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arxiv: 2603.00547 · v2 · submitted 2026-02-28 · 🌌 astro-ph.EP · astro-ph.HE

Planetary Desert around Compact Binaries: Dynamical Instability Triggered by Resonance-Induced Eccentricity Excitation

Bin Liu , Dong Lai This is my paper

Pith reviewed 2026-05-15 18:39 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.HE
keywords circumbinary planetsplanet desertdynamical instabilityeccentricity excitationsecular resonancetidal decayplanet scatteringbinary evolution
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The pith

Resonance with a decaying binary pumps planet eccentricities until orbits cross and scatter, emptying inner regions around short-period binaries.

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

The paper examines the absence of transiting planets around compact binaries with orbital periods shorter than about 7 days, known as the circumbinary planet desert. Using single-averaged secular equations that include planet-planet interactions, the simulations show that tidal decay of an eccentric binary can capture an outer planet into resonance advection in eccentricity. This locks the planet's apsidal precession to the binary's and drives extreme eccentricity growth. In single-planet cases the effect stays localized, but in multi-planet systems the inflated orbit crosses neighbors, triggering violent scatterings that produce collisions or ejections and clear the inner zones. The authors conclude that this resonance-induced chain reaction supplies a natural dynamical explanation for the observed desert.

Core claim

When an eccentric binary decays via tides, an outer planet can be captured into resonance advection in eccentricity, a state in which its apsidal precession locks with that of the binary, driving extreme eccentricity growth. While such growth can occur in a binary-single planet system, the parameter space is limited and may not necessarily induce instability. In a multi-planet system, however, the excited orbit inevitably crosses those of its neighbors, which triggers violent planet-planet scatterings and produces collisions or ejections. These mutual gravitational interactions amplify the localized instability into a system-wide chain reaction that drastically reshapes the orbital架构 and can

What carries the argument

resonance advection in eccentricity, in which a planet's apsidal precession locks with the binary's during tidal decay, pumping the planet's eccentricity to high values while the binary shrinks.

If this is right

  • Mutual planet-planet interactions turn limited single-planet eccentricity growth into system-wide clearing.
  • The process operates specifically when the binary is eccentric and decaying through tides.
  • Inner regions of multi-planet systems around compact binaries are preferentially emptied by the resulting scatterings.
  • Single-planet systems may remain stable even after the resonance-driven eccentricity increase.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Surviving planets at larger separations could retain eccentricity or inclination signatures from earlier resonance passages.
  • The mechanism predicts a sharp inner cutoff in planet occurrence that could be checked against transit survey statistics.
  • Higher-order effects or general-relativistic precession might shift the resonance locations and should be tested in refined models.
  • Similar resonance-driven clearing might appear around other classes of evolving binaries with tidal decay.

Load-bearing premise

The single-averaged secular equations remain valid and sufficient throughout the eccentricity excitation and scattering phases without requiring full N-body integration or higher-order corrections.

What would settle it

A full N-body integration of the same multi-planet circumbinary systems that shows no orbit crossings or scatterings despite the predicted resonance capture and eccentricity growth would falsify the instability mechanism.

Figures

Figures reproduced from arXiv: 2603.00547 by Bin Liu, Dong Lai.

Figure 1
Figure 1. Figure 1: — Evolution of a stellar binary (black) with four (non￾interacting) circumbinary planets in a coplanar configuration. The masses of the inner stellar binary are m1 = 0.56M⊙ and m2 = 0.46M⊙. The initial semimajor axis and eccentricity of the in￾ner binary are ab,0 = 0.09AU and eb,0 = 0.8. The outer or￾bits, ordered by increasing distance, have initial semimajor axes ap = 0.72AU, 1.24AU, 2.13AU and 2.81AU. A… view at source ↗
Figure 2
Figure 2. Figure 2: — Parameter space in the ap − eb,0 plane showing the regime for resonance capture and advection during the orbital de￾cay of the stellar binary. We consider coplanar configurations for all simulations presented in this figure. The orbital period Tp for planets at different distances is labeled at the top. We choose the same stellar binary as in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: — Similar to [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: — Same system as in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: — The evolution of 9−planet system during tidal decay of the host binary, with mutual planet-planet gravitational inter￾actions included. The system parameters are taken from [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: — Architecture of planetary orbits after the tidal evolution of the host binary has ceased. The results are based on statistical outcomes from 10 runs of the system depicted in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: — Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

