Pith. sign in

REVIEW 4 major objections 4 minor 16 references

1:1 orbital resonance of circumbinary planets

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read The paper claims that two migrating circumbinary planets can be captured into a stable 1:1 horseshoe resonance around low-eccentricity binaries, with aligned eccentric orbits, and that the configuration survives after the gas disc…

desk verdict A clean proof-of-existence that circumbinary disc migration can park two planets in a stable 1:1 horseshoe resonance, though the parameter regime is narrow and the Kepler-413 claim relies on an unseen planet. read the letter →

arxiv 1908.10395 v1 pith:HZ3QK5O4 submitted 2019-08-27 astro-ph.EP

Anna B.T. Penzlin , Sareh Ataiee , Wilhelm Kley This is my paper · ORCID
classification astro-ph.EP
keywords circumbinaryplanets1:1mean-motionresonancecoorbitalhorseshoeorbitsplanetmigrationprotoplanetarydiscsKepler-47Kepler-413
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

The paper sets out to explain how several planets can end up orbiting a binary star and, in particular, whether migration through the circumbinary disc can leave two planets sharing the same orbit. Through 2D viscous hydrodynamic simulations of Kepler-47 and Kepler-413, it argues that two low-mass planets of similar mass are captured into a $1{:}1$ mean-motion resonance at the disc's inner cavity, with fully aligned eccentric orbits and horseshoe motion. If this is right, it would be a new class of stable coorbital planet configuration around binary stars, different from the nearly circular coorbitals known in the Solar System and not yet observed among exoplanets.

What carries the argument

The central mechanism is the parking position: the inner edge of the precessing, eccentric circumbinary cavity acts as a trap that halts inward migration. Because the planets are small enough not to open a gap in the disc at $\alpha = 10^{-3}$, both settle at the same orbit near the cavity edge and their orbits align with the precessing cavity; the incoming outer planet catches up and the pair enters horseshoe libration around $\mathrm{L}_4$ and $\mathrm{L}_5$. The paper then removes the disc and uses n-body integrations to show that the resulting horseshoe pair is dynamically stable on its own.

What would settle it

A simulation with $\alpha = 10^{-4}$ for Kepler-47, which the paper itself reports, breaks the mechanism: the planets open a gap, the inner planet is ejected, and no coorbital resonance appears. Observationally, a re-analysis of the Kepler photometric archive for Kepler-413 that rules out a second planet of mass $\sim 0.21\,M_{\rm Jup}$ near the predicted coorbital separation would falsify the claim that this specific system hosts a 1:1 resonance.

Watch

Extended reading notes

Core claim

The central claim is that in the low-eccentricity binary systems Kepler-47 and Kepler-413, convergent migration in a viscous circumbinary disc naturally parks two equal-mass planets on the same orbit. The planets stop at the precessing, eccentric inner cavity edge, the parking position, without opening a gap, and the second planet catches up to the first; the pair then librates in a $1{:}1$ resonance, executing horseshoe motion about $\mathrm{L}_4$ and $\mathrm{L}_5$. Their orbits remain aligned with each other and with the cavity, with mean eccentricities of about 0.25 to 0.30, and the minimum mean-longitude separation stays above about $20^\circ$, so the planets never collide. After the disc is removed, n-body integrations over $22\,000$ to $78\,500$ binary periods show the horseshoe configuration is stable. The authors therefore conclude that stable coorbital circumbinary planets are a viable outcome of disc-driven migration, probably requiring low binary eccentricity.

Load-bearing premise

The main load-bearing premise is that the disc is viscous enough ($\alpha = 10^{-3}$) to prevent gap opening and that a second planet is present; if the real discs are less viscous, or Kepler-413 has only the one observed planet, the capture mechanism fails.

Editorial extensions

If this is right

  • Coorbital circumbinary planets should be added to the list of possible outcomes of planet formation around binaries, not treated as dynamically forbidden.
  • Observational searches for a second planet in Kepler-47 and Kepler-413 are the most direct test; the simulations give a specific expected configuration: aligned, eccentric, horseshoe motion with a minimum longitude separation near $20^\circ$.
  • The mechanism predicts a preference for low binary eccentricity: Kepler-35 ($e_{\rm bin} = 0.14$) and Kepler-34 ($e_{\rm bin} = 0.52$) did not produce coorbital capture, while $e_{\rm bin} = 0.02$ and $0.04$ did.
  • The resonance survives disc dispersal, so the observed population of circumbinary planets could contain such pairs even though the gas that formed them is gone.
  • Moderate planet mass ratios still allow capture: a 20% mass difference in Kepler-47 gave a tadpole-type coorbital rather than a horseshoe, showing the phenomenon is not limited to exactly equal masses.

