Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

A generic gas disk clearing from the inside out reproduces the Kuiper Cliff—the abrupt outer edge of the Cold Classical Kuiper belt—and its surface density, with no fine-tuning.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-02 11:23 UTC pith:VJS3FXAP

load-bearing objection A plausible but conditional explanation for the Kuiper Cliff that hinges on wind-driven clearing and has an untested gas–dust coupling inconsistency. the 3 major comments →

arxiv 2606.14704 v2 pith:VJS3FXAP submitted 2026-06-12 astro-ph.EP

The Edges of Planetary Systems: Falling Off the Kuiper Cliff in a Dissipating Gas Disk

Rixin Li , Eugene Chiang This is my paper
classification astro-ph.EP
keywords Kuiper CliffCold Classical Kuiper beltplanetesimal formationstreaming instabilityprotoplanetary disk dispersalmagnetized disk windphotoevaporationdust evolution
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that the Kuiper Cliff, the sharp drop in Cold Classical Kuiper belt objects beyond about 47 au, is a natural consequence of how the solar nebula dispersed: from the inside out. As the gas disk erodes, its expanding inner edge acts as a moving pressure maximum that gathers drifting dust, triggers the streaming instability, and lays down a disk of planetesimals. When the dust supply runs out, the planetesimal disk truncates, leaving a cliff. Using a global 1D model with generic parameters, the authors match both the location (~40–50 au) and the surface density (~1e-4 g/cm^2) of the observed belt. If correct, this ties the outer edge of the Kuiper belt directly to the mechanism of disk dispersal and gives a new way to read planetesimal formation from debris disk edges.

Core claim

The central claim is that the Kuiper Cliff and the CCKB surface density are reproduced by a gas disk that clears from the inside out under the combined action of a magnetized disk wind and photoevaporation, without fine-tuning. In the fiducial simulation, the planetesimal surface density crosses the observed CCKB value of Σ_CCKB = 1e-4 g/cm^2 at r ≈ 42 au and truncates between 40 and 50 au, matching the belt's observed outer edge. The mechanism is an outward-moving 'main dust spike' that follows the expanding inner edge of the gas disk; dust drifts toward this pressure maximum, grows, and the streaming instability converts it into planetesimals. The truncation follows from the finite dust ma

What carries the argument

The central object is the outward-propagating 'main dust spike'—a local maximum in dust surface density that tracks the receding inner edge (pressure bump) of the clearing gas disk. Dust drifts toward this pressure maximum, piles up, and reaches Stokes numbers large enough for the streaming instability to operate. Planetesimal formation is triggered when two criteria are met: the midplane density of dust particles with St > 0.1 exceeds the midplane gas density (criterion 8), and the gas surface density exceeds about 3% of the minimum-mass solar nebula (criterion 9), ensuring that compressed dust can exceed the Roche density. Planetesimals then decouple from the gas and remain in place as the

Load-bearing premise

The model assumes the solar nebula dispersed from the inside out primarily because angular momentum was transported by a magnetized disk wind rather than by turbulent viscosity; the viscosity-only alternative fails to form the Kuiper belt at all.

What would settle it

A deep survey of the trans-Neptunian region that finds a substantial population of cold classical bodies beyond 50 au with surface density comparable to Σ_CCKB would falsify the predicted truncation. Equivalently, evidence that angular momentum transport at 10–50 au in the solar nebula was dominated by turbulence (e.g., a viscosity parameter α comparable to or exceeding the wind torque) would invalidate the inside-out clearing wave the model requires.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The outer edge of a planetary system's first-generation planetesimal disk is set by the finite dust supply and the speed of disk clearing, not by an arbitrary outer boundary.
  • Systems whose disks clear via magnetized winds should show a characteristic radial profile in their debris/planetesimal disks: a sharp outer edge at tens of au with a surface density near 1e-4 g/cm^2.
  • The model implies the Cold Classical Kuiper belt formed in situ and was later stirred (e.g., by Neptune's migration) to its present eccentricities and inclinations, providing a timing constraint on the dynamical instability.
  • If the solar nebula had accreted primarily by turbulence rather than by a magnetized wind, the model predicts essentially no Cold Classical Kuiper belt—so the existence of the CCKB becomes evidence for magnetized wind accretion.
  • The truncation radius is robust to factor-of-ten variations in dust-to-gas ratio, initial grain size, and planetesimal formation efficiency, making the 40–50 au edge a stable prediction.

