Dynamics of Planetary Systems within Star Clusters: Aspects of the Solar System’s Early Evolution
Open accessAbstract
Most planetary systems—including our own—are born within stellar clusters, where interactions with neighboring stars can help shape the system architecture. This paper develops an orbit-averaged formalism to characterize the cluster’s mean-field effects, as well as the physics of long-period stellar encounters. Our secular approach allows for an analytic description of the dynamical consequences of the cluster environment on its constituent planetary systems. We analyze special cases of the resulting Hamiltonian, corresponding to eccentricity evolution driven by planar encounters, as well as hyperbolic perturbations upon dissipative disks. We subsequently apply our results to the early evolution of our solar system, where the cluster’s collective potential perturbs the solar system’s plane, and stellar encounters act to increase the velocity dispersion of the Kuiper Belt. Our results are twofold. First, we find that cluster effects can alter the mean plane of the solar system by ≲1° and are thus insufficient to explain the ψ ≈ 6° obliquity of the Sun. Second, we delineate the extent to which stellar flybys excite the orbital dispersion of the cold classical Kuiper Belt and show that while stellar flybys may grow the cold belt’s inclination by the observed amount, the resulting distribution is incompatible with the data. Correspondingly, our calculations place an upper limit on the product of the stellar number density and residence time of the Sun in its birth cluster, η τ ≲ 2 × 10 4 Myr pc −3 .
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The parameters necessary to match the data in Nesvorný et al. (2023) are close to the upper limit of the allowed range imposed by the dynamical structure of the cold classical belt.
“the parameters necessary to match the data are close to the upper limit of the allowed range.”
From Generation of Low-inclination, Neptune-crossing Trans-Neptunian Objects by Planet Nine (2024) · cites this paper as Batygin et al. 2020
Section 5.2 derives an upper bound of approximately χ ≲ 2–3 × 10⁴ Myr pc⁻³ from preservation of the cold classical belt’s orbital structure. It does not identify the parameters needed to match the data in Nesvorný et al. (2023) or establish that those parameters lie close to this bound. (LLM, conf=0.86)
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Spalding, C. (2019) · The Astrophysical Journal · doi:10.3847/1538-4357/ab23f5 · Cited by 16 · see citing works
Hamers, A. S., & Samsing, J. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz2029 · Cited by 16 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- Binney, J., & Tremaine, S. 1987, Galactic Dynamics (Princeton, NJ: Princeton Univ. Press)
- Murray, C. D., & Dermott, S. F. 1999, Solar System Dynamics (Cambridge: Cambridge Univ. Press)
Cited by
Sorted by citations
Stellar clustering shapes the architecture of planetary systems
Winter, A. J., Kruijssen, J. M. D., Longmore, S. N., & Chevance, M. (2020) · Nature · doi:10.1038/s41586-020-2800-0 · Cited by 82 · see citing works
Close encounters: How stellar flybys shape planet-forming discs
Cuello, N., Ménard, F., & Price, D. J. (2023) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-022-03602-w · Cited by 81 · see citing works
Bowler, B. P., Tran, Q. H., Zhang, Z., Morgan, M., Ashok, K. B., Blunt, S. C., Bryan, M. L., Evans, A. E., Franson, K., Huber, D., et al. (2023) · The Astronomical Journal · doi:10.3847/1538-3881/acbd34 · Cited by 65 · see citing works
The Great Inequality and the Dynamical Disintegration of the Outer Solar System
Zink, J. K., Batygin, K., & Adams, F. C. (2020) · The Astronomical Journal · doi:10.3847/1538-3881/abb8de · Cited by 43 · see citing works
Self-citationAn Aligned Orbit for the Young Planet V1298 Tau b
Johnson, M. C., David, T. J., Petigura, E. A., Isaacson, H. T., Zandt, J. V., Ilyin, I. V., Strassmeier, K. G., Mallonn, M., Zhou, G., Mann, A. W., et al. (2022) · The Astronomical Journal · doi:10.3847/1538-3881/ac6271 · Cited by 36 · see citing works
Self-citationTransfer of Rocks Between Planetary Systems: Panspermia Revisited
Adams, F. C., & Napier, K. J. (2022) · Astrobiology · doi:10.1089/ast.2021.0187 · Cited by 32 · see citing works
Self-citationOn the Capture of Interstellar Objects by Our Solar System
Napier, K. J., Adams, F. C., & Batygin, K. (2021) · The Planetary Science Journal · doi:10.3847/psj/abe76e/53 · Cited by 28 · see citing works
Self-citationNesvorný, D., Bernardinelli, P., Vokrouhlický, D., & Batygin, K. (2023) · Icarus · doi:10.1016/j.icarus.2023.115738 · Cited by 26 · see citing works
Self-citationAre WASP-107-like Systems Consistent with High-eccentricity Migration?
