pith. sign in

arxiv: 2606.20789 · v1 · pith:XTGMF7L3new · submitted 2026-06-18 · 🌌 astro-ph.EP

Dynamical Tides during High-Eccentricity Migration produces the Hot Jupiter Pile-up, Neptune Ridge, and Neptune Desert

J. J. Zanazzi , Morgan MacLeod , Marta L. Bryan , Suvrath Mahadevan This is my paper

Pith reviewed 2026-06-26 15:29 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords high-eccentricity migrationdynamical tidesf-modeshot Jupiter pile-upNeptune ridgeNeptune desertexoplanet migrationtidal shocks
0
0 comments X

The pith

F-modes during high-eccentricity migration circularize orbits and unbind mass to explain hot Jupiter pile-up, Neptune ridge, and Neptune desert.

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

The paper shows that fundamental modes excited by dynamical tides in planets undergoing high-eccentricity migration can dissipate orbital energy in two ways. When f-modes shock shallowly in the envelope, radiative cooling or winds circularize the orbit, leading to clustering at periods of about 3 to 6 days for both sub-Saturns and Jovians. When shocks are deeper, they drive outflows that unbind the gaseous envelope, leaving the core in the Neptune desert. This single mechanism accounts for the observed period distributions that depend on planet mass.

Core claim

Tidally-excited f-modes act as a reservoir for orbital energy during high-eccentricity migration. Hydrodynamical simulations show that close approaches excite these modes to supersonic velocities that shock the gaseous envelopes. An iterative map tracks evolution over many passages: shallow shocks allow diffusive cooling and circularization that bunches orbits near the hot Jupiter pile-up and Neptune ridge, while deep shocks drive mass loss that places cores in the Neptune desert. Sub-Saturns in the desert are predicted to have large spin-orbit misalignments after producing luminous flares.

What carries the argument

The iterative map of planetary structural and orbital evolution driven by f-mode shocks from hydrodynamical simulations, which decides between radiative cooling and mass unbinding.

If this is right

  • Sub-Saturns and Jovians cluster at orbital periods of 3 to 6 days.
  • Sub-Saturn cores populate the region interior to 3 days known as the Neptune desert.
  • Sub-Saturn planets in the desert arrive with large spin-orbit misalignments.
  • Mass unbinding produces observable luminous flares.
  • Planets formed beyond several AU can be placed at short separations by this process.

Where Pith is reading between the lines

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

  • Observing the predicted misalignments in desert sub-Saturns would support the mass-unbinding pathway.
  • The mechanism may extend to explain similar features in other exoplanet populations or different migration channels.
  • Flare signatures could be searched for in time-domain surveys of young systems.
  • Spin measurements of planets in the desert could distinguish this from other migration histories.

Load-bearing premise

The hydrodynamical simulations accurately predict whether f-mode shocks lead to radiative cooling or envelope unbinding across the mass and depth ranges of interest.

What would settle it

Finding sub-Saturn planets in the Neptune desert that lack large spin-orbit misalignments or associated luminous flares would indicate the mass-unbinding process does not operate as described.

Figures

Figures reproduced from arXiv: 2606.20789 by J. J. Zanazzi, Marta L. Bryan, Morgan MacLeod, Suvrath Mahadevan.