Where Pith is reading between the lines

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

  • The same mechanism could be tested on extrasolar debris disks: if most disks clear via winds, the radial edges of their planetesimal belts should correlate with disk dispersal timescales and dust masses, a population-level prediction beyond this paper.
  • Because planetesimal formation in the outer system occurs very late in the disk lifetime (the last ~1 Myr), CCKBOs might carry chemical or isotopic signatures of a gas-poor, low-pressure formation environment—an observable extension.
  • The model suggests a general rule: the location of a debris disk's sharp edge may encode the clearing history of its parent gas disk, allowing future surveys to infer dispersal physics from edge morphology alone.
  • If future observations find a significant population of small cold classical bodies beyond 50 au, the truncation mechanism would be immediately falsified, making this a clean test of the inside-out clearing scenario.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents global, 1D (radial) dust evolution models (DustPy-GPU) embedded in time-dependent gas disk models from Kunitomo et al. (2020, KSI20). In the fiducial run (MDW+PEW, Model C-i), the gas disk clears from the inside out; a pressure maximum at the expanding cavity edge collects dust, triggers the streaming instability, and leaves behind a planetesimal disk. The surface density crosses the observed CCKB value Σ_CCKB ≈ 1e-4 g/cm^2 at r ≈ 42 au and truncates near 40–50 au. The result is tested against variations in Z, ζ, the minimum-gas criterion, and an additional Π threshold; a PEW-only model fails to produce a CCKB. The authors argue the scenario is generic and requires no fine-tuning.

Significance. If correct, the paper offers a compelling origin for the Kuiper Cliff: it emerges naturally from inside-out clearing of a wind-driven disk, with the truncation radius and surface density matching observations to order unity. The parameter exploration and resolution test strengthen the qualitative picture, and the connection to local SI simulations of Li & Chiang (2025) provides a coherent multi-scale narrative. However, the quantitative claim of 'no fine-tuning' is weakened by the calibration of formation criteria to CCKB properties, and the omission of wind-driven gas advection in the dust transport leaves a key modeling uncertainty that needs to be addressed before the central prediction can be accepted.

major comments (3)
  1. [Section 2.2, Eqs. (2)–(4), footnote 1] The dust transport equations use v_g = A v_visc + 2B ηv_K, with v_visc ∝ α (Eq. 4). In Run Fid, α is set to 0, so the dust is advected neither by viscous diffusion nor by the wind-driven radial flow that actually evacuates the KSI20 Model C-i gas disk. The footnoted justification that the inconsistency is small because accretion is MDW-dominated is not quantified. Since the central result depends on the trajectory of the main dust spike, please provide a control run that either includes α = 8e-5 in DustPy or adds an explicit wind-advection term, and report the resulting crossing radius and Σ_pl. Without this, the fiducial prediction may be an artifact of decoupling dust from the clearing gas.
  2. [Section 3.1, Eqs. (7)–(9)] The planetesimal formation criteria (Eqs. 8–9) and ζ = 1e-4 are taken from Li & Chiang (2025), a model designed to reproduce CCKB properties (mass, sizes, binary fraction). Using these criteria in a global model and finding Σ_pl ≈ Σ_CCKB at 40–50 au is therefore partially a consistency test, not an independent prediction. The phrase 'with no fine-tuning' in the abstract is too strong. Please either (i) demonstrate that the match is insensitive to order-of-magnitude changes in the criteria derived from independent SI simulations, or (ii) soften the claim and discuss the degree of inherited calibration.
  3. [Section 3.2] The PEW-only run (viscous α = 8e-5 + photoevaporation) also clears the disk from the inside out, but produces essentially no CCKB (0.03 M⊕ in a single cell). Thus the mechanism does not operate for generic inside-out clearing; it requires fast, MDW-dominated cavity expansion. The abstract's phrase 'generic gas disk clearing from the inside out' is therefore misleading. Please qualify the summary to 'wind-driven inside-out clearing' and discuss the PEW failure in the abstract or Section 4.
minor comments (5)
  1. [Title] The title contains a spacing artifact: 'F alling' should be 'Falling'.
  2. [Section 2.2, Eq. (7)] The units of ζ are not explicitly stated; clarify that ζ is the formation efficiency per dynamical time (Ω^-1) for St = 1 particles.
  3. [Figure 2 caption] The caption says 'triangles in the bottom row' but the bottom row appears to be a color map; clarify what markers are being referenced.
  4. [Section 3.1, first paragraph] The phrase 'fortuitously close' is subjective; consider replacing with 'close'.
  5. [Table 1] For Fid-hiZ, the final dust mass (475 M⊕) plus planetesimal mass (230.9 M⊕) is less than the initial dust mass (951.2 M⊕); state whether the remainder is lost through the boundaries or converted into other forms.

