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Very-wide-orbit planets from dynamical instabilities during the stellar birth cluster phase

Nature Astronomy volume 9, pages 982–994 (2025)Cite this article

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Abstract

Gas-giant planets have been detected on eccentric orbits several hundreds of astronomical units in size around other stars. It has been proposed that even the Sun hosts a wide-orbit planet of 5–10 Earth masses, often called Planet Nine, which influences the dynamics of distant trans-Neptunian objects. However, the formation mechanism of such planets remains uncertain. Here we use numerical simulations to show that very-wide-orbit planets are a natural by-product of dynamical instabilities that occur in planetary systems while their host stars are still embedded in natal stellar clusters. A planet is first brought to an eccentric orbit with an apoastron of several hundred astronomical units by repeated gravitational scattering by other planets, then perturbations from nearby stellar flybys stabilize the orbit by decoupling the planet from the interaction with the inner system. In our Solar System, the two main events likely conducive to planetary scattering were the growth of Uranus and Neptune, and the giant planets instability. We estimate a 5–10% likelihood of creating a very-wide-orbit planet if either happened while the Sun was still in its birth cluster, increasing to 40% if both were. In our simulated exoplanetary systems, the trapping efficiency is 1–5%. Our results imply that planets on wide, eccentric orbits occur at least 10−3 per star.

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Fig. 1: Snapshots of the dynamical evolution of a stellar cluster with 200 stars.
Fig. 2: Trapping of wide-orbit planets in an extrasolar gas-giant instability simulation and a Solar System early dynamical instability simulation.
Fig. 3: Final orbital distribution of planets produced in early dynamical planetary instabilities taking place in different planetary systems embedded in stellar clusters with different configurations.
Fig. 4: Wide-orbit-planet trapping efficiency in different planetary systems embedded in star clusters with different configurations.

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Data availability

Simulation data that support the findings of this study or were used to make plots are available from the corresponding author upon reasonable request. The source data of the main figures of the paper are available at https://andreizidoro.com/simulation-data.

Code availability

Simulations presented here were performed using modified versions of the Mercury N-body integrator91, publicly available on GitHub at https://github.com/smirik/mercury (ref. 129).

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Acknowledgements

A. Izidoro is grateful to R. Dasgupta for insightful discussions, help with proofreading, valuable input on paper clarity and partial financial support for this project. A. Izidoro and N.A.K. thank support from the NASA Emerging Worlds Program Grant 80NSSC23K0868. Contributions from N.A.K. were also supported by NASA Exoplanets Research Program grant 80NSSC19K0445 and NSF CAREER Award 2405121. S.N.R. acknowledges funding from the Programme Nationale de Planetologie (PNP) of the INSU (CNRS), and in the framework of the Investments for the Future programme IdEx, Université de Bordeaux/RRI ORIGINS. A.M. acknowledges support from ERC grant 101019380 HolyEarth. This work was supported in part by the Big-Data Private-Cloud Research Cyberinfrastructure MRI-award funded by NSF under grant CNS-1338099 and by Rice University’s Center for Research Computing (CRC).

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Authors and Affiliations

  1. Department of Earth, Environmental and Planetary Sciences, Rice University, Houston, TX, USA

    André Izidoro

  2. Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Pessac, France

    Sean N. Raymond

  3. Planetary Science Institute, Tucson, AZ, USA

    Nathan A. Kaib

  4. Collège de France, Paris, France

    Alessandro Morbidelli

  5. Department of Physics and Astronomy, Rice University, Houston, TX, USA

    Andrea Isella

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  1. André Izidoro
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  2. Sean N. Raymond
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Contributions

A. Izidoro, S.N.R., N.A.K. and A.M. conceived of the original idea of this project. N.A.K. and A. Izidoro wrote and tested the adapted versions of MERCURY code used in this work. A. Izidoro performed numerical simulations, analysed results and prepared all the figures in the paper. S.N.R., A. Izidoro and N.A.K. drafted the paper with inputs from A.M. and A. Isella. All authors contributed to the interpretation and discussion of the results, writing and editing of the paper.

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Correspondence to André Izidoro.