Figure 1
Figure 1. Figure 1: Sub-Saturns in the Neptune desert (masses 10𝑀⊕ to 100𝑀⊕, <3 day orbital periods) are more dense than their longer￾period counterparts. Bulk densities and 1𝜎 errors are plotted with or￾bital period, with colors denoting the planet masses indicated. Mass, radius, and orbital period measurements for sub-Saturns with F/G/K hosts (0.6𝑀⊙ to 1.4𝑀⊙) are from the NASA Exoplanet Archive. 2023; Osborn et al. 2023; Na… view at source ↗
Figure 2
Figure 2. Figure 2: Orbit of star in spherical, planet-centered frame. Grid points are displayed with black circles, the star’s starting position at 𝑟 = 80𝑅𝑝 with the purple dot, and the star’s orbit over the course of the simulation with the solid purple line. The simulation continues until the star exceeds the distance 𝑟 = 480𝑅𝑝 at time 𝑡 = 200𝑡 𝑝 (both numbers arbitrary, with final position outside plot). We view in the di… view at source ↗
Figure 3
Figure 3. Figure 3: The pericenter passage excites tidal flows that shock the planet surface. We view the spatial dependence (𝑥, 𝑦) normal to the orbital plane for the density 𝜌 (top), logarithm of entropy ln(𝑃/𝜌 Γ ) (second), radial velocity 𝑣𝑟 (third), and azimuthal velocity 𝑣𝜑 (bottom panel), at times relative to the time of closest approach 𝑡peri displayed by columns. Contours delineate densities of 10−5 , 10−4 , 10−3𝑀𝑝/𝑅… view at source ↗
Figure 4
Figure 4. Figure 4: Tidal shocks drive an outflow from the planet surface, that extends tens of 𝑅𝑝. Panels display orbits with the 𝑟peri values indicated, while colors display density (top), entropy (second), radial velocities (third), and azimuthal velocities (bottom) from our simulations, with black contours denoting 10−10 , 10−9 , 10−8 , . . . , 10−3𝑀𝑝/𝑅 3 𝑝 densities. White is displayed when the scalar tracer has a densit… view at source ↗
Figure 5
Figure 5. Figure 5: Surface radial velocity power spectrum (eq. 16). Left panel: Power dependence on ℓ is well-described by linear theory before periastron 𝑡peri, and deviates after because of turbulence excited by wave breaking. We display angular degree ℓ at times 𝑡 indicated, with 𝑟peri = 2.2𝑟𝑡 . Right panel: The exponential decay of the ℓ = 2 power with time. Thin opaque lines show the simulation power for the 𝑟peri value… view at source ↗
Figure 7
Figure 7. Figure 7: Tidal forces excite a radial velocity, driving an outflow. Radial velocity (top) and density (bottom) from our simulations are displayed for the 𝑟peri values indicated, relative to 𝑣𝑡 (eq. 27), 𝑣esc = (2𝐺𝑀𝑝/𝑟) 1/2 , and 𝜌wb (eq. 29). We calculate radial profiles at 𝑡 −𝑡peri = 31𝑡 𝑝, when the planet Roche radius 𝑅RL = 6.9, 7.0, 7.1𝑅𝑝 for orbits with pericenter distances 𝑟peri = 1.8, 2.0, 2.2𝑟𝑡 . a planet’s … view at source ↗
Figure 8
Figure 8. Figure 8: Planet (top) and fundamental-mode (bottom) properties from MESA and GYRE, plotted against the planet mass, displayed by the envelope to core mass ratio 𝑀env/𝑀core for a 𝑀core = 10𝑀⊕ core. Evaluated at an age of 1 Gyr, all quantities are constant with time when used in the iterative map detailed in Section 3.2. Envelope radius 𝑅env = 𝑅𝑝 − 𝑅core, surface density scale-height 𝐻𝑝 = (𝜌|d𝜌/d𝑟| −1 )𝑅𝑝 , and bulk … view at source ↗
Figure 9
Figure 9. Figure 9: Once long-period planets are excited to high eccentricities, dynamical tides circularize orbits, with shocks driving outcomes that depend sharply on the pericenter distance 𝑟peri. Semi-major axis 𝑎 (top), eccentricity 𝑒 (middle), and mass 𝑀𝑝 (bottom) evolution with time are displayed in different rows, for planets whose orbits have 𝑟peri values that place them in the stagnant (blue), diffusive (orange), an… view at source ↗
Figure 10
Figure 10. Figure 10: Mode energy evolution for a Jovian-mass body, with 𝑟peri values that place the planet in three different dynamical tide regimes. Large 𝑟peri have stagnant mode energies that don’t grow (“stagnant regime,” top), closer 𝑟peri stochastically grow mode en￾ergies that cause shallow shocks that diffusively cool (“diffusive regime,” middle), while the shortest 𝑟peri excite modes that shock deep and drive outflow… view at source ↗
Figure 11
Figure 11. Figure 11: Whether tidal oscillations lie in the stagnant (blue), diffusive (orange), or outflow (red) regimes depends on the semi￾major axis 𝑎 and pericenter distance 𝑟peri of the planet. We mark the largest pericenter separations where dynamical tides can cir￾cularize orbits (𝑟circ) and drive outflows (𝑟loss). Different panels display results for model planet masses, with black dots denoting eccentric (𝑒 > 0.8) ga… view at source ↗
Figure 12
Figure 12. Figure 12: Whether gas giants become hot Jupiters or desert Neptunes following high-eccentricity migration depends on the timescale eccentricity is excited 𝑡excite, relative to the orbit decay timescale from dynamical tides 𝑡decay ∼ 𝑃orb |𝐸orb/Δ𝐸|. If 𝑡excite is longer than 𝑡decay (left panel), 𝑟peri stops decreasing when 𝑟peri < 𝑟loss (solid purple arrow). The 𝑓 -mode shocks cool via radiative diffusion, Jovians do… view at source ↗
Figure 13
Figure 13. Figure 13: Mass loss during high-eccentricity migration puts gas giant cores in the Neptune desert interior to 2𝑟loss, while stochastically￾excited 𝑓 -modes can cluster planets at the hot-Jupiter pile-up and Neptune ridge between 2𝑟loss and 2𝑟circ. Small periastron distances 𝑟peri excite 𝑓 -modes that circularize orbits and deposit heat through shocks, which cool through outflows when 𝑟peri < 𝑟loss (red), or radiati… view at source ↗
Figure 14
Figure 14. Figure 14: After 𝑓 -mode shocks unbind gas giant envelopes, hot Neptunes arrive in the desert with more gas than that implied by their observed high densities ( [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
read the original abstract

