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# Early Solar System instability triggered by dispersal of the gaseous disk

## Abstract

The Solar System’s orbital structure is thought to have been sculpted by an episode of dynamical instability among the giant planets1,2,3,4. However, the instability trigger and timing have not been clearly established5,6,7,8,9. Hydrodynamical modelling has shown that while the Sun’s gaseous protoplanetary disk was present the giant planets migrated into a compact orbital configuration in a chain of resonances2,10. Here we use dynamical simulations to show that the giant planets’ instability was probably triggered by the dispersal of the gaseous disk. As the disk evaporated from the inside out, its inner edge swept successively across and dynamically perturbed each planet’s orbit in turn. The associated orbital shift caused a dynamical compression of the exterior part of the system, ultimately triggering instability. The final orbits of our simulated systems match those of the Solar System for a viable range of astrophysical parameters. The giant planet instability therefore took place as the gaseous disk dissipated, constrained by astronomical observations to be a few to ten million years after the birth of the Solar System11. Terrestrial planet formation would not complete until after such an early giant planet instability12,13; the growing terrestrial planets may even have been sculpted by its perturbations, explaining the small mass of Mars relative to Earth14.

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## Data availability

The data that support the plots within this paper and other findings of this study are available at https://github.com/bbliu-astro/solarsystem-rebound.git.

## Code availability

The source code and simulation output for the model used in this study are available on reasonable request from the corresponding authors. The original version of the HERMIT4 N-body code is available on Sverre Aarseth’s homepage https://people.ast.cam.ac.uk/sverre/web/pages/nbody.htm .

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## Acknowledgements

B.L. was supported by a start-up grant of the Bairen programme from Zhejiang University, the National Natural Science Foundation of China (grant nos. 12173035 and 12111530175), the Swedish Walter Gyllenberg Foundation and the European Research Council (ERC Consolidator Grant no. 724687- PLANETESYS). S.N.R. is grateful to the CNRS’s PNP program.

## Author information

Authors

### Contributions

S.N.R. and S.A.J. proposed this idea and initiated the collaboration. B.L. examined the feasibility and conducted numerical simulations. S.N.R. drafted the manuscript. All authors contributed to analysing and discussing the numerical results, and editing and revising the manuscript.

### Corresponding author

Correspondence to Beibei Liu.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature thanks Kleomenis Tsiganis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Metrics for surviving planetary systems of a subsample of our simulations in matching the Solar System, comparable to Figure 2.

The simulations on the left included the rebound effect and those on the right did not. Each simulation started with our four present-day giant planets. In the top panels, the giant planets were initially placed in a chain of 3:2 orbital resonances. In the bottom panels, Jupiter and Saturn were initially in a 2:1 resonance and each other neighboring planet pair was in a 3:2 resonance. Each symbol represents the outcome of a given simulation at t = 10 Myr. The color indicates the timing of the instability after the start of gas disk dispersal; pink systems did not undergo an instability (no collision and/or ejection). Circles and triangles correspond to systems with four and three or fewer surviving planets, respectively. The arrow gives the initial radial mass concentration of the system. The Solar System is marked as a red star for comparison.

### Extended Data Fig. 2 Metrics for surviving planetary systems of a subsample of our simulations in matching the Solar System, comparable to Figure 2.

The simulations on the left included the rebound effect and those on the right did not. Each simulation started with the giant planets in a chain of 2:1 orbital resonances. In the top panels, we initially included only our four giant planets, but in the bottom panels, we added an additional ice giant at the start of the simulation. Each symbol represents the outcome of a given simulation at t = 10 Myr. The color indicates the timing of the instability after the start of gas disk dispersal; pink systems did not undergo an instability (no collision and/or ejection). Diamonds, circles, and triangles correspond to systems with five, four, and three or fewer surviving planets, respectively. The arrow gives the initial radial mass concentration of the system. The Solar System is marked as a red star for comparison.

### Extended Data Fig. 3 Metrics for surviving planetary systems of a subsample of our simulations in matching the Solar System, comparable to Figure 2.

Both panels, left and right, included the rebound effect. Each simulation started with our four present-day giant planets plus two additional ice giant planets. In the left panel, the giant planets are in a chain of 3:2 orbital resonances. In the right panel, Jupiter and Saturn were initially in a 2:1 resonance and each other neighboring planet pair was in a 3:2 resonance. Each symbol represents the outcome of a given simulation at t = 10 Myr. The color indicates the timing of the instability after the start of gas disk dispersal; pink systems did not undergo an instability (no collision and/or ejection). Pentagons, diamonds, circles, and triangles correspond to systems with six, five, four, and three or fewer surviving planets, respectively. The arrow gives the initial radial mass concentration of the system. The Solar System is marked as a red star for comparison.

