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# Planetesimal rings as the cause of the Solar System’s planetary architecture

## Abstract

Astronomical observations reveal that protoplanetary disks around young stars commonly have ring- and gap-like structures in their dust distributions. These features are associated with pressure bumps trapping dust particles at specific locations, which simulations show are ideal sites for planetesimal formation. Here we show that our Solar System may have formed from rings of planetesimals—created by pressure bumps—rather than a continuous disk. We model the gaseous disk phase assuming the existence of pressure bumps near the silicate sublimation line (at T ~ 1,400 K), water snowline (at T ~ 170 K) and CO snowline (at T ~ 30 K). Our simulations show that dust piles up at the bumps and forms up to three rings of planetesimals: a narrow ring near 1 au, a wide ring between ~3–4 au and ~10–20 au and a distant ring between ~20 au and ~45 au. We use a series of simulations to follow the evolution of the innermost ring and show how it can explain the orbital structure of the inner Solar System and provides a framework to explain the origins of isotopic signatures of Earth, Mars and different classes of meteorites. The central ring contains enough mass to explain the rapid growth of the giant planets’ cores. The outermost ring is consistent with dynamical models of Solar System evolution proposing that the early Solar System had a primordial planetesimal disk beyond the current orbit of Uranus.

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## Data availability

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

## Code availability

Dust evolution simulations were performed using a modified version of the code Two-pop-py5, publicly available at https://github.com/birnstiel/two-pop-py, with modifications described in ref. 20. N-body simulations modelling the growth of planetesimals to planetary embryos were performed using LIPAD93. This is a proprietary software product funded by the Southwest Research Institute that is not publicly available. It is based on the N-body integrator SyMBA, which is publicly available at https://www.boulder.swri.edu/swifter/. Simulations of the late stage of accretion of terrestrial planets were performed using the Mercury N-body integrator94, publicly available at https://github.com/4xxi/mercury.

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## Acknowledgements

A. Izidoro, R. Dasgupta and A. Isella acknowledge NASA grant 80NSSC18K0828 for financial support during preparation and submission of the work. A. Isella and A. Izidoro acknowledge support from the Welch Foundation grant No. C-2035-20200401. B.B. thanks the European Research Council (ERC Starting Grant 757448-PAMDORA) for financial support. R. Deienno acknowledges support from the NASA Emerging Worlds program, grant 80NSSC21K0387. S.N.R. thanks the CNRS’s PNP programme for support. A. Izidoro thanks M. Maurice for numerous inspirational discussions, and the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES), in the scope of the Programme CAPES-PrInt, process number 88887.310463/2018-00, International Cooperation Project number 3266.

## Author information

Authors

### Contributions

A. Izidoro conceived the project in discussions with R. Dasgupta and B.B. A. Izidoro performed numerical simulations modelling dust evolution and planetesimal formation. S.N.R., R. Deienno and A. Izidoro conducted N-body numerical simulations. A. Izidoro analysed the results of numerical simulations and led the writing of the manuscript. R. Dasgupta helped with the cosmochemical implications of the model and constructed Fig. 5. All authors discussed the results and commented on the manuscript.

### Corresponding author

Correspondence to Andre Izidoro.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks Eiichiro Kokubo and Bradley Hansen for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 Final distribution of planetesimals in a simulation with three pressure bumps.

a) Including the effects of planetesimal formation via zonal flows80, see Eq. (8). b) Neglecting the effects of planetesimal formation via zonal flows21,65. Final distribution of planetesimals in a simulation with three pressure bumps. Top and middle panels show the evolution of the gas and pebble surface densities, respectively. The initial dust-to-gas ratio is Z0 = 1.3%, ϵ = 1 × 10−4, αt = αν/27. The final rings contain 2.5 M (inner), 85 M (central), and 18 M (outer) in planetesimals. In both simulations rc = 25 au.

### Extended Data Fig. 2 Final distribution of planetesimals in a simulation with two pressure bumps (β = 0.7).

Final distribution of planetesimals in a simulation with two pressure bumps (β = 0.7). Top and middle panels show the evolution of the gas and pebble surface densities, respectively. The planetesimal formation efficiency in this simulation is ϵ = 7.5 × 10−7. The initial dust-to-gas ratio is Z0 = 0.01, αt = αν/40, αMRI = 3αν, and rc = .

### Extended Data Fig. 3 Cumulative mass fraction distributions representing the feeding zones of terrestrial planets in simulations with Jupiter and Saturn in their current orbits.

a) Inner planetesimal ring with surface density profile given by Σplar−1. Curves are computed from 6 solar system analogues. b) Inner planetesimal ring with surface density profile given by Σplar−5.5. Curves are computed from 12 solar system analogues. Cumulative mass fraction distributions representing the feeding zones of terrestrial planets in simulations with Jupiter and Saturn in their current orbits. Thin green, blue and red curves represent Venus, Earth, and Mars analogues. Shaded regions encompassing each thin line represent 95% confidence bands derived from the Kolmogorov–Smirnov statistic. Each selected planetary system contains one single Venus, Earth, and Mars-analogue.

### Extended Data Fig. 4 Simulation using the same parameters of simulation shown in Extended Data Figure 2, but considering that the bump at the snowline forms later, at ~ 0.1 Myr after the beginning of the simulation.

Planetesimal formation efficiency is set at ϵ = 7.5 × 10−7.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–10, effects of different parameters of the model, additional methods and comparison with other Solar System models.

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Izidoro, A., Dasgupta, R., Raymond, S.N. et al. Planetesimal rings as the cause of the Solar System’s planetary architecture. Nat Astron 6, 357–366 (2022). https://doi.org/10.1038/s41550-021-01557-z

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• DOI: https://doi.org/10.1038/s41550-021-01557-z

• ### Planets form from rings

Nature Astronomy (2022)

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• Ankita Anirban

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