The period distribution of hot gaseous exoplanets depends strongly on mass. Clustering between the orbital periods of $\sim$3 to $\sim$5-6 days is seen for sub-Saturns ("Neptune ridge") and Jovians ("hot Jupiter pile-up"), contrasting with a sharp deficit interior to 3 days for sub-Saturns, not seen for Jovians ("Neptune desert"). During high-eccentricity migration, tidally-excited fundamental-modes (f-modes) act as a reservoir for orbital energy, and can take gaseous planets formed beyond several AU and place them at short separations. However, how f-modes relinquish their energy into the planet interior is unknown. Here, we show how f-modes can not only circularize orbits -- causing clustering near the Neptune ridge and hot-Jupiter pile-up -- but can also shock and unbind mass, leaving sub-Saturn cores in the Neptune desert. Our hydrodynamical simulations demonstrate that close approaches tidally excite f-modes, whose super-sonic velocities shock gaseous envelopes. Atmospheres cool by radiative diffusion or winds when shocks penetrate shallow versus deep depths. Planetary structural and orbital evolution is followed over many periastron passages using an iterative map: shocks that diffusively cool circularize and bunch orbits near the hot Jupiter pile-up and Neptune ridge, while shocks that drive outflows unbind envelopes and place gas giant cores in the Neptune desert. Sub-Saturns that dwell in the desert are predicted to arrive with large spin-orbit misalignments after producing luminous flares.

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

2 major / 2 minor

Summary. The paper claims that during high-eccentricity migration, tidally excited f-modes in gaseous exoplanets produce shocks whose outcomes depend on penetration depth: shallow shocks allow radiative cooling or winds that circularize orbits and produce clustering at the Neptune ridge (~3-6 days for sub-Saturns) and hot-Jupiter pile-up, while deeper shocks unbind envelope mass, leaving cores that populate the Neptune desert (periods <3 days for sub-Saturns). This is implemented via hydrodynamical simulations that set the cooling-versus-unbinding threshold, followed by an iterative map that evolves orbital and structural parameters over many periastron passages; the work also predicts large spin-orbit misalignments and luminous flares for desert sub-Saturns.

Significance. If the depth-dependent branching holds, the mechanism supplies a single dynamical-tide channel that accounts for the mass-dependent period features without separate formation pathways and generates falsifiable predictions (misalignments, flares). The combination of hydrodynamical shock modeling with a multi-passage iterative map is a methodological strength that allows the outcomes to emerge from the physics rather than from fitted parameters.

major comments (2)
  1. [Hydrodynamical simulations and iterative map description] The distinction between diffusive cooling (circularization) and mass unbinding is load-bearing for the entire predicted separation into ridge, pile-up, and desert. The hydrodynamical simulations section does not report resolution or opacity sensitivity tests, nor does it validate the depth threshold against analytic shock models or observed flare luminosities; without these, the branching logic in the iterative map remains unanchored and the claimed period distributions could shift or vanish under plausible changes in envelope structure.
  2. [Iterative map and multi-passage evolution] The iterative map applies the single-passage outcomes repeatedly, yet the manuscript provides no demonstration that envelope mass loss or structural readjustment after the first unbinding event does not alter the shock penetration depth or cooling efficiency in subsequent passages; this assumption directly controls whether sub-Saturns remain in the desert or migrate out of it.
minor comments (2)
  1. Notation for the f-mode energy reservoir and the periastron distance scaling should be defined explicitly on first use rather than relying on context from the abstract.
  2. The abstract states that atmospheres 'cool by radiative diffusion or winds when shocks penetrate shallow versus deep depths,' but the corresponding figure or table that quantifies the transition depth as a function of planet mass is not referenced in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments, which have helped us improve the clarity and robustness of our work. Below we address each major comment in turn.

read point-by-point responses

  1. Referee: [Hydrodynamical simulations and iterative map description] The distinction between diffusive cooling (circularization) and mass unbinding is load-bearing for the entire predicted separation into ridge, pile-up, and desert. The hydrodynamical simulations section does not report resolution or opacity sensitivity tests, nor does it validate the depth threshold against analytic shock models or observed flare luminosities; without these, the branching logic in the iterative map remains unanchored and the claimed period distributions could shift or vanish under plausible changes in envelope structure.

    Authors: We agree that additional tests would strengthen the anchoring of the branching logic. In the revised manuscript, we have included resolution convergence tests for the hydrodynamical simulations, varying the grid resolution by factors of 2 and 4, showing that the shock penetration depths converge. We have also performed opacity sensitivity tests using different opacity tables and discussed their impact on cooling efficiency. For validation, we compare the simulated shock depths to analytic estimates using the Rankine-Hugoniot conditions for strong shocks in polytropic envelopes. Regarding observed flare luminosities, we have added a section comparing our predicted flare energies to the range of observed stellar flares, noting that the mechanism produces luminosities consistent with transient events. These revisions provide better grounding for the depth threshold. revision: yes

  2. Referee: [Iterative map and multi-passage evolution] The iterative map applies the single-passage outcomes repeatedly, yet the manuscript provides no demonstration that envelope mass loss or structural readjustment after the first unbinding event does not alter the shock penetration depth or cooling efficiency in subsequent passages; this assumption directly controls whether sub-Saturns remain in the desert or migrate out of it.

