The formation of Jupiter’s diluted core by a giant impact

Abstract

The Juno mission1 has provided an accurate determination of Jupiter’s gravitational field2, which has been used to obtain information about the planet’s composition and internal structure. Several models of Jupiter’s structure that fit the probe’s data suggest that the planet has a diluted core, with a total heavy-element mass ranging from ten to a few tens of Earth masses (about 5 to 15 per cent of the Jovian mass), and that  heavy elements (elements other than hydrogen and helium) are distributed within a region extending to nearly half of Jupiter’s radius3,4. Planet-formation models indicate that most heavy elements are accreted during the early stages of a planet's formation to create a relatively compact core5,6,7 and that almost no solids are accreted during subsequent runaway gas accretion8,9,10. Jupiter’s diluted core, combined with its possible high heavy-element enrichment, thus challenges standard planet-formation theory. A possible explanation is erosion of the initially compact heavy-element core, but the efficiency of such erosion is uncertain and depends on both the immiscibility of heavy materials in metallic hydrogen and on convective mixing as the planet evolves11,12. Another mechanism that can explain this structure is planetesimal enrichment and vaporization13,14,15 during the formation process, although relevant models typically cannot produce an extended diluted core. Here we show that a sufficiently energetic head-on collision (giant impact) between a large planetary embryo and the proto-Jupiter could have shattered its primordial compact core and mixed the heavy elements with the inner envelope. Models of such a scenario lead to an internal structure that is consistent with a diluted core, persisting over billions of years. We suggest that collisions were common in the young Solar system and that a similar event may have also occurred for Saturn, contributing to the structural differences between Jupiter and Saturn16,17,18.

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Fig. 1: Three-dimensional cutaway snapshots of density distributions during a merger event between a proto-Jupiter with a 10M rock/ice core and a 10M impactor.
Fig. 2: Post-impact thermal evolution models.
Fig. 3: Two-dimensional snapshots of an off-centre collision between the proto-Jupiter with a 10M rock/ice core and a 10M impactor.

Data availability

The datasets generated and analysed during the current study are available from the corresponding authors upon reasonable request.

Code availability

The FLASH code is publicly available for download at http://flash.uchicago.edu/site/flashcode. The implementation of giant impact simulations in the framework of FLASH is available upon request. The REBOUND code is publicly available for download at https://github.com/hannorein/rebound. The MESA code is an open source stellar evolution code and is publicly available at http://mesa.sourceforge.net. The modified version of the MESA code is not yet ready for public release—it will be presented in future work (S.M., A. Cumming & R.H.; manuscript in preparation). Gnuplot, Jupyter Notebook, Mathematica, VisIt and yt python packages were used for data reduction and presentation in this study.

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Acknowledgements

We thank S. M. Wahl and Y. Miguel for sharing their results with us. We thank A. Cumming for technical support and discussions. We thank J. J. Fortney, P. Garaud and H. Rein for conversations. S.-F.L. acknowledges the support and hospitality provided by the Aspen Center for Physics during the early stage of this work. D.L. thanks the Institute for Advanced Study, Princeton, the Institute of Astronomy and Department of Applied Mathematics and Theoretical Physics, Cambridge University, for support and hospitality while this work was being completed. R.H. acknowledges support from SNSF grant number 200021_169054. A.I. acknowledges support from the National Aeronautics and Space Administration under award number 80NSSC18K0828 and from the National Science Foundation under grant number AST-1715719.

Author information

D.L. had the idea of the impact scenario. S.-F.L. and A.I. examined its feasibility. S.-F.L. coordinated this study. S.-F.L. and Y.H. designed and analysed the hydrodynamic simulations. X.Z. and S.-F.L. performed and analysed the N-body simulations. S.M. and R.H. designed the long-term thermal evolution study. All authors contributed to discussions, as well as to editing and revising the manuscript.

Correspondence to Shang-Fei Liu.

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Extended data figures and tables

Extended Data Fig. 1 Statistics of outcomes of four planetary embryos under the influence of an emerging Jupiter.

a, The initial configurations of four planetary embryos divided into four groups based on the fixed parameters shown under the group numbers. In groups 1–3, half of the embryos are placed inside Jupiter’s orbit (labelled ‘Inward’); the other half are outside Jupiter’s orbit (labelled ‘Outward’). In group 4, all embryos are outside Jupiter’s orbit. The exact location of every embryo is shown in Extended Data Table 1. b, The statistical outcomes of the dynamic evolution after 10tgrow. Jupiter’s growth can substantially modify the orbits of those embryos. Some embryos collided with Jupiter (labelled ‘Merge’), and some have been ejected from the Solar System (labelled ‘Escape’). Colours indicate different choices of the free parameters (inflation factor f and orbital separation factor k; see methods section ‘A statistical N-body study of embryo collisions’) as shown for each group. The height of each bar (‘Frac’) indicates the percentage of each state.