Yu, H., & Dai, F. (2024) · The Astrophysical Journal · doi:10.3847/1538-4357/ad5ffb · Cited by 26 · see citing works
A Rogue Planet Helps to Populate the Distant Kuiper Belt
Huang, Y., Gladman, B., Beaudoin, M., & Zhang, K. (2022) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ac9480 · Cited by 25 · see citing works
Significant interstellar object production by close stellar flybys
Pfalzner, S., Vargas, L. L. A., Bhandare, A., & Veras, D. (2021) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202140587 · Cited by 24 · see citing works
Kepler-1656b’s Extreme Eccentricity: Signature of a Gentle Giant
Angelo, I., Naoz, S., Petigura, E., Macdougall, M., Stephan, A., Isaacson, H., & Howard, A. (2022) · Astronomical Journal · doi:10.3847/1538-3881/ac6094 · Cited by 18 · see citing works
Self-citationExciting spiral arms in protoplanetary discs from flybys
Smallwood, J. L., Yang, C.-C., Zhu, Z., Martin, R. G., Dong, R., Cuello, N., & Isella, A. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad742 · Cited by 20 · see citing works
Injection of Inner Oort Cloud Objects into the Distant Kuiper Belt by Planet Nine
Batygin, K., & Brown, M. E. (2021) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/abee1f · Cited by 20 · see citing works
Self-citationSignificant interstellar object production by close stellar flybys
Pfalzner, S., Vargas, L. L. A., Bhandare, A., & Veras, D. (2021) · Springer Link (Chiba Institute of Technology) · doi:10.1051/0004-6361/202140587/pdf · Cited by 19 · see citing works
Linking the formation and fate of exo-Kuiper belts within Solar system analogues
Veras, D., Reichert, K., Dotti, F. F., Cai, M. X., Mustill, A. J., Shannon, A., McDonald, C. H., Zwart, S. P., Kouwenhoven, M. B. N., & Spurzem, R. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa559 · Cited by 18 · see citing works
Bernardinelli, P. H., Bernstein, G. M., Abbott, T. M. C., Aguena, M., Allam, S., Brooks, D., Rosell, A. C., Carretero, J., da Costa, L. N., Pereira, M. E. S., et al. (2025) · The Astronomical Journal · doi:10.3847/1538-3881/adc459 · Cited by 16 · see citing works
Sefilian, A. A., Kratter, K. M., Wyatt, M. C., Petrovich, C., Thébault, P., Malhotra, R., & Faramaz, V. (2025) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staf1555 · Cited by 16 · see citing works
Dynamics of young stellar clusters as planet-forming environments
Reiter, M., & Parker, R. J. (2022) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-022-03265-7 · Cited by 15 · see citing works
The Case for an Early Solar Binary Companion
Siraj, A., & Loeb, A. (2020) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/abac66 · Cited by 15 · see citing works
Inclination Excitation of Solar System Debris Disk Due to Stellar Flybys
Moore, N. W. H., Li, G., & Adams, F. C. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/abb08f · Cited by 14 · see citing works
Self-citationGeneration of Low-inclination, Neptune-crossing Trans-Neptunian Objects by Planet Nine
Batygin, K., Morbidelli, A., Brown, M. E., & Nesvorný, D. (2024) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ad3cd2 · Cited by 11 · see citing works
“Following this reasoning, in Batygin & Brown (2021), we generated initial conditions by simulating the formation of the inner Oort Cloud, while accounting for constraints emanating from the orbital structure of the cold classical belt (Batygin et al. 2020).”