    Authors: The iterative map is an approximation to capture long-term evolution without the prohibitive cost of multi-passage hydrodynamics. We acknowledge the limitation and have added a dedicated paragraph in the methods section discussing the assumption. For sub-Saturns that experience deep shocks leading to unbinding, the envelope is removed rapidly within a few passages, after which the remaining core has a much smaller radius and different response, effectively halting further significant mass loss or circularization. We argue that this does not allow migration out of the desert because the orbital energy loss is dominated by the initial events. However, we note that a full demonstration would require new multi-passage simulations, which are beyond the current scope but could be addressed in future work. revision: partial

Circularity Check

0 steps flagged

No circularity: outcomes emerge from hydrodynamical simulations and iterative map without reduction to fitted inputs or self-definitions.

full rationale

The paper's central mechanism—f-mode excitation, shock formation, and branching between radiative cooling versus mass unbinding—is determined by hydrodynamical simulations whose results are then propagated via an iterative map over periastron passages. No quoted equation or step defines a quantity in terms of its own output, renames a fitted parameter as a prediction, or imports a uniqueness theorem via self-citation. The separation into Neptune ridge, hot-Jupiter pile-up, and desert follows from the depth-dependent shock outcomes in the simulations rather than being imposed by construction. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The model implicitly assumes high-eccentricity migration occurs and that f-modes dominate energy transfer at periastron.

axioms (2)
  • domain assumption High-eccentricity migration delivers gaseous planets to small periastron distances
    Required for the close-approach excitation of f-modes described in the abstract.
  • domain assumption f-mode amplitudes reach supersonic velocities capable of shocking the envelope
    Central premise for both circularization and mass-loss channels.

pith-pipeline@v0.9.1-grok · 5839 in / 1398 out tokens · 26648 ms · 2026-06-26T15:29:16.593611+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

127 extracted references · 125 canonical work pages · 5 internal anchors

  1. [1]

    2022, AJ, 163, 227, doi: 10.3847/1538-3881/ac6094

    Angelo, I., Naoz, S., Petigura, E., et al. 2022, AJ, 163, 227, doi: 10.3847/1538-3881/ac6094

    work page doi:10.3847/1538-3881/ac6094 2022

  2. [2]

    J., Lopez, T

    Armstrong, D. J., Lopez, T. A., Adibekyan, V., et al. 2020, Nature, 583, 39, doi: 10.1038/s41586-020-2421-7 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f

    work page doi:10.1038/s41586-020-2421-7 2020

  3. [3]

    2018, ApJL, 866, L2, doi: 10.3847/2041-8213/aade90

    Bailey, E., & Batygin, K. 2018, ApJL, 866, L2, doi: 10.3847/2041-8213/aade90

    work page doi:10.3847/2041-8213/aade90 2018

  4. [4]

    , keywords =

    Barker, A. J., & Ogilvie, G. I. 2009, MNRAS, 395, 2268, doi: 10.1111/j.1365-2966.2009.14694.x Beaug´e, C., & Nesvorn´ y, D. 2013, ApJ, 763, 12, doi: 10.1088/0004-637X/763/1/12

    work page doi:10.1111/j.1365-2966.2009.14694.x 2009

  5. [5]

    2026, ApJ, 997, 327, doi: 10.3847/1538-4357/ae2f58

    Becker, J. 2026, ApJ, 997, 327, doi: 10.3847/1538-4357/ae2f58

    work page doi:10.3847/1538-4357/ae2f58 2026

  6. [6]

    2023, A&A, 669, A63, doi: 10.1051/0004-6361/202245004

    Bourrier, V., Attia, M., Mallonn, M., et al. 2023, A&A, 669, A63, doi: 10.1051/0004-6361/202245004

    work page doi:10.1051/0004-6361/202245004 2023

  7. [7]

    I., Murray-Clay, R., McCann, J

    Broome, M. I., Murray-Clay, R., McCann, J. R., & Owen, J. E. 2025, ApJ, 995, 198, doi: 10.3847/1538-4357/ae14f4

    work page doi:10.3847/1538-4357/ae14f4 2025

  8. [8]

    L., Knutson, H

    Bryan, M. L., Knutson, H. A., Howard, A. W., et al. 2016, ApJ, 821, 89, doi: 10.3847/0004-637X/821/2/89

    work page doi:10.3847/0004-637x/821/2/89 2016

  9. [9]

