarus 233, 83–100 (2014)

  32. 32.

    , & Settling and growth of dust particles in a laminar phase of a low-mass solar nebula. Icarus 67, 375–390 (1986)

  33. 33.

    , , , & Protoplanetary disk structures in Ophiuchus. II. Extension to fainter sources. Astrophys. J. 723, 1241–1254 (2010)

  34. 34.

    Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula. Prog. Theor. Phys. 70 (Supplement), 35–53 (1981)

  35. 35.

    et al. Spitzer observations of the λ Orionis cluster. I. The frequency of young debris disks at 5 Myr. Astrophys. J. 707, 705–715 (2009)

  36. 36.

    & Spectral energy distributions of T Tauri stars with passive circumstellar disks. Astrophys. J. 490, 368–376 (1997)

  37. 37.

    , , & Asteroids were born big. Icarus 204, 558–573 (2009)

  38. 38.

    Solar System abundances and condensation temperatures of the elements. Astrophys. J. 591, 1220–1247 (2003)

  39. 39.

    & Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973)

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This work was supported by an NSF Astronomy and Astrophysics Research Grant (principal investigator H.F.L.). We thank A. Johansen, M. Lambrechts, A. Morbidelli, D. Nesvorny and C. Ormel for discussions.

Author information


  1. Southwest Research Institute and NASA Solar System Exploration Research Virtual Institute, 1050 Walnut Street, Suite 300, Boulder, Colorado 80302, USA

    • Harold F. Levison
    •  & Katherine A. Kretke
  2. Department of Physics, Engineering Physics, and Astronomy, Queen’s University, Kingston, Ontario K7L 3N6, Canada

    • Martin J. Duncan


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H.F.L. and K.A.K. jointly conceived of the paper and carried out the bulk of the numerical and semi-analytic calculations. M.J.D. developed a semi-analytic model of viscous stirring and growth rates in a population distribution. All authors contributed to the discussion of the results and to the crafting of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Harold F. Levison.

Extended data

Supplementary information


  1. 1.

    The cumulative mass distribution of planetesimals and embryos

    The growth of planetary embryos in our fiducial simulation as illustrated by cumulative mass distributions. The initial distribution is shown in pale blue, while the evolving distribution is show in dark blue and red (for embryos larger than 1 Earth-masses). This is an animated version of Figure 1b in the main text.

  2. 2.

    The vertical distribution of pebbles and embryos.

    A comparison between the vertical distribution, as represented by tan(i), of pebbles (the time averaged cyan gradient) and embryos (black circles) as a function of time in the fiducial simulation. This is an animated version of Figure 2 in the main text.

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