Extended Data Fig. 2 Histograms of collision angles of each dataset presented in Extended Data Fig. 1.

a, Group 1; b, group 2; c, group 3; d, group 4. The bin size is 5°, and there are 18 bins in each plot. The collision angle is measured in degrees. The red dashed line indicates the median value in each case. The results suggest that head-on collisions are more common (greater percentage probability) than grazing collisions. Each case has a different N, but they all fall in the range between 1,000 to 1,500.

Extended Data Fig. 3 Two-dimensional snapshots of a merger between the proto-Jupiter with a 10M rock/ice core and a 10M impactor.

a, Density contours in the orbital plane before the impact; b, before the impactor arriving at the core; c, after the destruction of the core; d, at about 10 h after the impact. Time in each panel is measured since the start of the simulation.

Extended Data Fig. 4 The change of internal energy caused by the merger between the proto-Jupiter with a 10M rock/ice core and a 10M impactor.

a, The enclosed internal energy Einternal of Jupiter before and after the impact as a function of radius. b, The net change of enclosed internal energy ΔEinternal of Jupiter as a function of radius.

Extended Data Fig. 5 Two-dimensional snapshots of a merger between the proto-Jupiter with a 17M core and a 1M impactor.

a, Density contours in the orbital plane before the impact; b, before the impactor arriving at the core; c, after the merger with the core; d, at about 10 h after the impact. Time in each panel is measured since the start of the simulation.

Extended Data Fig. 6 Initial conditions for post-impact evolution.

a, The initial post-impact heavy-element profile; b, temperature profiles of the models used for the thermal evolution. The heavy-element distribution is taken from the hydro-simulation 10 h after the giant impact. Solid lines correspond to a head-on collision, while dashed-dotted lines show the result of an oblique collision at a 45° angle. The colours depict models with different initial thermal states. See text and Extended Data Table 2 for further details. The radius is normalized by the present-day radius of Jupiter RJ.

Extended Data Fig. 7 Density versus normalized radius for the head-on collision after 4.56 Gyr of evolution.

The colours correspond to distinct model assumptions: models H-4.3, H-4.5 and H-4.7 correspond to initial thermal profiles with different central temperatures at the time of the impact, whereas model H-radenv assumes a proto-Jupiter with a radiative envelope. Model H-4.5-lowα uses a shorter mixing length, model H-4.5-semiconv allows for semi-convective mixing, and in model H-4.5-rock the heavy elements are represented by rock instead of water for EOS purposes. The inset zooms in on the region with a normalized radius between 0.15 and 0.5. See text and Extended Data Table 2 for further details.

Extended Data Fig. 8 Density versus normalized radius for the oblique collision after 4.56 Gyr of evolution.

The colours correspond to distinct model assumptions: models O-4.3, O-4.5 and O-4.7 correspond to initial thermal profiles with different central temperatures at the time of the impact. Model O-4.5-lowα uses a shorter mixing length, model O-4.5-semiconv allows for semi-convective mixing, and in model O-4.5-rock the heavy elements are represented by rock instead of water for EOS purposes. The inset zooms in on the region with a normalized radius between 0.15 and 0.4. See text and Extended Data Table 2 for further details.

Extended Data Table 1 Initial orbital semi-major axes for each embryo of our N-body simulation suite
Extended Data Table 2 Evolutionary models discussed in this work

Supplementary information

Video 1

3D cutaway animation of consequence of a head-on collision between a proto-Jupiter and a massive planetary embryo. Snapshots of the animation are presented in Figure 1 in the main text.

Video 2

2D animation of the density contours of a head-on collision between a proto-Jupiter and a massive planetary embryo. Snapshots of the animation are presented in Extended Data Figure 3.

Video 3

2D animation of the density contours of an oblique collision between a proto-Jupiter and a massive planetary embryo. Snapshots of the animation are presented in Figure 3.

Video 4

2D animation of the density contours of a head-on collision between a proto-Jupiter with a massive core and a small planetary embryo. Snapshots of the animation are presented in Extended Data Figure 5.

Video 5

Animation of the evolution of temperature, density, specific entropy and heavy-element mass fraction of model H-4.5 over 4.5 Gyr. At the end of the simulation, a diluted core is formed. See Methods for details.

Video 6

Animation of the evolution of temperature, density, specific entropy and heavy-element mass fraction of model H-4.5-semiconv over 4.5 Gyr. At the end of the simulation, a diluted core is formed. See Methods for details.

Video 7

Animation of the evolution of temperature, density, specific entropy and heavy-element mass fraction of model H-4.7 over 4.5 Gyr. At the end of the simulation, the compositional gradient established after the impact disappears due to a very hot interior. See Methods for details.

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