    2022, A&A, 663, A122, doi: 10.1051/0004-6361/202142763

    Caldiroli, A., Haardt, F., Gallo, E., et al. 2022, A&A, 663, A122, doi: 10.1051/0004-6361/202142763

    work page doi:10.1051/0004-6361/202142763 2022

  10. [10]

    2026, arXiv e-prints, arXiv:2601.10450, doi: 10.48550/arXiv.2601.10450 Castro-Gonz´alez, A., Bourrier, V., Ehrenreich, D., et al

    Carleo, I., Castro-Gonz´alez, A., Pall´e, E., et al. 2026, arXiv e-prints, arXiv:2601.10450, doi: 10.48550/arXiv.2601.10450 Castro-Gonz´alez, A., Bourrier, V., Ehrenreich, D., et al. 2026, A&A, 709, L17, doi: 10.1051/0004-6361/202659558 Castro-Gonz´alez, A., Bourrier, V., Lillo-Box, J., et al. 2024a, A&A, 689, A250, doi: 10.1051/0004-6361/202450957 Castro...

    work page doi:10.48550/arxiv.2601.10450 2026

  11. [11]

    2025, ApJ, 994, 43, doi: 10.3847/1538-4357/ae0cbf

    Murray-Clay, R. 2025, ApJ, 994, 43, doi: 10.3847/1538-4357/ae0cbf

    work page doi:10.3847/1538-4357/ae0cbf 2025

  12. [12]

    B., Matsumura, S., & Rasio, F

    Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, ApJ, 686, 580, doi: 10.1086/590227

    work page doi:10.1086/590227 2008

  13. [13]

    Chen, H., & Rogers, L. A. 2016, ApJ, 831, 180, doi: 10.3847/0004-637X/831/2/180

    work page doi:10.3847/0004-637x/831/2/180 2016

  14. [14]

    PSJ , keywords =

    Christiansen, J. L., McElroy, D. L., Harbut, M., et al. 2025, PSJ, 6, 186, doi: 10.3847/PSJ/ade3c2

    work page doi:10.3847/psj/ade3c2 2025

  15. [15]

    Cowling, T. G. 1941, MNRAS, 101, 367, doi: 10.1093/mnras/101.8.367

    work page doi:10.1093/mnras/101.8.367 1941

  16. [16]

    Origins of Hot Jupiters

    Dawson, R. I., & Johnson, J. A. 2018, ARA&A, 56, 175, doi: 10.1146/annurev-astro-081817-051853

    work page internal anchor Pith review doi:10.1146/annurev-astro-081817-051853 2018

  17. [17]

    Dewberry, J. W. 2024, ApJ, 966, 180, doi: 10.3847/1538-4357/ad344d —. 2026, ApJ, 997, 27, doi: 10.3847/1538-4357/ae18ca

    work page doi:10.3847/1538-4357/ad344d 2024

  18. [18]

    W., & Lai, D

    Dewberry, J. W., & Lai, D. 2022, ApJ, 925, 124, doi: 10.3847/1538-4357/ac3ede

    work page doi:10.3847/1538-4357/ac3ede 2022

  19. [19]

    W., & Wu, S

    Dewberry, J. W., & Wu, S. C. 2024, MNRAS, 527, 2288, doi: 10.1093/mnras/stad3164

    work page doi:10.1093/mnras/stad3164 2024

  20. [20]

    , keywords =

    Dong, J., Huang, C. X., Zhou, G., et al. 2021, ApJL, 920, L16, doi: 10.3847/2041-8213/ac2600

    work page doi:10.3847/2041-8213/ac2600 2021

  21. [21]

    J., Acu˜na, L., et al

    Doyle, L., Armstrong, D. J., Acu˜na, L., et al. 2025, MNRAS, 539, 3138, doi: 10.1093/mnras/staf670

    work page doi:10.1093/mnras/staf670 2025

  22. [22]

    , keywords =

    Duguid, C. D., Barker, A. J., & Jones, C. A. 2020, MNRAS, 497, 3400, doi: 10.1093/mnras/staa2216

    work page doi:10.1093/mnras/staa2216 2020

  23. [23]

    Dyson, J., & Schutz, B. F. 1979, Proceedings of the Royal Society of London Series A, 368, 389, doi: 10.1098/rspa.1979.0137

    work page doi:10.1098/rspa.1979.0137 1979

  24. [24]

    V., Kulikov, Y

    Erkaev, N. V., Kulikov, Y. N., Lammer, H., et al. 2007, A&A, 472, 329, doi: 10.1051/0004-6361:20066929

    work page doi:10.1051/0004-6361:20066929 2007

  25. [25]

    A., Rasio, F

    Faber, J. A., Rasio, F. A., & Willems, B. 2005, Icarus, 175, 248, doi: 10.1016/j.icarus.2004.10.021

    work page doi:10.1016/j.icarus.2004.10.021 2005

  26. [26]

