Pith. sign in

REVIEW 3 major objections 4 minor 75 references

The Gap-Giant Association: Are Planets Hiding in the Gaps?

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read In all four systems with an inner gap and an outer giant, the giant cannot tilt a hidden gap planet out of transit, so the secular-tilt explanation for the gap-giant association is strongly disfavoured.

desk verdict A careful, worthwhile test of the secular-tilt explanation for gaps in systems with outer giants; the negative result is credible under typical misalignment priors, though the abstract overstates how strongly the data exclude large outer-giant inclinations. read the letter →

arxiv 2506.10969 v2 pith:IP2BJ7VD submitted 2025-06-12 astro-ph.EP

Caleb Lammers , Joshua N. Winn This is my paper · ORCID
classification astro-ph.EP
keywords exoplanetsextrasolargaseousgiantplanetsplanetarydynamicstransitsgap-giantassociationsecularinclinationexcitationgapcomplexityKeplersystems
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Four stars are known to host both a compact system of transiting inner planets and an outer giant planet, and all four show an unusually large gap between inner orbits. The paper tests a leading explanation: the outer giant tilts an unseen planet in the gap out of the transit view. N-body and secular simulations show each gap could stably hold a typical $1$–$20\,M_\oplus$ planet, but Monte Carlo transit calculations find the giant cannot excite enough mutual inclination to hide it: the observed gap configurations appear in only $5.3\%$, $0.001\%$, and $9.1\%$ of realizations for Kepler-48, Kepler-65, and Kepler-139, with Kepler-90 excluded because its giant transits. The authors conclude that the secular-tilt hypothesis is strongly disfavoured. The gaps may instead contain planets smaller than about $1\,R_\oplus$ that Kepler could not detect, or be empty.

What carries the argument

The load-bearing diagnostic is the dynamical coupling parameter $\epsilon_{12}$, the ratio of the precession rates that an outer giant would impose on two neighbouring inner planets to the mutual precession rate between those planets. When $\epsilon_{12}\lesssim 1$ the inner pair precesses as a coupled unit and the giant can induce only a small mutual inclination; when $\epsilon_{12}\gtrsim 1$ the pair decouples and mutual inclination can grow to the giant's inclination. The authors combine this diagnostic with Laplace-Lagrange secular equations for the inclination evolution, Monte Carlo sampling of viewing directions to compute transit probabilities, N-body and machine-learning stability checks for the injected gap planet, and Kepler detection-efficiency contours to set the largest radius a gap planet could have and still be missed. The coupling parameter identifies why the mechanism fails: median values are roughly $0.02$, $0.001$, $0.2$, and $0.07$ for Kepler-48, -65, -90, and -139, meaning the inner planets stay coupled and the giant's tilt is largely absorbed.

What would settle it

Measure the true mutual inclination between each outer giant and the inner transiting system (e.g., with astrometry or Rossiter-McLaughlin observations); if any of Kepler-48e, Kepler-65e, or Kepler-139e is inclined by more than roughly $20^\circ$ relative to the inner planets, the assumed $10^\circ$-scale misalignment distribution fails and the secular excitation hypothesis would need to be re-tested with those larger inclinations.

Watch

Extended reading notes

Core claim

The paper's central claim is that the 'secular inclination excitation' theory of the gap-giant association fails for the only four systems on which the association rests. In each system, an undetected planet of roughly $1$–$20\,M_\oplus$ could occupy the gap without dynamical instability: N-body survival rates over $10^9$ inner periods were $97\%$, $87\%$, $96\%$, and $62\%$ for Kepler-48, -65, -90, and -139, and secular integrations over $10^5$ secular periods gave $93\%$, $90\%$, $87\%$, and $39\%$. Yet when the secular equations are propagated and transit probabilities are averaged over viewing directions, the observed three-or-four-transiting-planet configuration is rarely reproduced, with probabilities of only $5.3\%$ (Kepler-48), $0.001\%$ (Kepler-65), and $9.1\%$ (Kepler-139); Kepler-90 is set aside because its outer giant is itself transiting, indicating alignment with the inner system. The conclusion is that the outer giant's gravity is insufficient to tilt a hypothetical gap planet out of transit, so the observed gaps are not explained by hidden planets made nontransiting.