Compact binaries with orbital periods shorter than about 7 days show an absence of transiting planets, a feature known as the ``circumbinary planet desert". The physical mechanism behind this desert remains unclear. We investigate its origin by simulating the long-term dynamics of multi-planet circumbinary systems with evolving inner binaries. Our simulations are based on the single-averaged secular equations that average only over the binary orbital period and fully incorporate planet-planet interactions. When an eccentric binary decays via tides, an outer planet can be captured into resonance advection in eccentricity, a state in which its apsidal precession locks with that of the binary, driving extreme eccentricity growth. While such growth can occur in a binary-single planet system, the parameter space is limited and may not necessarily induce instability. In a multi-planet system, however, the excited orbit inevitably crosses those of its neighbors, which triggers violent planet-planet scatterings and produces collisions or ejections. Crucially, these mutual gravitational interactions amplify the ``localized" instability of a single planet into a system-wide chain reaction, drastically reshaping the orbital architecture and potentially clearing out the inner regions of planetary systems. Our results suggest that the resonance-induced instability provides a natural explanation for the observed circumbinary planet desert.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that the observed circumbinary planet desert around compact binaries (P_bin < 7 days) originates from resonance-induced eccentricity excitation. Using single-averaged secular equations that incorporate planet-planet interactions and tidal binary decay, the authors find that apsidal resonance advection drives extreme eccentricity growth; in single-planet systems this effect is limited, but in multi-planet systems it triggers orbit crossings, violent scatterings, collisions, and ejections that clear the inner regions.

Significance. If the mechanism is robust, the work supplies a dynamical explanation for a clear observational feature in circumbinary exoplanets and illustrates how mutual gravitational interactions can amplify localized instabilities into system-wide clearing. The long-term secular approach is computationally efficient for exploring evolutionary timescales, which is a methodological strength.

major comments (1)
  1. [Methods (single-averaged secular equations) and abstract] The central results rest on the single-averaged secular equations remaining valid through resonance capture, eccentricity excitation to orbit-crossing values, and subsequent scattering. The abstract and methods description state that these equations average only over the binary period while retaining planet-planet terms, yet standard secular theory assumes moderate eccentricities and slow evolution; at high e the neglected short-period terms and close-encounter dynamics become non-perturbative. No explicit comparison to full N-body integrations is reported for the high-e regime, which is load-bearing for the claim that multi-planet amplification clears the inner disk.
minor comments (2)
  1. [Abstract] The abstract would benefit from a brief statement of the explored ranges in binary period, planet mass, and number of planets to allow readers to assess the generality of the reported instability.
  2. [Methods] Notation for the resonance advection state and the definition of the secular Hamiltonian could be clarified with an explicit equation reference in the methods.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address the major concern regarding the validity of the single-averaged secular equations below and have revised the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: [Methods (single-averaged secular equations) and abstract] The central results rest on the single-averaged secular equations remaining valid through resonance capture, eccentricity excitation to orbit-crossing values, and subsequent scattering. The abstract and methods description state that these equations average only over the binary period while retaining planet-planet terms, yet standard secular theory assumes moderate eccentricities and slow evolution; at high e the neglected short-period terms and close-encounter dynamics become non-perturbative. No explicit comparison to full N-body integrations is reported for the high-e regime, which is load-bearing for the claim that multi-planet amplification clears the inner disk.

    Authors: We agree that the single-averaged secular equations have limitations at high eccentricities, where short-period terms and close-encounter dynamics are no longer perturbative. Our approach uses these equations to follow the slow secular evolution and resonance advection during binary tidal decay, which drives eccentricity growth until orbits cross in multi-planet systems. Once crossings occur, the resulting instabilities and clearing are a generic outcome of orbit crossing. To address the concern, we will add a new subsection discussing the validity range of the secular approximation and include direct comparisons with full N-body integrations for representative cases at the onset of high eccentricity to confirm the transition to instability. revision: yes

Circularity Check

0 steps flagged

No significant circularity: forward secular simulations yield independent dynamical outcomes

full rationale

The paper's derivation consists of forward numerical integration of single-averaged secular equations that incorporate planet-planet interactions and binary tidal decay. The resonance-capture and eccentricity-excitation behavior, followed by scattering in multi-planet cases, emerges directly from the time evolution of those equations rather than from any parameter fit, self-definition, or self-citation chain that would force the final architecture. No quoted step equates a claimed prediction to an input by construction; the central claim that such instability clears the inner region is therefore an output of the dynamics, not a renaming or tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the single-averaged secular approximation for long-term dynamics and the occurrence of resonance capture during slow binary tidal decay.