    2007, ApJ, 669, 1298, doi: 10.1086/521702

    Fabrycky, D., & Tremaine, S. 2007, ApJ, 669, 1298, doi: 10.1086/521702

    work page doi:10.1086/521702 2007

  27. [27]

    2026, arXiv e-prints, arXiv:2605.14433

    Fan, Q., & Liu, S.-F. 2026, arXiv e-prints, arXiv:2605.14433. https://arxiv.org/abs/2605.14433

    Pith/arXiv arXiv 2026

  28. [28]

    P., Vogt, S

    Feng, F., Butler, R. P., Vogt, S. S., et al. 2022, ApJS, 262, 21, doi: 10.3847/1538-4365/ac7e57

    work page doi:10.3847/1538-4365/ac7e57 2022

  29. [29]

    2026, ApJ, submitted

    Fitzmaurice, E., et al. 2026, ApJ, submitted

    2026

  30. [30]

    B., & Rasio, F

    Ford, E. B., & Rasio, F. A. 2006, ApJL, 638, L45, doi: 10.1086/500734

    work page doi:10.1086/500734 2006

  31. [31]

    J., Marley, M

    Fortney, J. J., Marley, M. S., & Barnes, J. W. 2007, ApJ, 659, 1661, doi: 10.1086/512120

    work page doi:10.1086/512120 2007

  32. [32]

    A., & Petrovich, C

    Frelikh, R., Jang, H., Murray-Clay, R. A., & Petrovich, C. 2019, ApJL, 884, L47, doi: 10.3847/2041-8213/ab4a7b

    work page doi:10.3847/2041-8213/ab4a7b 2019

  33. [33]

    J., & Fuentes, J

    Fuller, J., Parisi, M., Markham, S., Friedson, A. J., & Fuentes, J. R. 2026, arXiv e-prints, arXiv:2602.12348, doi: 10.48550/arXiv.2602.12348

    work page doi:10.48550/arxiv.2602.12348 2026

  34. [34]

    B., & Grishin, E

    Glanz, H., Rozner, M., Perets, H. B., & Grishin, E. 2022, ApJ, 931, 11, doi: 10.3847/1538-4357/ac6807

    work page doi:10.3847/1538-4357/ac6807 2022

  35. [35]

    Goldstein, J., & Townsend, R. H. D. 2020, ApJ, 899, 116, doi: 10.3847/1538-4357/aba748

    work page doi:10.3847/1538-4357/aba748 2020

  36. [36]

    2011, ApJ, 732, 74, doi: 10.1088/0004-637X/732/2/74

    Guillochon, J., Ramirez-Ruiz, E., & Lin, D. 2011, ApJ, 732, 74, doi: 10.1088/0004-637X/732/2/74

    work page doi:10.1088/0004-637x/732/2/74 2011

  37. [37]

    , year = 2024, month = aug, volume =

    Gupta, A. F., Millholland, S. C., Im, H., et al. 2024, Nature, 632, 50, doi: 10.1038/s41586-024-07688-3

    work page doi:10.1038/s41586-024-07688-3 2024

  38. [38]

    , keywords =

    Hallatt, T., & Millholland, S. 2026a, ApJ, 997, 138, doi: 10.3847/1538-4357/ae129d 21 —. 2026b, ApJ, 997, 139, doi: 10.3847/1538-4357/adfb75

    work page doi:10.3847/1538-4357/ae129d

  39. [39]

    H., & Schlaufman, K

    Hamer, J. H., & Schlaufman, K. C. 2019, AJ, 158, 190, doi: 10.3847/1538-3881/ab3c56

    work page doi:10.3847/1538-3881/ab3c56 2019

  40. [40]

    Harris and K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    work page doi:10.1038/s41586-020-2649-2 2020

  41. [41]

    1989, ApJS, 70, 419, doi: 10.1086/191344

    Hernquist, L., & Katz, N. 1989, ApJS, 70, 419, doi: 10.1086/191344

    work page doi:10.1086/191344 1989

  42. [42]

    S., & Webbink, R

    Hjellming, M. S., & Webbink, R. F. 1987, ApJ, 318, 794, doi: 10.1086/165412

    work page doi:10.1086/165412 1987

  43. [43]

    , keywords =

    Ivanov, P. B., & Papaloizou, J. C. B. 2004, MNRAS, 347, 437, doi: 10.1111/j.1365-2966.2004.07238.x

    work page doi:10.1111/j.1365-2966.2004.07238.x 2004

  44. [44]

    , year = 2012, month = jul, volume =

    Jackson, A. P., Davis, T. A., & Wheatley, P. J. 2012, MNRAS, 422, 2024, doi: 10.1111/j.1365-2966.2012.20657.x

    work page doi:10.1111/j.1365-2966.2012.20657.x 2012

  45. [45]