Load-bearing premise

The conclusion rests on the assumption that each outer giant is misaligned from the inner system by at most about $10^\circ$ and that linear Laplace-Lagrange secular theory captures the inclination evolution; if real misalignments are much larger, or if higher-order secular resonances act, the induced mutual inclinations could be larger than modelled.

Editorial extensions

If this is right

  • Every one of the four systems can dynamically accommodate an additional planet of roughly $1$–$20\,M_\oplus$ in its gap for at least $10^9$ inner orbital periods, so stability alone does not rule out hidden gap planets.
  • Secular perturbations from the outer giants cannot hide such a planet: the observed gap configurations are reproduced in only $5.3\%$, $0.001\%$, and $9.1\%$ of Monte Carlo realizations for Kepler-48, Kepler-65, and Kepler-139, and Kepler-90 is excluded because its giant transits.
  • In Kepler-48, Kepler-65, and Kepler-139, any transiting planet in the gap must be smaller than about $0.7\,R_\oplus$, $0.5\,R_\oplus$, and $1.0\,R_\oplus$, respectively, to have escaped detection; inserting such a planet would make the radius dispersion only mildly atypical.
  • Kepler-90's gap could hide a planet as large as the known $1.3\,R_\oplus$ planets, because the detection efficiency at the gap midpoint is below $50\%$.
  • The gap-giant association is therefore unlikely to be a product of outer giants tilting inner planets out of transit; if the association is real, it more likely reflects formation conditions or coincidence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the authors' $10^\circ$-scale misalignment assumption is relaxed, the falsifying test is direct: a measured giant-inner misalignment above roughly $20^\circ$ in Kepler-48, -65, or -139 would re-open the secular-tilt scenario, so future astrometry will settle this.
  • The coupling parameter offers a cheap triage for new discoveries: any system with an outer giant and $\epsilon_{12}\ll 1$ can be set aside as unable to hide a gap planet by tilting, concentrating search effort on sub-Earth-sized transits or empty gaps.
  • A population-level radial-velocity test should distinguish the scenarios: if gaps are mostly empty or contain sub-Earths, RV-detected inner systems with outer giants should show gaps as often as transit-detected ones; the conflicting cases of HD 164922 (gap) and HD 219134 (no gap) show the sample is not yet decisive.
  • Kepler-90 is the natural target for a direct search: a dedicated transit or transit-timing search at the gap period could recover a roughly $1\,R_\oplus$ planet and discriminate between the empty-gap and small-planet explanations.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies four Kepler systems (Kepler-48, -65, -90, -139) that host both multiple transiting inner planets and an outer giant, and asks whether the prominent orbital gaps in these systems could hide undetected planets or arise from secular inclination excitation by the outer giant. Using N-body integrations (REBOUND/WHFast) and secular integrations (celmech), the authors find that a 1-20 Earth-mass planet placed in each gap is often dynamically stable over the integration durations. They then perform Monte Carlo transit probability calculations with linear Laplace-Lagrange theory for fixed outer-giant inclinations of 5, 10, and 20 degrees, finding that the observed gap configurations are reproduced in only 5.3% (Kepler-48), 0.001% (Kepler-65), and 9.1% (Kepler-139) of realizations. They conclude that the secular inclination excitation hypothesis is strongly disfavored, and that the gaps may instead contain very small undetected planets or no planet at all. The paper also uses KeplerPORTs to show that planets smaller than about 1 Earth radius could hide in the gaps of Kepler-48, -65, and -139.

Significance. If the conclusions hold, this is a valuable negative result for a specific, testable explanation of the gap-giant association, and it sharpens the case that these gaps are either empty or contain sub-Earth-sized planets. The study is methodologically transparent: it uses public codes (REBOUND, celmech, KeplerPORTs), forward-simulates from observed parameters without fitting the target conclusion, and explicitly reports survival fractions and detection efficiencies. The main claims are, however, more sensitive to assumptions about the unconstrained outer-giant inclination and about the adequacy of linear secular theory than the abstract suggests, so the strength of the conclusion needs to be recalibrated.