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Extended data

Extended Data Fig. 1 Final eccentricity distribution of giant exoplanets surviving in the inner systems after dynamical instabilities.

It shows only giant planets with semi-major axis smaller than 40 au. The eccentricity distribution of radial velocity exoplanets is shown in grey.

Extended Data Fig. 2 Unsuccessful trapping of a wide-orbit planet in an exoplanet gas giant instability simulation.

A planetary dynamical instability takes place at about 3 kyr which scatters Planet-1 and 2 on wide orbits. Planet-2 is ejected from the host star at 25 kyr. Planet-1 evolves onto a high eccentricity orbit and is eventually kicked by Star-4 at about 0.4 Myr. A passage of the host star near the cluster barycenter at 0.7 Myr also affects the orbit of Planet-1. Planet-1 is ultimately ejected from the host start due to multiple flybys of stars 1, 47, 153, and 181, which take place after 1-2 Myr. The simulation stops at 3 Myr. Orbital elements are given with respect to the barycenter of the host-star system.

Extended Data Fig. 3 Planetary system architecture at the end of the gas disk phase in two different simulations modelling the accretion of Uranus and Neptune.

These simulations produced planetary systems that broadly match solar system constraints (almost unitary mass ratio of the ice giants, two planets with masses larger than about 12M⊕, and a dynamically cold planetesimal disk population consistent with the dynamically cold kernel of the Kuiper-belt). Each plot (panels a and b) is composed by two stacked panels. The top-component shows semi-major axis versus eccentricity. The bottom-component shows semi-major axis versus orbital inclination. Jupiter and Saturn are represented by the big black filled circles showed at about 5.25 and about 7.18 AU (near the 3:2 MMR). Color-coded circles represent the formed ice giants and their sizes scale as M1/3, where M is the mass. The color-coding shows the masses of the final planets. The small black circles represent primordial planetesimals. The gray-region show the expected location of Planet-9. The orange-ish regions (a ≈ 45 au, e < 0.1, and i < 10 degrees) are used to represent the Kernel of the current Kuiper-belt. Note that, in both simulations, the dynamical excitation of the primordial disk – after the accretion of the ice giants – is broadly consistent with the cold dynamical architecture of the Kuiper-belt kernel.

Supplementary information

Supplementary Information

Supplementary Text and Figs. 1–6.

Supplementary Video 1

This video corresponds to the simulation shown in Fig. 2a. The large left-side panel shows a top-view projection of the stellar cluster. The top-right panel shows a zoomed-in region around the central star and the bottom-right panel illustrates the dynamical evolution of the planets orbiting the central star in a semi-major axis versus eccentricity diagram. It illustrates the trapping of a wide-orbit exoplanet during a dynamical instability in a system of gas-giant planets. The host star is a solar-mass star embedded in a stellar cluster with 200 members and a Plummer radius of Rc = 40,000 au. The simulation begins with fully formed planets. Planet-2 is scattered onto a wide, eccentric orbit during a planetary instability around 10 kyr. At 100 kyr, a close encounter with Star-197 lifts Planet-2’s pericentre, trapping it on a stable wide orbit. The video stops at 1.35 Myr. Planet-2 remains bound until the simulation ends at 10 Myr (Fig. 2a).

Supplementary Video 2

This video corresponds to the simulation shown in Fig. 2b, which models a similar wide-orbit planet trapping process of Supplementary Video 1, but in the context of a Solar System-like early dynamical instability. The large left-side panel shows a top-view projection of the stellar cluster. The top-right panel shows a zoomed-in region around the Sun and the bottom-right panel illustrates the dynamical evolution of the Solar System giant planets orbiting the central star in a semi-major axis versus eccentricity diagram. The trapped planet survives in a wide orbit consistent with that expected for the putative Planet-9 until the end of the simulation at 6 Myr. This video was rendered with a variable frame rate (VFR) to better illustrate the dynamics and effects of stellar flybys.

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Izidoro, A., Raymond, S.N., Kaib, N.A. et al. Very-wide-orbit planets from dynamical instabilities during the stellar birth cluster phase. Nat Astron 9, 982–994 (2025). https://doi.org/10.1038/s41550-025-02556-0

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