### Extended Data Fig. 4 Outcomes of rebound simulations with initially four planets as a function of disk parameters: onset mass-loss rate, the disk dispersal timescale, and the rate of expansion of the inner cavity.

Each simulation started with our four present-day giant planets in a chain of 2:1 orbital resonances (top panels), a chain of 3:2 orbital resonances (middle panels), or a combination of a 2:1 orbital resonance and an ensuing chain of 3:2 orbital resonances (bottom panels). The color bar corresponds to the system’s angular momentum deficit (AMD). The circles with a grey edge color refer to the systems whose planets all survive in the end, while the black dots represent the Solar System analogs, defined as systems with four surviving planets in the correct order and their AMDs and RMCs are within a factor of three compared to those of our Solar System.

### Extended Data Fig. 5 Outcomes of rebound simulations with initially five and six planets as a function of disk parameters: onset mass-loss rate, the disk dispersal timescale, and the rate of expansion of the inner cavity, comparable to Extended Data Fig. 4.

Each simulation started with our four present-day giant planets plus one additional ice giant planet in a chain of 2:1 resonances (1st row), a chain of 3:2 resonances (2nd row), or a combination of 2:1 and 3:2 resonances (3rd row), or started with our four present-day giant planets plus two additional ice giants in a chain of 3:2 resonances (4th row), or a combination of 2:1 and 3:2 resonances (5th row).

### Extended Data Fig. 6 Jupiter’s eccentricity mode M55 as a function of the period ratio of Saturn to Jupiter obtained in simulations with and without a planetesimal disk.

The simulations without and with planetesimal disks are plotted in triangles and circles, respectively, and the Solar System is marked as a star. Only systems that finish with four planets are shown here.

### Extended Data Fig. 7 Gap opening mass as a function of disk aspect ratio and midplane viscous αt.

The background color refers to the gap opening mass criterion from Equation (12), and the grey lines indicate the masses of four Solar System giant planets and 8 M. The color symbols represent the disk setups we have explored in Methods section ‘Low-viscosity disks’, where the red symbols refer to the circumstances where only Jupiter opens a deep gap (P0 is the same as the fiducial run in the main text), the magenta symbols correspond to the circumstances where both Jupiter and Saturn are in the gap opening regime, and the orange symbol indicates the circumstance that Jupiter, Saturn, Uranus, and Neptune open gaps while the additional ice giant planet with the lowest mass is in the non-gap opening regime. The values of αt and disk aspect ratio parameters can be found in Extended Data Table 2.

### Extended Data Fig. 8 An early dynamical instability triggered by the dispersal of the Sun’s protoplanetary disk, assuming that the disk has a low viscosity.

The initial system consisted of five giant planets: Jupiter, Saturn, and three ice giants. The curves show the orbital evolution of each body including its semimajor axis (thick), perihelion and aphelion (thin). The black dashed line tracks the edge of the disk’s expanding inner cavity. We do not follow the early evolution through the entire gas-rich disk phase, so the onset of disk dispersal is set arbitrarily to be 0.5 Myr after the start the simulation. The semimajor axes and eccentricities of the present-day giant planets are shown at the right, with vertical lines extending from perihelion to aphelion. The disk model is adopted from run_B5R_P4 where midplane turbulent strength (αt = 10−4) is 50 times lower compared to the example shown in Fig. 1. The other disk parameters are: $${\dot{M}}_{{\rm{pho}}}$$ = 1.1 × 10−11 M yr−1, τd = 5.0 × 105 yr, and vr = 42 AU Myr−1.

### Extended Data Fig. 9 Cumulative distributions of delay times across three different suites of simulations.

On the left, the cumulative distribution of the time to the first instability regardless of which planets are involved. On the right, a cumulative distribution of the time delay between when the ice giant planets undergo orbital instability (typically occurs first), and when the gas giant planets undergo orbital instability. The black, blue and orange curves represent the simulations of run_B5R_P0, run_B5R_P2 and run_B5R_P4 in Extended Data Table 2.

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Liu, B., Raymond, S.N. & Jacobson, S.A. Early Solar System instability triggered by dispersal of the gaseous disk. Nature 604, 643–646 (2022). https://doi.org/10.1038/s41586-022-04535-1

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-022-04535-1

• ### The dissipation of the solar nebula constrained by impacts and core cooling in planetesimals

• Alison C. Hunt
• Karen J. Theis
• Maria Schönbächler

Nature Astronomy (2022)