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

Abstract

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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Figure 1: The cumulative mass distribution of planetesimals and embryos.
Figure 2: The vertical distribution of pebbles and embryos.
Figure 3: Embryo growth rate as a function of mass.

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Acknowledgements

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

Authors and Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to Harold F. Levison.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Table 1 Our completed simulations.
Extended Data Table 2 More simulations.

Supplementary information

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. (MP4 93 kb)

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. (MP4 529 kb)

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Levison, H., Kretke, K. & Duncan, M. Growing the gas-giant planets by the gradual accumulation of pebbles. Nature 524, 322–324 (2015). https://doi.org/10.1038/nature14675

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