axioms (1)
  • domain assumption Single-averaged secular equations accurately capture the long-term dynamics including planet-planet interactions and resonance effects.
    Basis for all simulations described in the abstract.

pith-pipeline@v0.9.0 · 5527 in / 1202 out tokens · 56752 ms · 2026-05-15T18:39:51.637993+00:00 · methodology

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Works this paper leans on

85 extracted references · 85 canonical work pages

  1. [1]

    J., Osborn, H

    Armstrong, D. J., Osborn, H. P., Brown, D. J. A., et al. 2014, MNRAS,444, 1873

    work page 2014

  2. [2]

    Bate, M. R. 2009, MNRAS,392, 590

    work page 2009

  3. [3]

    Bate, M. R. 2019, MNRAS,484, 2341

    work page 2019

  4. [4]

    A., Santerne, A., Triaud, A

    Baycroft, T. A., Santerne, A., Triaud, A. H. M. J., et al. 2025, MNRAS,541, 2801

    work page 2025

  5. [5]

    P., Rhie, S

    Bennett, D. P., Rhie, S. H., Udalski, A., et al. 2016, AJ,152, 125

    work page 2016

  6. [6]

    2017, A&A,608, A106

    Bonavita, M., D’Orazi, V., Mesa, D., et al. 2017, A&A,608, A106

    work page 2017

  7. [7]

    2016, MNRAS, 455, 4136

    Borkovits, T., Hajdu, T., Sztakovics, J., et al. 2016, MNRAS, 455, 4136

    work page 2016

  8. [8]

    L., Bowler, B

    Bryan, M. L., Bowler, B. P., Knutson, H. A., et al. 2016, ApJ, 827, 100

    work page 2016

  9. [9]

    J., Simcoe, R

    Burgasser, A. J., Simcoe, R. A., Bochanski, J. J., et al. 2010, ApJ,725, 1405

    work page 2010

  10. [10]

    G., & Nixon, C

    Chen, C., Martin, R. G., & Nixon, C. J. 2023, MNRAS,525, 3781

    work page 2023

  11. [11]

    G., Lubow, S

    Chen, C., Martin, R. G., Lubow, S. H., & Nixon, C. J. 2024, ApJL,961, L5

    work page 2024

  12. [12]

    C., Martin, R

    Childs, A. C., Martin, R. G., Lepp, S., et al. 2023, ApJL,945, L11

    work page 2023

  13. [13]

    Coleman, G. A. L. 2024, MNRAS,530, 630

    work page 2024

  14. [14]

    Cuello, N., & Giuppone, C. A. 2019, A&A,628, A119

    work page 2019

  15. [15]

    Correia, A. C. M., Udry, S., Mayor, M., et al. 2005, A&A,440, 751 de El´ ıa, G. C., Zanardi, M., Dugaro, A., & Naoz, S. 2019, A&A, 627, A17

    work page 2005

  16. [16]

    H., et al

    Delorme, P., Gagn´ e, J., Girard, J. H., et al. 2013, A&A,553, L5

    work page 2013

  17. [17]

    1991, Ap&SS,181, 313

    Demircan, O., & Kahraman, G. 1991, Ap&SS,181, 313

    work page 1991

  18. [18]

    Doolin, S., & Blundell, K. M. 2011, MNRAS,418, 2656

    work page 2011

  19. [19]

    R., Carter, J

    Doyle, L. R., Carter, J. A., Fabrycky, D. C., et al. 2011, Science, 333, 1602

    work page 2011

  20. [20]

    J., Liu, M

    Dupuy, T. J., Liu, M. C., Allers, K. N., et al. 2018, AJ,156, 57

    work page 2018

  21. [21]

    J., Liu, M

    Dupuy, T. J., Liu, M. C., Evans, E. L., et al. 2023, MNRAS,519, 1688

    work page 2023

  22. [22]

    P., & Kiseleva-Eggleton, L

    Eggleton, P. P., & Kiseleva-Eggleton, L. 2001, ApJ,562, 1012

    work page 2001

  23. [23]

    2007, ApJ,669, 1298

    Fabrycky, D., & Tremaine, S. 2007, ApJ,669, 1298

    work page 2007

  24. [24]