major comments (3)
  1. [Section 3.1, Figure 3] The transit probability calculations are performed only for outer-giant inclinations iG = 5, 10, and 20 degrees. The conclusion that the secular inclination excitation hypothesis is 'strongly disfavored' therefore depends on excluding larger misalignments. For Kepler-139, which has coupling parameter epsilon ~ 0.07, the observed-gap probability at iG = 20 degrees is already 9.1%, and within linear theory the induced mutual inclination grows with iG; a 30-40 degree misalignment could plausibly raise this probability substantially. The RV data do not constrain iG for these giants, and the Rayleigh sigma = 10 degree prior from Masuda et al. (2020) is a population average, not an upper limit. Please report the observed-gap probability as a function of iG over a wider range and/or marginalize over a stated prior with a sensitivity analysis.
  2. [Section 3.1, Kepler-90 paragraph] The exclusion of Kepler-90 rests on the argument that because the outer giant transits, a large misalignment with the inner system is statistically unlikely, since a randomly oriented orbit has only a 0.55% geometric transit probability. This conflates alignment with the line of sight with alignment with the inner system. A transiting outer giant can have a large mutual inclination with the inner transiting planets if its longitude of ascending node differs; conditioning on both the inner system and the giant transiting does not by itself suppress large mutual inclinations. Please either justify the exclusion with an explicit calculation of P(mutual inclination > theta | giant transits, inner system transits), or include Kepler-90 in the transit probability analysis.
  3. [Sections 2.2 and 2.3] The stability demonstrations cover only 10^9 inner orbital periods (13-20 Myr for the four systems) or 10^5 secular periods (16-200 Myr), which are far shorter than the likely Gyr system ages. For Kepler-139, the secular survival fraction is only 39% over a median 200 Myr and 53% even over 20 Myr. The abstract's statement that a typical small planet 'could reside in the gap without inducing dynamical instability' is therefore not established on the timescales relevant to the observed systems. Even though the authors note that their Hill-sphere instability criterion may overflag instabilities, the lower-limit survival fractions for Kepler-139 are low enough that the positive stability claim needs to be tempered or supported with longer-timescale evidence.
minor comments (4)
  1. [Table 1] The footnote marker in Table 1 appears as 'aKepler-90h' in the table body; please move the marker to the planet name so it reads as a footnote.
  2. [Sections 2.2 and 2.3] The text uses '109 P1' and '105 Tsec,1' where superscripts are missing; these should read '10^9 P1' and '10^5 Tsec,1'.
  3. [Section 3.1, Kepler-48 bullet] The bullet reports a 5.5% chance of seeing a gap at iG = 20 degrees and then a 5.3% chance for the specific configuration of planets 1, 2, and 4 transiting; please clarify how the 5.5% value is defined relative to Figure 3.
  4. [Section 5.1] For HD 191939, the text states that 'just an 8% chance of observing the system when a gap is present'; please specify whether this is the probability of the observed configuration or of any configuration with Cinner > 0.3, for consistency with Figure 3.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: conclusion is a forward Monte Carlo result; self-citations are non-load-bearing observational inputs.

full rationale

The paper's derivation chain is forward-modeled rather than self-referential. Observed orbital parameters for Kepler-48, -65, -90, and -139 are used as initial conditions; hypothetical gap planets are drawn from prescribed mass and period distributions; and the transit probabilities in Section 3.1 are computed by Laplace-Lagrange secular integration plus random viewing geometry. The low probabilities quoted in Figure 3 (5.3%, 0.001%, and 9.1%) are simulation outputs, not quantities fitted to the observed gap configurations, so the disfavoring of the secular-inclination hypothesis is not forced by construction. The stability analysis similarly integrates N-body and secular equations and reports survival fractions; no parameter is tuned to make the survival rates high. The only self-references are observational inputs: Lammers & Winn (2025) supplies the Kepler-139f orbital constraint, and Masuda et al. (2020) supplies a population inclination prior. Neither is load-bearing for the negative conclusion: the transit-probability experiment tests fixed outer-giant inclinations of 5, 10, and 20 degrees rather than relying on the Rayleigh prior, and the Kepler-139f constraint is an external RV measurement. The skeptical concern that inclinations above 20 degrees or nonlinear secular effects could raise the gap probabilities is a prior or sensitivity limitation, not circularity, because the paper does not derive the disfavoring conclusion from an assumption that large misalignments are impossible.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

No invented physical entities are introduced. The analysis rests on standard celestial mechanics, published observational parameters, and two disclosed modeling choices: a Rayleigh inclination distribution for outer giants and circular/coplanar initial conditions for Kepler-90. The simulation durations are shorter than the estimated system ages, so the stability claim is bounded.