Reading between the lines

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

  • An implicit extension is to map the boundary of the capture region in binary eccentricity and disc viscosity; the paper's failure cases suggest the mechanism occupies a low-eccentricity, high-viscosity corner of parameter space.
  • The long libration periods, roughly $10^3$ binary orbits, imply that detecting such pairs photometrically would require monitoring over many years, a signature the paper does not quantify.
  • If real, this configuration offers a clean test of disc-driven migration theory: the coorbital pair's presence would pin down the disc's viscosity at the time of planet migration, since low-viscosity discs destroy the resonance.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper reports 2D hydrodynamic simulations of circumbinary discs around Kepler-47 and Kepler-413 with two embedded, equal-mass planets that migrate inward under disc torques. In both systems the inner planet parks at the eccentric cavity edge and the outer planet subsequently converges onto the same orbit, producing a 1:1 coorbital configuration with horseshoe-type motion, orbital eccentricities of about 0.25 to 0.30, and aligned orbits. The authors extract the final states and show in pure n-body integrations without the disc that the configurations remain stable for at least 22,000 binary periods. They conclude that stable coorbital circumbinary planets can be a natural outcome of convergent disc migration and suggest that such systems should be searched for in the Kepler data.

Significance. If the result holds, it identifies a plausible formation channel for a previously unrecognized class of circumbinary resonant systems, and the paper gives a clear dynamical mechanism (parking at the same cavity edge) that is physically reasonable. The study has genuine strengths: the 1:1 resonance is an emergent outcome of the migration calculation rather than being inserted by hand; the follow-up n-body runs test long-term stability without the disc; and the authors explicitly acknowledge that their simulated planets lie farther from the binary than the observed planets. However, the significance is limited by the narrow parameter coverage and, for Kepler-413, by the insertion of an unseen equal-mass companion. The result is best read as a proof of existence for a specific disc model, not as a demonstrated general outcome for the observed systems.

major comments (4)
  1. [Section 4, viscosity dependence] The claim that coorbital capture is a natural outcome of convergent migration rests on a single viscosity and initial-condition slice. The authors themselves report that lowering alpha from 0.001 to 1e-4 in Kepler-47 causes gap opening and ejection of the inner planet, so a factor-of-ten change in viscosity destroys the phenomenon. Because alpha controls whether both planets remain gapless and park at the same cavity edge, the paper should either present a small parameter study (intermediate alpha, varied h, varied initial separations) or explicitly soften the wording from 'natural outcome' to 'possible outcome for the chosen disc parameters'.
  2. [Section 2, Kepler-413 model setup] In the Kepler-413 model, a second planet of exactly the observed planet's mass is embedded at 11.5 a_bin, but only one planet is detected in that system. The abstract's statement that 'in Kepler-47 and -413 the planets are captured in a 1:1 resonance' therefore presumes an unseen equal-mass companion. The paper should state this assumption prominently in the abstract and frame the Kepler-413 result as conditional on a hypothetical second planet rather than as a statement about the observed system.
  3. [Section 2, numerical convergence] No convergence tests or quantitative error estimates are reported. Section 2 states that the 684x584 grid has been shown sufficient in earlier work, but the capture times, libration periods, and eccentricity values quoted in Section 3 could depend on resolution, on the 20,000 T_bin disc convergence criterion, and on the reported time-step. A convergence check or at least an explicit estimate of numerical uncertainty is needed before the quantitative values can be taken at face value.
  4. [Section 4, radial mismatch with observations] The paper acknowledges that the simulated planets park farther from the binary than the observed planets and states that coorbitals are not expected to form very close to the stars, but no quantitative support for that expectation is given. Since this radius mismatch directly limits the applicability of the result to Kepler-47 and Kepler-413, the paper should either provide a physical argument based on existing simulations or explicitly identify this as an open question for future work.
minor comments (4)
  1. [Section 2, first paragraph] There is a typo in 'we discuss out results'; it should read 'our results'.
  2. [Section 4, first paragraph] In 'stable coorbital configurations can exits', 'exits' should be 'exist'.
  3. [Section 4, footnote 1] The footnote 'These results will be published in a future study' is not a citable reference; the relevant results should be cited instead, or the statement should be marked as unpublished work.
  4. [Figure 3 caption] The caption says the top panels show semi-major axis difference against difference in mean longitude, but the reader must infer which color corresponds to which time; adding a color bar or stating the time interval more explicitly would improve clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No meaningful circularity: the 1:1 resonance is an emergent hydrodynamical outcome, not a fitted input or a self-citation chain.