    2025, ApJL,995, L23

    Farhat, M., & Touma, J. 2025, ApJL,995, L23

    work page 2025

  25. [25]

    H., Naoz, S., Wei, L., & Farr, W

    Faridani, T. H., Naoz, S., Wei, L., & Farr, W. M. 2022, ApJ,932, 78

    work page 2022

  26. [26]

    P., Barnes, R., Graham, D

    Fleming, D. P., Barnes, R., Graham, D. E., et al. 2018, ApJ,858, 86

    work page 2018

  27. [27]

    2012, MNRAS,420, 3126

    Fuller, J., & Lai, D. 2012, MNRAS,420, 3126

    work page 2012

  28. [28]

    K., Carter, B., King, R., & O’Toole, S

    Getley, A. K., Carter, B., King, R., & O’Toole, S. 2017, MNRAS, 468, 2932

    work page 2017

  29. [29]

    V., et al

    Goldberg, M., Fabrycky, D., Martin, D. V., et al. 2023, MNRAS, 525, 4628

    work page 2023

  30. [30]

    1980, ApJ,241, 425

    Goldreich, P., & Tremaine, S. 1980, ApJ,241, 425

    work page 1980

  31. [31]

    S., Perets, H

    Hamers, A. S., Perets, H. B., & Portegies Zwart, S. F. 2016, MNRAS,455, 3180

    work page 2016

  32. [32]

    K., et al

    Han, C., Udalski, A., Jung, Y. K., et al. 2024, A&A,685, A16

    work page 2024

  33. [33]

    Hansen, B. M. S., & Naoz, S. 2020, MNRAS,499, 1682

    work page 2020

  34. [34]

    J., & Wiegert, P

    Holman, M. J., & Wiegert, P. A. 1999, AJ,117, 621

    work page 1999

  35. [35]

    Ivanova, N., & Taam, R. E. 2003, ApJ,599, 516

    work page 2003

  36. [36]

    2019, A&A, 626, A99

    Janson, M., Asensio-Torres, R., Andr´ e, D., et al. 2019, A&A, 626, A99

    work page 2019

  37. [37]

    2021, Natur,600, 231

    Janson, M., Gratton, R., Rodet, L., et al. 2021, Natur,600, 231

    work page 2021

  38. [38]

    2015, A&A,581, A20

    Kley, W., & Haghighipour, N. 2015, A&A,581, A20

    work page 2015

  39. [39]

    Kley, W., & Nelson, R. P. 2012, ARA&A,50, 211

    work page 2012

  40. [40]

    B., Orosz, J

    Kostov, V. B., Orosz, J. A., Feinstein, A. D., et al. 2020, AJ,159, 253

    work page 2020

  41. [41]

    B., Powell, B

    Kostov, V. B., Powell, B. P., Orosz, J. A., et al. 2021, AJ,162, 234

    work page 2021

  42. [42]

    K., et al

    Kuang, R., Zang, W., Jung, Y. K., et al. 2022, MNRAS,516, 1704

    work page 2022

  43. [43]

    2011, AJ,141, 119

    Kuzuhara, M., Tamura, M., Ishii, M., et al. 2011, AJ,141, 119

    work page 2011

  44. [44]

    2010, A&A,516, A64

    Leconte, J., Chabrier, G., Baraffe, I., et al. 2010, A&A,516, A64

    work page 2010

  45. [45]

    Leung, G. C. K., & Lee, M. H. 2013, ApJ,763, 107

    work page 2013

  46. [46]

    2014, ApJ,785, 116

    Li, G., Naoz, S., Kocsis, B., & Loeb, A. 2014, ApJ,785, 116

    work page 2014

  47. [47]

    J., & Tao, M

    Li, G., Holman, M. J., & Tao, M. 2016, ApJ,831, 96

    work page 2016

  48. [48]

    2022, ApJ,934, 154

    Li, J., Lai, D., & Rodet, L. 2022, ApJ,934, 154

    work page 2022

  49. [49]

    Lidov, M. L. 1962, P&SS,9, 719

    work page 1962

  50. [50]

    2018, ApJ,863, 68

    Liu, B., & Lai, D. 2018, ApJ,863, 68

    work page 2018

  51. [51]

    2020, PhRvD,102, 023020

    Liu, B., & Lai, D. 2020, PhRvD,102, 023020

    work page 2020

  52. [52]