free parameters (4)
  • Gap planet mass sampling parameters = Mean and sigma equal to mean mass of known inner planets; 90% of draws in 1-20 Earth masses
    Adopted in Section 2.1 to generate hypothetical gap planets. The stability and transit conclusions are tested over a range of masses, so this is a hand-chosen model input rather than a fitted constant.
  • Outer giant inclination scale sigma = 10 degrees for stability runs; 5, 10, and 20 degrees in transit probability runs
    Adopted from Masuda et al. (2020) rather than measured per system. The tilt conclusion depends on the assumed misalignment distribution, though the paper explores several values.
  • Inner planet Rayleigh eccentricity and inclination scales = sigma_e = 0.02, sigma_I = 1.5 degrees
    Adopted from population constraints in Section 2.1. These affect the survival fractions but not the qualitative tilt result.
  • Simulation durations = 10^9 inner periods for N-body; 10^5 secular periods; 10^6 years for transit Monte Carlo
    Chosen practical timescales that are shorter than the estimated system ages, so the 'could reside in the gap' statement is bounded rather than a Gyr-scale proof.
assumptions (6)
  • domain assumption Laplace-Lagrange linear secular theory accurately describes the long-term inclination evolution of these inner systems over the simulated intervals.
    Used in Section 3.1 for the transit probability calculations via the LaplaceLagrangeSystem class in celmech. Higher-order secular resonances or chaos could alter the tilt evolution.
  • standard math The Hill-sphere overlap criterion in Eq. (1) is a reliable proxy for dynamical instability in the secular integrations.
    The authors use ai+1(1-ei+1) - ai(1+ei) < rH,i+1 + rH,i to flag instability, noting it ignores mutual inclinations and may underestimate instability timescales.
  • ad hoc to paper Kepler-90 may be initialized with all planets on circular, coplanar orbits without invalidating the stability conclusion for that system.
    Section 2.1 states that observationally motivated initial conditions for Kepler-90 were unstable even without a gap planet, so the authors instead forced circular and coplanar orbits.
  • domain assumption Outer giant inclinations are drawn from a Rayleigh distribution with sigma = 10 degrees relative to the inner system.
    Section 2.1 follows Masuda et al. (2020). This is a population-level assumption applied to individual systems with unknown giant inclinations.
  • domain assumption Simulated durations are representative enough to infer that a gap planet can remain stable over the relevant lifetimes of these systems.
    The N-body runs cover 13-20 Myr and the secular runs cover 16-200 Myr, both far shorter than the likely multi-Gyr ages of these Kepler systems.
  • domain assumption SPOCK and the empirical stability criteria of Obertas et al. (2017) and Lammers et al. (2024) give valid stability expectations for these systems.
    Used in Section 2 as preliminary stability baselines before the full N-body and secular integrations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Gap-Giant Association: Are Planets Hiding in the Gaps?." pith.science (2026). https://pith.science/paper/IP2BJ7VD

@misc{pith2026250610969,
  author       = {Pith},
  title        = {Pith review of: The Gap-Giant Association: Are Planets Hiding in the Gaps?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IP2BJ7VD}},
  note         = {Machine review of arXiv:2506.10969}
}
abstract

A handful of stars are known to host both an inner system of multiple transiting planets and an outer giant planet. These systems all feature a prominent gap between the orbits of two of the transiting planets, distinguishing them from typical multiplanet systems with more uniform orbital spacings. The reason for the association between inner gaps and outer giants is unknown. In this paper, we assess whether undiscovered planets might occupy these gaps in systems with outer giants. For each of the four relevant systems - Kepler-48, Kepler-65, Kepler-90, and Kepler-139 - we found that a typical small planet ($\sim 1 - 20 M_\oplus$) could reside in the gap without inducing dynamical instability. However, in each case, the gravitational influence of the outer giant planet is insufficient to tilt the orbit of the hypothetical planet by enough to prevent transits, strongly disfavoring a proposed theory for the observed gap-giant association. The gaps might instead contain smaller, undetected planets ($\lesssim 1 R_\oplus$), or be entirely devoid of planets.

Figures

Figures reproduced from arXiv: 2506.10969 by the authors.