MethodInfluentialSelf-citationOort Cloud and sednoid formation in an embedded cluster, I: Populations and size distributions
Wajer, P., Rickman, H., Kowalski, B., & Wiśniowski, T. (2024) · Icarus · doi:10.1016/j.icarus.2024.116065 · Cited by 11 · see citing works
Moore, N., Li, G.-J., Hassenzahl, L., Nesvold, E., Naoz, S., & Adams, F. (2022) · Astrophysical Journal · doi:10.3847/1538-4357/aca766 · Cited by 7 · see citing works
Self-citationThe ALMA survey to Resolve exoKuiper belt Substructures (ARKS)
Zawadzki, B., Fehr, A., Hughes, A. M., Mansell, E., Kittling, J., Han, Y., Hou, C., Pan, M., Milli, J., Olofsson, J., et al. (2026) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202556505 · Cited by 10 · see citing works
The Sun’s Birth Environment: Context for Meteoritics
Desch, S. J., & Miret-Roig, N. (2024) · Space Science Reviews · doi:10.1007/s11214-024-01113-x · Cited by 11 · see citing works
Dynamics of Binary Planets within Star Clusters
Huang, Y., Zhu, W., & Kokubo, E. (2024) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ad8925 · Cited by 8 · see citing works
Primordial Orbital Alignment of Sednoids
Huang, Y., & Gladman, B. (2024) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ad2686 · Cited by 9 · see citing works
In Situ Formation of the Cold Classical Kuiper Belt
李, R. 日. L., & Chiang, E. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/ae18c3 · Cited by 6 · see citing works
Stellar Obliquity Excitation via Disk-dispersal-driven Resonances in Binaries
Su, Y., & Lai, D. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/adfcbf · Cited by 4 · see citing works
Dynamical fates of S-type planetary systems in embedded cluster environments
Ellithorpe, E. A., & Kaib, N. A. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac1973 · Cited by 4 · see citing works
An upper limit for the growth of inner planets?
Winter, A. J., & Alexander, R. D. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab1302 · Cited by 4 · see citing works
Was the Solar System’s dynamical instability triggered by a (sub)stellar flyby?
Raymond, S. N., & Kaib, N. A. (2025) · Icarus · doi:10.1016/j.icarus.2025.116910 · Cited by 3 · see citing works
Self-gravitational dynamics within the inner Oort cloud
Batygin, K., & Nesvorný, D. (2024) · Celestial Mechanics and Dynamical Astronomy · doi:10.1007/s10569-024-10195-2 · Cited by 3 · see citing works
Self-citationFormation of the inner Oort cloud in the presence of an early solar binary
Raush, D., & Batygin, K. (2024) · Monthly Notices of the Royal Astronomical Society Letters · doi:10.1093/mnrasl/slae060 · Cited by 2 · see citing works
Self-citationLimits on Stellar Flybys in the Solar Birth Cluster
Siraj, A., Chyba, C. F., & Tremaine, S. D. (2025) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ae1025 · Cited by 2 · see citing works
No Influence of Passing Stars on Paleoclimate Reconstructions Over the Past 56 Million Years
Zeebe, R. E., & Hernandez, D. M. (2025) · The Astronomical Journal · doi:10.3847/1538-3881/ade1d3 · Cited by 1 · see citing works
Hu, Q., Huang, Y., Gladman, B., & Zhu, W. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/ae0a30 · Cited by 1 · see citing works
Life in the Milky Way: The Panspermia Prospects
Vukotić, B., & Gordon, R. (2021) · doi:10.1002/9781119640912.ch4 · Cited by 1 · see citing works
Secular dynamics of a test particle perturbed by a Miyamoto–Nagai disc
Liu, T., Gong, S., & Liao, X. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab2342
Tilting the Solar System in its parent star cluster
Li, D. (2026) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stag1010
Bansal, A., Brunton, I., Batygin, K., Pichierri, G., & Nesvorný, D. (2026) · Icarus · doi:10.1016/j.icarus.2026.117248
Self-citationThe Edges of Planetary Systems: Falling Off the Kuiper Cliff in a Dissipating Gas Disk
Li, R., & Chiang, E. (2026) · The Astrophysical Journal · doi:10.3847/1538-4357/ae91d1
- Authors
- Batygin, K., Adams, F. C., Batygin, Y. K., & Petigura, E. A.
- Affiliations
- California Institute of Technology (US)
- University of Michigan (US)
- Los Alamos National Laboratory (US)
- University of California, Los Angeles (US)
- Venue
- The Astronomical Journal
- Publisher
- American Astronomical Society
- Published
- 2020-02-12
- Volume
- 159
- Issue
- 3
- Pages
- 101
- ISSN
- 0004-6256 (ISSN-L)
- 1538-3881
- OpenAlex
- W3005985066
- Cited by
- 43
- References
- 116
- Citations by year
- 2026: 4 · 2025: 8 · 2024: 8 · 2023: 5 · 2022: 6 · 2021: 7 · 2020: 5
- FWCI
- 2.56
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- The Astronomical Journal (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Sloan Foundation (10565)
- Packard Foundation (66808)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astro and Planetary Science
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astrophysics and Star Formation Studies
- Keywords
- planetary system formation, star clusters, stellar encounters, Kuiper belt, orbital inclination, mean motion resonance, secular dynamics, stellar flybys
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