    J., Vigna-G´ omez, A., et al

    Liu, B., D’Orazio, D. J., Vigna-G´ omez, A., et al. 2022, PhRvD, 106, 123010

    work page 2022

  53. [53]

    2024, PhRvL,132, 231403

    Liu, B., & Lai, D. 2024, PhRvL,132, 231403

    work page 2024

  54. [54]

    G., & Lubow, S

    Martin, R. G., & Lubow, S. H. 2017, ApJL,835, L28

    work page 2017

  55. [55]

    G., et al

    Martin, R. G., et al. 2022, ApJL,927, L26

    work page 2022

  56. [56]

    G., & Lubow, S

    Martin, R. G., & Lubow, S. H. 2025, MNRAS,541, 2036

    work page 2025

  57. [57]

    1979, A&A,77, 145

    Mazeh, T., & Shaham, J. 1979, A&A,77, 145

    work page 1979

  58. [58]

    Moe, M., & Kratter, K. M. 2018, ApJ,854, 44

    work page 2018

  59. [59]

    Mogan, S., & Zanazzi, J. J. 2025, ApJ,988, 150 M¨ uller, S., Baron, J., Helled, R., et al. 2024, A&A,686, A296 Mu˜ noz, D. J., & Lai, D. 2015, PNAS,112, 9264

    work page 2025

  60. [60]

    Naoz, S., & Fabrycky, D. C. 2014, ApJ,793, 137

    work page 2014

  61. [61]

    M., Lithwick, Y., et al

    Naoz, S., Farr, W. M., Lithwick, Y., et al. 2013, MNRAS,431, 2155

    work page 2013

  62. [62]

    2017, AJ,154, 18

    Naoz, S., Li, G., Zanardi, M., et al. 2017, AJ,154, 18

    work page 2017

  63. [63]

    Nelson, R. P. 2003, MNRAS,345, 233

    work page 2003

  64. [64]

    A., Welsh, W

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

    work page 2019

  65. [65]

    B., Kley, W., & Nelson, R

    Penzlin, A. B., Kley, W., & Nelson, R. P. 2021, A&A,645, A68

    work page 2021

  66. [66]

    2015, ApJ,805, 75

    Petrovich, C. 2015, ApJ,805, 75

    work page 2015

  67. [67]

    2021, MNRAS,508, 597

    Pu, B., & Lai, D. 2021, MNRAS,508, 597

    work page 2021

  68. [68]

    R., & Silsbee, K

    Rafikov, R. R., & Silsbee, K. 2014, ApJ,798, 69

    work page 2014

  69. [69]

    E., Orosz, J

    Schwamb, M. E., Orosz, J. A., Carter, J. A., et al. 2013, ApJ, 768, 127

    work page 2013

  70. [70]

    J., Welsh, W

    Socia, Q. J., Welsh, W. F., Orosz, J. A., et al. 2020, AJ,159, 94

    work page 2020

  71. [71]

    R., Sairam, L., Martin, D

    Standing, M. R., Sairam, L., Martin, D. V., et al. 2023, NatAs,7, 702

    work page 2023

  72. [72]

    2018, A&A,616, A47

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

    work page 2018

  73. [73]

    2020, MNRAS,491, 5158

    Tokovinin, A., & Moe, M. 2020, MNRAS,491, 5158

    work page 2020

  74. [74]

    1998, AJ,115, 1653

    Touma, J., & Wisdom, J. 1998, AJ,115, 1653

    work page 1998

  75. [75]

    R., Tremaine, S., & Kazandjian, M

    Touma, J. R., Tremaine, S., & Kazandjian, M. V. 2009, MNRAS, 394, 1085

    work page 2009

  76. [76]

    1981, A&A,100, L7

    Verbunt, F., & Zwaan, C. 1981, A&A,100, L7

    work page 1981

  77. [77]

    Vick, M., Lai, D., & Anderson, K. R. 2019, MNRAS,484, 5645

    work page 2019

  78. [78]

    R., & Chiang, E

    Vinson, B. R., & Chiang, E. 2018, MNRAS,474, 4855 von Zeipel, H. 1910, AN,183, 345

    work page 2018

  79. [79]

    Wei, L., Naoz, S., Faridani, T., & Farr, W. M. 2021, ApJ,923, 118

    work page 2021

  80. [80]

    F., Orosz, J

    Welsh, W. F., Orosz, J. A., Carter, J. A., et al. 2012, Natur,481, 475

    work page 2012

Showing first 80 references.