Figure 1
Figure 1. Orbital architectures of systems in the Kepler Giant Planet Survey with three or more transiting planets. Inner planets are represented by blue circles, outer giant planets by red circles, and nontransiting planets by lighter￾colored circles. Circle size is proportional to the square root of planet radius (as measured, or based on the Chen & Kip￾ping 2017 mass-radius relationship if unmeasured). Systems are sorted b… view at source ↗
Figure 2
Figure 2. Top: Schematic illustration of the “secular inclination excitation” hypothesis, in which the gravitational influence of an outer giant planet tilts the orbit of an inner planet away from the line of sight, creating an apparent gap in the sequence of transiting planets. Bottom: secular evolution in a representative realization of Kepler-48 (left), Kepler-65 (middle), and Kepler-139 (right). For clarity, the inclinati… view at source ↗
Figure 3
Figure 3. Probability of various combinations of planets transiting simultaneously, assuming at least three planets transit. Each system includes a hypothetical planet in the gap, resulting in four inner planets (numbered as in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Transit detection efficiency contours for Kepler￾48, -65, -90, and -139, estimated with the help of the KeplerPORTS software. To have avoided detection in Kepler￾48, -65, and -139, a hypothetical gap planet must be some￾what smaller than the known planets (≲ 0.7 R⊕, ≲ …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

75 extracted references · 10 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [3]

    ݷ0JݸqZ6s j:2̘N3 U4xm #t 0 `aa |W/ \ 0 & > G`raq j ɓ'=^XX M k;<K\ 0 & > G`ra#`6`` : F 3`` : F 3`` : F 3```8#q亮ժd LӔi 7v6Q . < 3ЃB˗/P(teYbp̆mrr]LT4 U

    thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

    2021

  4. [4]

    C., & Adams , F

    Becker , J. C., & Adams , F. C. 2017, , 468, 549, 10.1093/mnras/stx461

    work page doi:10.1093/mnras/stx461 2017

  5. [5]

    A., & Petrovich , C

    Best , M., Sefilian , A. A., & Petrovich , C. 2024, , 960, 89, 10.3847/1538-4357/ad0965

    doi:10.3847/1538-4357/ad0965 2024

  6. [6]

    2023, , 674, A178, 10.1051/0004-6361/202245040

    Bitsch , B., & Izidoro , A. 2023, , 674, A178, 10.1051/0004-6361/202245040

    doi:10.1051/0004-6361/202245040 2023

  7. [7]

    S., Dumusque , X., Massa , A., et al

    Bonomo , A. S., Dumusque , X., Massa , A., et al. 2023, , 677, A33, 10.1051/0004-6361/202346211

    doi:10.1051/0004-6361/202346211 2023

  8. [8]

    Bou \'e , G., & Fabrycky , D. C. 2014, , 789, 110, 10.1088/0004-637X/789/2/110

    work page doi:10.1088/0004-637x/789/2/110 2014

Show all 75 references
  1. [9]

    L., Knutson , H

    Bryan , M. L., Knutson , H. A., Lee , E. J., et al. 2019, , 157, 52, 10.3847/1538-3881/aaf57f

    2019 doi

  2. [10]

    L., & Lee , E

    Bryan , M. L., & Lee , E. J. 2024, , 968, L25, 10.3847/2041-8213/ad5013

    2024 doi

  3. [11]

    J., & Catanzarite , J

    Burke , C. J., & Catanzarite , J. 2017, Planet Detection Metrics: Per-Target Detection Contours for Data Release 25 , Kepler Science Document KSCI-19111-002, id. 19. Edited by Michael R. Haas and Natalie M. Batalha

    2017

  4. [12]

    2014, , 781, 18, 10.1088/0004-637X/781/1/18

    Cabrera , J., Csizmadia , S., Lehmann , H., et al. 2014, , 781, 18, 10.1088/0004-637X/781/1/18

    2014 doi

  5. [13]

    Chachan , Y., & Lee , E. J. 2023, , 952, L20, 10.3847/2041-8213/ace257

    2023 doi

  6. [14]

    E., Wetherill , G

    Chambers , J. E., Wetherill , G. W., & Boss , A. P. 1996, , 119, 261, 10.1006/icar.1996.0019

    1996

  7. [15]