Circularity Check

0 steps flagged

No significant circularity: the Kuiper Cliff and CCKB surface density emerge from an externally provided gas disk model rather than from the fitted parameters by construction.

full rationale

The derivation chain is: KSI20 gas disk models (external, containing no information about the Kuiper belt) -> DustPy-GPU dust transport -> SI-based planetesimal formation prescription -> comparison to observed Sigma_CCKB. The paper never fits a parameter to the observed 42-47 au edge or to Sigma_CCKB ~ 1e-4; the gas surface densities, temperatures, and scale heights are taken directly from KSI20 and interpolated, with no feedback loop from the CCKB. The formation efficiency zeta and the criteria in eqs. (8) and (9) are inherited from Li & Chiang 2025 and Li & Youdin 2021, which are prior, published local simulations; those simulations addressed CCKB object sizes, numbers, and binaries, but not the global radial truncation at the Kuiper Cliff. The paper supplies the previously missing global backstory. Robustness tests show the cliff radius is not controlled by a tuned threshold: changing the eq. (9) minimum gas density by an order of magnitude (Fid-Sigma) moves the outer edge only from ~49 to ~55 au, and varying zeta by 10x does not alter the results. The PEW-only run fails to reproduce the CCKB, so the model is falsifiable rather than constructed to match. The acknowledged inconsistencies (footnote 1: alpha=0 versus KSI20 Model C-i's alpha=8e-5; the broader self-consistency caveat in Section 2) are physical limitations that could affect accuracy, but they do not make the output equal to an input. The authors themselves describe the near-perfect radius match as partly fortuitous, and no uniqueness theorem, self-citation chain, or ansatz-from-self-citation is used to force the conclusion. Thus the central claim has independent content and no significant circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The model's central claim rests on several calibrated parameters and adopted gas-disk models. The outer truncation itself is not fitted, but the planetesimal formation recipe is inherited from the authors' prior simulations, so the quantitative match is partly a re-test of those simulations.

free parameters (5)
  • Initial global dust-to-gas ratio Z = 0.01 (fiducial); varied 0.003–0.03
    Sets the total dust mass available for planetesimal formation; chosen as standard ISM value and varied for robustness.
  • Planetesimal formation efficiency ζ = 1e-4 (per dynamical time)
    Motivated by Runs C and D of Li & Chiang (2025); varied to 1e-3 without changing results.
  • Minimum gas threshold for SI clumping to exceed Roche density (eq. 9) = 0.03 Σ_MMSN
    Translated from Li & Chiang (2025) simulations; varied to 0.003 in Run Fid-Σ, still reproducing the outer edge.
  • Dust diffusivity δ mapping = δ = 1e-6 for St≤0.01, δ = 1e-4 for St≥0.5, curve from Li & Youdin (2021)
    Used in eq. (10) for dust diffusion; endpoints simplified, not tuned to CCKB.
  • Π* threshold in eq. (14) = 0.01 (most stringent test)
    Added to require nonzero pressure gradient for SI; tested 0.001–0.01, outer edge insensitive.
axioms (4)
  • domain assumption Gas disk evolution is correctly described by KSI20 Model C-i (magnetized wind + photoevaporation)
    The entire paper uses this gas model as input; the PEW (viscous) alternative fails to produce a CCKB, so this assumption is load-bearing.
  • ad hoc to paper The streaming instability behaves in a moving pressure bump as parameterized by Li & Chiang (2025)
    The planetesimal formation criteria (eqs. 8–9) are derived from local bumps-free SI simulations and applied to the expanding cavity wall; the paper tests a Π* criterion but does not directly simulate the bump with SI.
  • domain assumption Dust feedback on gas is negligible
    The DustPy-GPU models are grafted onto KSI20 gas models that ignore dust feedback; the authors argue the local dust-to-gas ratio is always ≪1.
  • domain assumption A 1D radial model captures the essential dynamics of dust drift and planetesimal formation
    The model omits azimuthal structure, 3D instabilities, and detailed gas-dust interactions; the authors connect to 3D simulations only informally.