full rationale

The paper's central claim, capture into a 1:1 coorbital resonance at the circumbinary cavity edge, is produced by the simulations themselves. The planets are inserted at different radii (Kepler-47 at 7.5, 14, and 20 abin; Kepler-413 at 9 and 11.5 abin) on circular orbits, with no resonant initial condition, and the convergent migration to a common parking radius followed by horseshoe libration is explicitly evolved in the hydrodynamical runs. The n-body stability check uses the extracted final state as an initial condition, so it is a continuation rather than a refit. No parameter is adjusted to force the resonance; Section 4 shows that lowering alpha to 1e-4 leads to gap opening and ejection of the inner planet, and that systems with higher binary eccentricity do not form coorbitals, demonstrating the outcome is parameter-dependent rather than definitionally guaranteed. The self-citations, especially Thun & Kley (2018) and Kley et al. (2019), supply the code, the locally isothermal disc equilibrium, and the cavity properties, but they do not contain or assert the 1:1 resonance result, so they are methodological background rather than load-bearing circular support. The caveats about Kepler-413 requiring an unseen equal-mass companion and the limited viscosity/initial-condition coverage are scientific limitations, not circularity, because they do not reduce the conclusion to its inputs by construction. Overall, the derivation is self-contained with only minor, non-load-bearing self-citation.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper's central claim rests on a set of numerical model choices (viscosity, aspect ratio, disc mass, initial positions, an unseen companion in Kepler-413) rather than on fitted parameters. None of these were tuned to force the 1:1 resonance, but the negative control with alpha = 1e-4 shows the outcome is sensitive to them.

free parameters (5)
  • Disc aspect ratio h = 0.04
    Chosen from Kley et al. (2019) as a representative equilibrium value; not fitted to the resonance, but it affects cavity size and parking position.
  • Viscosity parameter alpha = 0.001
    Chosen model parameter; the authors show that alpha = 1e-4 changes the outcome and prevents coorbital capture, so the central result depends on this choice.
  • Disc mass = 1% of binary mass
    Model initialization choice for the gas disc mass.
  • Planet initial semimajor axes = Kepler-47: 7.5, 14, 20 abin; Kepler-413: 9, 11.5 abin
    Hand-chosen starting radii for migration; the capture outcome may depend on these initial conditions.
  • Kepler-413 second planet mass = 0.21 MJup
    The second planet is not observed; its mass is set equal to the single detected planet in the system. This is an assumption, not a fit.
assumptions (5)
  • domain assumption A 2D locally isothermal disc with h = 0.04 approximates the thermal structure of real circumbinary discs.
    Invoked in Section 2; the final equilibrium of radiative discs is claimed to be similar to locally isothermal models (Kley et al. 2019), but no full radiation calculation is performed here.
  • domain assumption The disc converges to its equilibrium cavity after 20,000 binary orbits, so the pre-planet disc is a valid initial state.
    Stated in Section 2 without a convergence analysis against initial conditions.
  • domain assumption Planets are treated as non-accreting point masses embedded in the disc.
    Stated in Section 2; accretion and finite size could change migration and resonance capture.
  • domain assumption The modified PLUTO hydrodynamics code and the 4th-order Runge-Kutta n-body integrator are accurate enough for this problem.
    The accuracy is asserted via citations to Thun et al. (2017) and a statement about time-step size; no convergence tests are shown.
  • domain assumption Long-term n-body stability over 22,000 Tbin is representative of much longer timescales.
    Section 3; no Lyapunov or secular stability analysis is presented.