    2017, , 834, 17, 10.3847/1538-4357/834/1/17

    Chen , J., & Kipping , D. 2017, , 834, 17, 10.3847/1538-4357/834/1/17

    2017 doi

  8. [16]

    L., Jenkins , J

    Christiansen , J. L., Jenkins , J. M., Caldwell , D. A., et al. 2012, , 124, 1279, 10.1086/668847

    2012 doi

  9. [17]

    L., Clarke , B

    Christiansen , J. L., Clarke , B. D., Burke , C. J., et al. 2016, , 828, 99, 10.3847/0004-637X/828/2/99

    2016 doi

  10. [18]

    2020, , 160, 159, 10.3847/1538-3881/abab0b

    ---. 2020, , 160, 159, 10.3847/1538-3881/abab0b

    2020 doi

  11. [19]

    2021, Proceedings of the National Academy of Science, 118, e2026053118, 10.1073/pnas.2026053118

    Cranmer , M., Tamayo , D., Rein , H., et al. 2021, Proceedings of the National Academy of Science, 118, e2026053118, 10.1073/pnas.2026053118

    2021 doi

  12. [20]

    P., Marcy , G

    Cumming , A., Butler , R. P., Marcy , G. W., et al. 2008, , 120, 531, 10.1086/588487

    2008 doi

  13. [21]

    C., Lissauer , J

    Fabrycky , D. C., Lissauer , J. J., Ragozzine , D., et al. 2014, , 790, 146, 10.1088/0004-637X/790/2/146

    2014 doi

  14. [22]

    2012, , 761, 92, 10.1088/0004-637X/761/2/92

    Fang , J., & Margot , J.-L. 2012, , 761, 92, 10.1088/0004-637X/761/2/92

    2012 doi

  15. [23]

    2013, , 767, 115, 10.1088/0004-637X/767/2/115

    ---. 2013, , 767, 115, 10.1088/0004-637X/767/2/115

    2013 doi

  16. [24]

    J., & Petigura , E

    Fulton , B. J., & Petigura , E. A. 2018, , 156, 264, 10.3847/1538-3881/aae828

    2018 doi

  17. [25]

    M., Giuliatti Winter , S

    Gaslac Gallardo , D. M., Giuliatti Winter , S. M., Winter , O., Callegari , N., & Mu \ n oz-Guti \'e rrez , M. A. 2024, , 535, 3198, 10.1093/mnras/stae2518

    2024 doi

  18. [26]

    S., Seager , S., & Mallen-Ornelas , G

    Gaudi , B. S., Seager , S., & Mallen-Ornelas , G. 2005, , 623, 472, 10.1086/428478

    2005 doi

  19. [27]

    J., & Fabrycky , D

    Gilbert , G. J., & Fabrycky , D. C. 2020, , 159, 281, 10.3847/1538-3881/ab8e3c

    2020 doi

  20. [28]

    J., Petigura , E

    Gilbert , G. J., Petigura , E. A., & Entrican , P. M. 2025, Proceedings of the National Academy of Science, 122, e2405295122, 10.1073/pnas.2405295122

    2025 doi

  21. [29]

    P., & Boley , A

    Granados Contreras , A. P., & Boley , A. C. 2018, , 155, 139, 10.3847/1538-3881/aaac82

    2018 doi

  22. [30]

    2017, , 154, 5, 10.3847/1538-3881/aa71ef

    Hadden , S., & Lithwick , Y. 2017, , 154, 5, 10.3847/1538-3881/aa71ef

    2017 doi

  23. [31]

    2022, , 164, 179, 10.3847/1538-3881/ac8d01

    Hadden , S., & Tamayo , D. 2022, , 164, 179, 10.3847/1538-3881/ac8d01

    2022 doi

  24. [32]

    Y., & Weiss , L

    He , M. Y., & Weiss , L. M. 2023, , 166, 36, 10.3847/1538-3881/acdd56

    2023 doi

  25. [33]

    X., Petrovich , C., & Deibert , E

    Huang , C. X., Petrovich , C., & Deibert , E. 2017, , 153, 210, 10.3847/1538-3881/aa67fb

    2017 doi

  26. [34]

    N., Morbidelli , A., Hersant , F., & Pierens , A

    Izidoro , A., Raymond , S. N., Morbidelli , A., Hersant , F., & Pierens , A. 2015, , 800, L22, 10.1088/2041-8205/800/2/L22

