Higher-order Mean-motion Resonances Can Form in Type I Disk Migration
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1.
Brown University
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2.
Arizona State University
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3.
University of Hawaii at Manoa
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4.
California Institute of Technology
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5.
Flatiron Institute
Abstract
Type I disk migration can form a chain of planets engaged in first-order mean-motion resonances (MMRs) parked at the disk inner edge. However, while second- or even third-order resonances were deemed unlikely due to their weaker strength, they have been observed in some planetary systems, e.g., TOI-178 bc (5:3), TOI-1136 ef (7:5), and TRAPPIST-1 bcd (8:5–5:3). We performed >6000 Type I simulations of multiplanet systems that mimic the observed Kepler sample in terms of stellar mass, planet size, multiplicity, and intra-system uniformity over a parameter space encompassing transitional and truncated disks. We found that Type I migration coupled with a disk inner edge can indeed produce second- and third-order resonances (in a state of libration) in ∼10% and 2% of resonant-chain systems, respectively. Moreover, the relative occurrence of first- and second-order MMRs in our simulations is consistent with observations (e.g., 3:2 is more common than 2:1; while second-order 5:3 is more common than 7:5). The formation of higher-order MMRs favors slower disk migration and a smaller outer planet mass. Higher-order resonances do not have to form with the help of a Laplace-like three-body resonance, as was proposed for TRAPPIST-1. Instead, the formation of higher-order resonances is assisted by breaking a preexisting first-order resonance, which generates small but nonzero initial eccentricities (e ≈ 10−3 to 10−2). We predict that (1) librating higher-order resonances have higher equilibrium e (∼0.1), (2) are more likely found as an isolated pair in an otherwise first-order chain, and (3) more likely emerge in the inner pairs of a chain.
Copyright and License
© 2025. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Acknowledgement
We thank Caleb Lammers, Max Goldberg, Daniel Tamayo, Nick Choksi, Renu Malhotra, Zhecheng Hu, Tian Yi, Shuo Huang, Konstantin Batygin, Mutian Wang, Eric Agol, Rixin Li, Fred Adams, and Daniel Fabrycky for useful conversations and suggestions. To provide observational radii and masses, this research made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Most of the dynamical simulations were conducted using computational resources and services at the Center for Computation and Visualization, Brown University. This material is based upon work supported by the U.S. National Science Foundation under Award No. 2441950. F.M.K. thanks Gregory Tucker and the Undergraduate Teaching and Research Award at Brown University for their support of his undergraduate research.
Software References
REBOUND (H. Rein & S. F. Liu 2012), REBOUNDx (D. Tamayo et al. 2020), celmech (S. Hadden & D. Tamayo 2022), forecaster (J. Chen & D. Kipping 2017), pandas (W. McKinney 2010; Pandas Development Team, T. 2020), numpy (C. R. Harris et al. 2020), scipy (P. Virtanen et al. 2020), astropy (Astropy Collaboration et al. 2022), Matplotlib (J. D. Hunter 2007), Seaborn (M. L. Waskom 2021), label–lines (C. Cadiou 2022).
Files
Keller_2026_ApJ_996_12.pdf
Additional details
Related works
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- Discussion Paper: arXiv:2504.12596 (arXiv)
Funding
- National Science Foundation
- AST-2441950
- Brown University
Dates
- Submitted
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2025-04-16
- Accepted
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2025-10-31
- Available
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2025-12-22Published
Caltech Custom Metadata
- Caltech groups
- Division of Geological and Planetary Sciences (GPS)
- Publication Status
- Published