how reviews work

0 comments
Cite this review

Pith. "Pith review of 1:1 orbital resonance of circumbinary planets." pith.science (2026). https://pith.science/paper/HZ3QK5O4

@misc{pith2026190810395,
  author       = {Pith},
  title        = {Pith review of: 1:1 orbital resonance of circumbinary planets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HZ3QK5O4}},
  note         = {Machine review of arXiv:1908.10395}
}
read the original abstract

The recent detection of the third planet in Kepler-47 has shown that binary stars can host several planets in circumbinary orbits. To understand the evolution of such systems we have performed two-dimensional hydrodynamic simulations of the circumbinary disc with two embedded planets for several Kepler systems. In two cases, Kepler-47 and -413, the planets are captured in a 1:1 mean-motion resonance at the planet parking position near the inner edge of the disc. The orbits are fully aligned, have mean eccentricities of about 0.25 to 0.30, and the planets are entangled in a horseshoe type of motion. Subsequent n-body simulations without the disc show that the configurations are stable. Our results point to the existence of a new class of stable resonant orbits around binary stars. It remains to be seen if such orbits exist in reality.

Figures

Figures reproduced from arXiv: 1908.10395 by the authors.

Figure 2
Figure 2. Density distribution at the time right before the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. Time evolution of the orbital elements of the inserted [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Dynamical structure of the 1:1 resonances while the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Evolution of semi-major axes and eccentricities of the two planets orbiting Kepler-413 and -47 for the pure n-body [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: The difference in mean longitude of the two planets [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 10 canonical work pages

  1. [1]

    2007, A&A, 463, 359

    Beaugé, C., Sándor, Z., Érdi, B., & Süli, Á. 2007, A&A, 463, 359

    work page 2007

  2. [2]

    & Nelson, R

    Cresswell, P. & Nelson, R. P. 2006, A&A, 450, 833

    work page 2006

  3. [3]

    & Nelson, R

    Cresswell, P. & Nelson, R. P. 2009, A&A, 493, 1141

    work page 2009

  4. [4]

    Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90

    2007

  5. [5]

    Kley, W., Thun, D., & Penzlin, A. B. T. 2019, A&A, 627, A91

    work page 2019

  6. [6]

    B., McCullough, P

    Kostov, V. B., McCullough, P. R., Carter, J. A., et al. 2014, ApJ, 784, 14

    2014

  7. [7]

    Stability of the co-orbital resonance under dissipation: Application to its evolution in protoplanetary discs

    Leleu, A., Coleman, G., & Ataiee, S. 2019a, arXiv e-prints, arXiv:1901.07640

    work page Pith review arXiv 1901

  8. [8]

    Leleu, A., Robutel, P., & Correia, A. C. M. 2018, Celestial Mechanics and Dynamical Astronomy, 130, 24

    work page 2018

Show all 16 references
  1. [9]

    & Grigorelis, F

    Michalodimitrakis, M. & Grigorelis, F. 1989, Journal of Astrophysics and Astronomy, 10, 347

    1989

  2. [10]

    2007, ApJS, 170, 228

    Mignone, A., Bodo, G., Massaglia, S., et al. 2007, ApJS, 170, 228

    2007

  3. [11]

    A., & Murray, C

    Namouni, F., Christou, A. A., & Murray, C. D. 1999, Phys. Rev. Lett., 83, 2506

    1999

  4. [12]

    A., Welsh, W

    Orosz, J. A., Welsh, W. F., Haghighipour, N., et al. 2019, AJ, 157, 174

    2019

  5. [13]

    & Raymond, S

    Pierens, A. & Raymond, S. N. 2014, MNRAS, 442, 2296 Rodríguez, A., Correa-Otto, J. A., & Michtchenko, T. A. 2019, MN- RAS, 487, 1973

    2014

  6. [14]

    & Kley, W

    Thun, D. & Kley, W. 2018, A&A, 616, A47

    2018

  7. [15]

    2017, A&A, 604, A102

    Thun, D., Kley, W., & Picogna, G. 2017, A&A, 604, A102

    2017

  8. [16]

    F., Colombo, G., Synnott, S

    Yoder, C. F., Colombo, G., Synnott, S. P., & Yoder, K. A. 1983, Icarus, 53, 431 1 These results will be published in a future study. Article number, page 5 of 5

    1983

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.