    2015 doi

  27. [35]

    H., & Zhu , Z.-H

    Kong , Z., Johansen , A., Lambrechts , M., Jiang , J. H., & Zhu , Z.-H. 2024, , 687, A121, 10.1051/0004-6361/202349043

    2024 doi

  28. [36]

    2017, , 153, 42, 10.3847/1538-3881/153/1/42

    Lai , D., & Pu , B. 2017, , 153, 42, 10.3847/1538-3881/153/1/42

    2017 doi

  29. [37]

    A., et al

    Lambrechts , M., Morbidelli , A., Jacobson , S. A., et al. 2019, , 627, A83, 10.1051/0004-6361/201834229

    2019 doi

  30. [38]

    2024, , 972, 53, 10.3847/1538-4357/ad5be6

    Lammers , C., Hadden , S., & Murray , N. 2024, , 972, 53, 10.3847/1538-4357/ad5be6

    2024 doi

  31. [39]

    Lammers , C., & Winn , J. N. 2025, , 984, L39, 10.3847/2041-8213/adce01

    2025 doi

  32. [40]

    1990, , 88, 266, 10.1016/0019-1035(90)90084-M

    Laskar , J. 1990, , 88, 266, 10.1016/0019-1035(90)90084-M

    1990 doi

  33. [41]

    1994, , 287, L9

    ---. 1994, , 287, L9

    1994

  34. [42]

    Laskar , J., & Petit , A. C. 2017, , 605, A72, 10.1051/0004-6361/201630022

    2017 doi

  35. [43]

    2021, , 161, 202, 10.3847/1538-3881/abe6a7

    Liang , Y., Robnik , J., & Seljak , U. 2021, , 161, 202, 10.3847/1538-3881/abe6a7

    2021 doi

  36. [44]

    J., Fabrycky , D

    Lissauer , J. J., Fabrycky , D. C., Ford , E. B., et al. 2011 a , , 470, 53, 10.1038/nature09760

    2011 doi

  37. [45]

    J., Ragozzine , D., Fabrycky , D

    Lissauer , J. J., Ragozzine , D., Fabrycky , D. C., et al. 2011 b , , 197, 8, 10.1088/0067-0049/197/1/8

    2011 doi

  38. [46]

    2011, , 739, 31, 10.1088/0004-637X/739/1/31

    Lithwick , Y., & Wu , Y. 2011, , 739, 31, 10.1088/0004-637X/739/1/31

    2011 doi

  39. [47]

    R., & Becker , J

    Livesey , J. R., & Becker , J. 2025, , 979, 202, 10.3847/1538-4357/ada28b

    2025 doi

  40. [48]

    N., & Kawahara , H

    Masuda , K., Winn , J. N., & Kawahara , H. 2020, , 159, 38, 10.3847/1538-3881/ab5c1d

    2020 doi

  41. [49]

    2020, , 160, 160, 10.3847/1538-3881/abab9e

    Murchikova , L., & Tremaine , S. 2020, , 160, 160, 10.3847/1538-3881/abab9e

    2020 doi

  42. [50]

    D., & Dermott , S

    Murray , C. D., & Dermott , S. F. 1999, Solar system dynamics

    1999

  43. [51]

    J., Davies , M

    Mustill , A. J., Davies , M. B., & Johansen , A. 2017, , 468, 3000, 10.1093/mnras/stx693

    2017 doi

  44. [52]

    2023, , 10.1093/mnras/stad1921

    Obertas , A., Tamayo , D., & Murray , N. 2023, , 10.1093/mnras/stad1921

    2023 doi

  45. [53]

    2017, , 293, 52, 10.1016/j.icarus.2017.04.010

    Obertas , A., Van Laerhoven , C., & Tamayo , D. 2017, , 293, 52, 10.1016/j.icarus.2017.04.010

    2017 doi

  46. [54]

    Pepper , J., Gould , A., & Depoy , D. L. 2003, , 53, 213, 10.48550/arXiv.astro-ph/0208042

    2003 doi arXiv

  47. [55]

    Ragozzine , D., & Holman , M. J. 2010, arXiv e-prints, arXiv:1006.3727, 10.48550/arXiv.1006.3727

    2010 doi arXiv

  48. [56]