pith-pipeline@v1.3.0-alltime-deepseek · 241 in / 8688 out tokens · 142449 ms · 2026-08-02T11:23:10.496978+00:00 · methodology

0 comments
read the original abstract

Probably the last planetesimals to have formed from dust in the solar nebula are Cold Classical Kuiper belt objects (CCKBOs). To the extent that they are isolated and unchanged since birth, CCKBOs offer direct insights into nebular processes. Their population density drops abruptly beyond a heliocentric radius of $\sim$47 au, a feature known as the "Kuiper Cliff". We show with global, 1D (radial), time-dependent models how gaseous protoplanetary disks that disperse from magnetic and photoevaporative winds leave behind planetesimal disks with Cliff-like outer edges. The gas disperses from the inside out, creating transitional disks whose inner cavities expand from $\lesssim$ 1 au to $\gtrsim$ 100 au. Gas at the cavity boundary presents a pressure maximum toward which dust particles drift, triggering the streaming instability which clumps dust into planetesimals massive enough to decouple from gas. The receding cavity wall thus paves a disk of planetesimals which truncates when dust and gas are spent. With no fine-tuning, we show how a generic gas disk clearing from the inside out reproduces the Kuiper Cliff and the CCKB surface density. Connecting these global 1D results with published local 3D simulations of dust and gas, we see how many properties of the CCKB -- its radial extent, total mass, individual object sizes, and binary statistics -- follow from the streaming instability at work in a late-stage transition disk.

Figures

Figures reproduced from arXiv: 2606.14704 by Eugene Chiang, Rixin Li.

Figure 1
Figure 1. Figure 1: Snapshots of surface density profiles from Run Fid, which includes a magnetically driven disk wind (MDW), a photoevaporative wind (PEW), and particle diffusivities from gas-dust interactions. Gas profiles (blue) are taken from Model C-i of KSI20, and curves for dust (orange), large-sized dust (green), and planetesimals (red) are computed in-house using DustPy-GPU. The “main dust spike” (coincident orange a… view at source ↗
Figure 2
Figure 2. Figure 2: Space-time diagrams showing the evolution of surface densities (in units of g/cm2 ) and the mass-weighted Stokes number ⟨St⟩ of dust particles in Runs Fid-loZ (left column), Fid (middle column), and Fid-hiZ (right column). The bright yellow streamer in the middle two rows traces the “main spike” of dust particles that moves outward following the expanding inner edge of the gas disk. Planetesimal formation … view at source ↗
Figure 3
Figure 3. Figure 3: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Same surface density snapshot sequence as in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Surface density snapshot sequence for Run PEW which accounts for a photoevaporative wind and replaces the Fid MDW accretion torque with an α = 8 × 10−5 shear viscosity. Unlike the Fid models where the inner gas disk immediately starts clearing from the inside out to create a pressure bump at t ≲ 1 Myr, here for PEW a pressure bump does not appear until after ∼10 Myr, when the viscous accretion rate in the … view at source ↗
Figure 6
Figure 6. Figure 6: Space-time diagrams for Run PEW showing the evolution of surface densities (in units of g/cm2 ) and the mass-weighted Stokes number ⟨St⟩ of dust particles. At t ≲ 10 Myr, prior to the clearing of the inner gas disk, dust particles hardly grow; ⟨St⟩ < 10−2 . At ∼12 Myr, a gas pressure bump and attendant dust spike appear at r ≃ 15 au, enabling planetesimals to form, but only in a single radial grid cell. an… view at source ↗

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Influence of Dust Composition on Accretion Outbursts

    astro-ph.EP 2026-07 conditional novelty 6.0

    Using 1D simulations with dust evaporation and condensation, the paper shows that dead-zone accretion outbursts vaporize dust out to about 0.5 au and that higher dust sublimation temperatures produce stronger but less...