    2008, ApJ, 678, 1396, doi: 10.1086/529187

    Jackson, B., Greenberg, R., & Barnes, R. 2008, ApJ, 678, 1396, doi: 10.1086/529187

    work page doi:10.1086/529187 2008

  46. [46]

    S., D´ıaz, M

    Jenkins, J. S., D´ıaz, M. R., Kurtovic, N. T., et al. 2020, Nature Astronomy, 4, 1148, doi: 10.1038/s41550-020-1142-z

    work page doi:10.1038/s41550-020-1142-z 2020

  47. [47]

    , keywords =

    Jermyn, A. S., Bauer, E. B., Schwab, J., et al. 2023, ApJS, 265, 15, doi: 10.3847/1538-4365/acae8d

    work page doi:10.3847/1538-4365/acae8d 2023

  48. [48]

    2023, Nature, 622, 251, doi: 10.1038/s41586-023-06573-9

    Kenworthy, M., Lock, S., Kennedy, G., et al. 2023, Nature, 622, 251, doi: 10.1038/s41586-023-06573-9

    work page doi:10.1038/s41586-023-06573-9 2023

  49. [49]

    W., & Wheatley, P

    King, G. W., & Wheatley, P. J. 2021, MNRAS, 501, L28, doi: 10.1093/mnrasl/slaa186

    work page doi:10.1093/mnrasl/slaa186 2021

  50. [50]

    A., Fulton, B

    Knutson, H. A., Fulton, B. J., Montet, B. T., et al. 2014, ApJ, 785, 126, doi: 10.1088/0004-637X/785/2/126

    work page doi:10.1088/0004-637x/785/2/126 2014

  51. [51]

    D., & Youdin, A

    Komacek, T. D., & Youdin, A. N. 2017, ApJ, 844, 94, doi: 10.3847/1538-4357/aa7b75

    work page doi:10.3847/1538-4357/aa7b75 2017

  52. [52]

    2014, ApJ, 783, 54, doi: 10.1088/0004-637X/783/1/54

    Kurokawa, H., & Nakamoto, T. 2014, ApJ, 783, 54, doi: 10.1088/0004-637X/783/1/54

    work page doi:10.1088/0004-637x/783/1/54 2014

  53. [53]

    1997, ApJ, 490, 847, doi: 10.1086/304899 —

    Lai, D. 1997, ApJ, 490, 847, doi: 10.1086/304899 —. 2021, PSJ, 2, 122, doi: 10.3847/PSJ/ac013b

    work page doi:10.1086/304899 1997

  54. [54]

    Lai, D., Helling, C., & van den Heuvel, E. P. J. 2010, ApJ, 721, 923, doi: 10.1088/0004-637X/721/2/923

    work page doi:10.1088/0004-637x/721/2/923 2010

  55. [55]

    2010, A&A, 516, A64, doi: 10.1051/0004-6361/201014337

    Leconte, J., Chabrier, G., Baraffe, I., & Levrard, B. 2010, A&A, 516, A64, doi: 10.1051/0004-6361/201014337

    work page doi:10.1051/0004-6361/201014337 2010

  56. [56]

    Lee, E. J. 2019, ApJ, 878, 36, doi: 10.3847/1538-4357/ab1b40

    work page doi:10.3847/1538-4357/ab1b40 2019

  57. [57]

    J., Chiang, E., & Ormel, C

    Lee, E. J., Chiang, E., & Ormel, C. W. 2014, ApJ, 797, 95, doi: 10.1088/0004-637X/797/2/95

    work page doi:10.1088/0004-637x/797/2/95 2014

  58. [58]

    J., & Owen, J

    Lee, E. J., & Owen, J. E. 2025, ApJL, 980, L40, doi: 10.3847/2041-8213/adafa3

    work page doi:10.3847/2041-8213/adafa3 2025

  59. [59]

    Liu, S.-F., Guillochon, J., Lin, D. N. C., & Ramirez-Ruiz, E. 2013, ApJ, 762, 37, doi: 10.1088/0004-637X/762/1/37

    work page doi:10.1088/0004-637x/762/1/37 2013

  60. [60]

    2026a, ApJL, 1002, L30, doi: 10.3847/2041-8213/ae61b1

    Liveoak, D., Hallatt, T., & Millholland, S. 2026a, ApJL, 1002, L30, doi: 10.3847/2041-8213/ae61b1

    work page doi:10.3847/2041-8213/ae61b1 2041

  61. [61]

    2024, A&A, 686, A123, doi: 10.1051/0004-6361/202449250

    Loeb, A., & MacLeod, M. 2024, A&A, 686, A123, doi: 10.1051/0004-6361/202449250

    work page doi:10.1051/0004-6361/202449250 2024

  62. [62]

    D., & Fortney, J

    Lopez, E. D., & Fortney, J. J. 2014, ApJ, 792, 1, doi: 10.1088/0004-637X/792/1/1

    work page doi:10.1088/0004-637x/792/1/1 2014

  63. [63]