    2015, , 452, 376, 10.1093/mnras/stv1257

    Rein , H., & Tamayo , D. 2015, , 452, 376, 10.1093/mnras/stv1257

    2015 doi

  49. [57]

    J., Knutson , H

    Rosenthal , L. J., Knutson , H. A., Chachan , Y., et al. 2022, , 262, 1, 10.3847/1538-4365/ac7230

    2022 doi

  50. [58]

    2016, , 817, 104, 10.3847/0004-637X/817/2/104

    Rowan , D., Meschiari , S., Laughlin , G., et al. 2016, , 817, 104, 10.3847/0004-637X/817/2/104

    2016 doi

  51. [59]

    F., Bryson , S

    Rowe , J. F., Bryson , S. T., Marcy , G. W., et al. 2014, , 784, 45, 10.1088/0004-637X/784/1/45

    2014 doi

  52. [60]

    2021, , 656, A71, 10.1051/0004-6361/202038554

    Schlecker , M., Mordasini , C., Emsenhuber , A., et al. 2021, , 656, A71, 10.1051/0004-6361/202038554

    2021 doi

  53. [61]

    R., Wang , J., Fischer , D

    Schmitt , J. R., Wang , J., Fischer , D. A., et al. 2014, , 148, 28, 10.1088/0004-6256/148/2/28

    2014 doi

  54. [62]

    J., & Vanderburg , A

    Shallue , C. J., & Vanderburg , A. 2018, , 155, 94, 10.3847/1538-3881/aa9e09

    2018 doi

  55. [63]

    W., & Lissauer , J

    Smith , A. W., & Lissauer , J. J. 2009, , 201, 381, 10.1016/j.icarus.2008.12.027

    2009 doi

  56. [64]

    2020, Proceedings of the National Academy of Science, 117, 18194, 10.1073/pnas.2001258117

    Tamayo , D., Cranmer , M., Hadden , S., et al. 2020, Proceedings of the National Academy of Science, 117, 18194, 10.1073/pnas.2001258117

    2020 doi

  57. [65]

    E., Coughlin , J

    Thompson , S. E., Coughlin , J. L., Hoffman , K., et al. 2018, , 235, 38, 10.3847/1538-4365/aab4f9

    2018 doi

  58. [66]

    2023, Dynamics of Planetary Systems

    Tremaine , S. 2023, Dynamics of Planetary Systems

    2023

  59. [67]

    2015, , 808, 126, 10.1088/0004-637X/808/2/126

    Van Eylen , V., & Albrecht , S. 2015, , 808, 126, 10.1088/0004-637X/808/2/126

    2015 doi

  60. [68]

    M., Marcy , G

    Weiss , L. M., Marcy , G. W., Petigura , E. A., et al. 2018, , 155, 48, 10.3847/1538-3881/aa9ff6

    2018 doi

  61. [69]

    M., Isaacson , H., Howard , A

    Weiss , L. M., Isaacson , H., Howard , A. W., et al. 2024, , 270, 8, 10.3847/1538-4365/ad0cab

    2024 doi

  62. [70]

    N., & Petigura , E

    Winn , J. N., & Petigura , E. 2024, arXiv e-prints, arXiv:2401.16451, 10.48550/arXiv.2401.16451

    2024 doi arXiv

  63. [71]

    1991, , 102, 1528, 10.1086/115978

    Wisdom , J., & Holman , M. 1991, , 102, 1528, 10.1086/115978

    1991 doi

  64. [72]

    A., Butler , R

    Wittenmyer , R. A., Butler , R. P., Tinney , C. G., et al. 2016, , 819, 28, 10.3847/0004-637X/819/1/28

    2016 doi

  65. [73]

    A., Wang , S., Horner , J., et al

    Wittenmyer , R. A., Wang , S., Horner , J., et al. 2020, , 492, 377, 10.1093/mnras/stz3436

    2020 doi

  66. [74]

    2020, , 159, 188, 10.3847/1538-3881/ab7814

    Zhu , W. 2020, , 159, 188, 10.3847/1538-3881/ab7814

    2020 doi

  67. [75]

    2018, , 156, 92, 10.3847/1538-3881/aad22a

    Zhu , W., & Wu , Y. 2018, , 156, 92, 10.3847/1538-3881/aad22a

    2018 doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.