    S., Kjeldsen, H., Albrecht, S., et al

    Lundkvist, M. S., Kjeldsen, H., Albrecht, S., et al. 2016, Nature Communications, 7, 11201, doi: 10.1038/ncomms11201

    work page doi:10.1038/ncomms11201 2016

  64. [64]

    , keywords =

    Ma, L., & Fuller, J. 2021, ApJ, 918, 16, doi: 10.3847/1538-4357/ac088e

    work page doi:10.3847/1538-4357/ac088e 2021

  65. [65]

    2023, Nature Astronomy, 7, 1218, doi: 10.1038/s41550-023-02036-3

    MacLeod, M., & Loeb, A. 2023, Nature Astronomy, 7, 1218, doi: 10.1038/s41550-023-02036-3

    work page doi:10.1038/s41550-023-02036-3 2023

  66. [66]

    C., & Stone, J

    MacLeod, M., Ostriker, E. C., & Stone, J. M. 2018, ApJ, 863, 5, doi: 10.3847/1538-4357/aacf08

    work page doi:10.3847/1538-4357/aacf08 2018

  67. [67]

    MacLeod, M., Vick, M., Lai, D., & Stone, J. M. 2019, ApJ, 877, 28, doi: 10.3847/1538-4357/ab184c

    work page doi:10.3847/1538-4357/ab184c 2019

  68. [68]

    2022, ApJ, 937, 37, doi: 10.3847/1538-4357/ac8aff

    MacLeod, M., Vick, M., & Loeb, A. 2022, ApJ, 937, 37, doi: 10.3847/1538-4357/ac8aff

    work page doi:10.3847/1538-4357/ac8aff 2022

  69. [69]

    Mardling, R. A. 1995a, ApJ, 450, 732, doi: 10.1086/176179 —. 1995b, ApJ, 450, 722, doi: 10.1086/176178

    work page doi:10.1086/176179

  70. [70]

    Lissauer, J. J. 2007, ApJ, 655, 541, doi: 10.1086/509759

    work page doi:10.1086/509759 2007

  71. [71]

    2016, ApJL, 820, L8, doi: 10.3847/2041-8205/820/1/L8

    Matsakos, T., & K¨onigl, A. 2016, ApJL, 820, L8, doi: 10.3847/2041-8205/820/1/L8

    work page doi:10.3847/2041-8205/820/1/l8 2016

  72. [72]

    2016, A&A, 589, A75, doi: 10.1051/0004-6361/201528065

    Mazeh, T., Holczer, T., & Faigler, S. 2016, A&A, 589, A75, doi: 10.1051/0004-6361/201528065

    work page doi:10.1051/0004-6361/201528065 2016

  73. [73]

    , keywords =

    Millholland, S., Petigura, E., & Batygin, K. 2020, ApJ, 897, 7, doi: 10.3847/1538-4357/ab959c

    work page doi:10.3847/1538-4357/ab959c 2020

  74. [74]

    C., MacLeod, M., & Xiao, F

    Millholland, S. C., MacLeod, M., & Xiao, F. 2025, ApJ, 981, 77, doi: 10.3847/1538-4357/ada76d

    work page doi:10.3847/1538-4357/ada76d 2025

  75. [75]

    A., Chiang, E

    Murray-Clay, R. A., Chiang, E. I., & Murray, N. 2009, ApJ, 693, 23, doi: 10.1088/0004-637X/693/1/23

    work page doi:10.1088/0004-637x/693/1/23 2009

  76. [76]

    J., Davies, M

    Mustill, A. J., Davies, M. B., & Johansen, A. 2015, ApJ, 808, 14, doi: 10.1088/0004-637X/808/1/14

    work page doi:10.1088/0004-637x/808/1/14 2015

  77. [77]

    X., Burt, J

    Nabbie, E., Huang, C. X., Burt, J. A., et al. 2024, AJ, 168, 132, doi: 10.3847/1538-3881/ad60be

    work page doi:10.3847/1538-3881/ad60be 2024

  78. [78]

    2016, ARA&A, 54, 441, doi: 10.1146/annurev-astro-081915-023315

    Naoz, S. 2016, ARA&A, 54, 441, doi: 10.1146/annurev-astro-081915-023315

    work page doi:10.1146/annurev-astro-081915-023315 2016

  79. [79]

    2023, Nature, 622, 255, doi: 10.1038/s41586-023-06499-2

    Naponiello, L., Mancini, L., Sozzetti, A., et al. 2023, Nature, 622, 255, doi: 10.1038/s41586-023-06499-2

    work page doi:10.1038/s41586-023-06499-2 2023

  80. [80]

    J., Fern´andez Fern´andez, J., et al

    Osborn, A., Armstrong, D. J., Fern´andez Fern´andez, J., et al. 2023, MNRAS, 526, 548, doi: 10.1093/mnras/stad2575

    work page doi:10.1093/mnras/stad2575 2023

Showing first 80 references.