Reference graph

Works this paper leans on

48 extracted references · 4 canonical work pages · cited by 1 Pith paper

  1. [1]

    2014, in Protostars and Planets VI, ed

    Cieza, L. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning, 475–496, doi: 10.2458/azu_uapress_9780816531240-ch021

    doi:10.2458/azu_uapress_9780816531240-ch021 2014

  2. [2]

    D., Clarke, C

    Alexander, R. D., Clarke, C. J., & Pringle, J. E. 2006a, MNRAS, 369, 216, doi: 10.1111/j.1365-2966.2006.10293.x —. 2006b, MNRAS, 369, 229, doi: 10.1111/j.1365-2966.2006.10294.x

    arXiv 2006

  3. [3]

    2016, ApJ, 821, 80, doi: 10.3847/0004-637X/821/2/80

    Bai, X.-N. 2016, ApJ, 821, 80, doi: 10.3847/0004-637X/821/2/80

    doi:10.3847/0004-637x/821/2/80 2016

  4. [4]

    Bai, X.-N., & Stone, J. M. 2010, ApJL, 722, L220, doi: 10.1088/2041-8205/722/2/L220 —. 2013, ApJ, 769, 76, doi: 10.1088/0004-637X/769/1/76

    doi:10.1088/2041-8205/722/2/l220 2010

  5. [5]

    C., Batygin, Y

    Batygin, K., Adams, F. C., Batygin, Y. K., & Petigura, E. A. 2020, AJ, 159, 101, doi: 10.3847/1538-3881/ab665d

    doi:10.3847/1538-3881/ab665d 2020

  6. [6]

    P., & Brauer, F

    Birnstiel, T., Dullemond, C. P., & Brauer, F. 2010, A&A, 513, A79, doi: 10.1051/0004-6361/200913731

    doi:10.1051/0004-6361/200913731 2010

  7. [7]

    2016, SSRv, 205, 41, doi: 10.1007/s11214-016-0256-1

    Birnstiel, T., Fang, M., & Johansen, A. 2016, SSRv, 205, 41, doi: 10.1007/s11214-016-0256-1

    doi:10.1007/s11214-016-0256-1 2016

  8. [8]

    Brown, M. E. 2001, AJ, 121, 2804, doi: 10.1086/320391

    doi:10.1086/320391 2001

  9. [9]

    2010, Annual Review of Earth and Planetary Sciences, 38, 493, doi: 10.1146/annurev-earth-040809-152513

    Chiang, E., & Youdin, A. 2010, Annual Review of Earth and Planetary Sciences, 38, 493, doi: 10.1146/annurev-earth-040809-152513

    doi:10.1146/annurev-earth-040809-152513 2010

  10. [10]

    D., Jankovic, M

    Chiang, E., Pearce, T. D., Jankovic, M. R., et al. 2026, arXiv e-prints, arXiv:2604.19743, doi: 10.48550/arXiv.2604.19743

    Pith/arXiv arXiv doi:10.48550/arxiv.2604.19743 2026

  11. [11]

    I., Joung, M

    Chiang, E. I., Joung, M. K., Creech-Eakman, M. J., et al. 2001, ApJ, 547, 1077, doi: 10.1086/318427

    doi:10.1086/318427 2001

  12. [12]

    J., Gendrin, A., & Sotomayor, M

    Clarke, C. J., Gendrin, A., & Sotomayor, M. 2001, MNRAS, 328, 485, doi: 10.1046/j.1365-8711.2001.04891.x

    arXiv 2001

  13. [13]

    I., & Murray-Clay, R

    Dawson, R. I., & Murray-Clay, R. 2012, ApJ, 750, 43, doi: 10.1088/0004-637X/750/1/43

    work page doi:10.1088/0004-637x/750/1/43 2012

  14. [14]

    C., Bannister, M

    Fraser, W. C., Bannister, M. T., Pike, R. E., et al. 2017, Nature Astronomy, 1, 0088, doi: 10.1038/s41550-017-0088

    doi:10.1038/s41550-017-0088 2017

  15. [15]

    C., Benecchi, S

    Fraser, W. C., Benecchi, S. D., Kavelaars, J. J., et al. 2021, PSJ, 2, 90, doi: 10.3847/PSJ/abf04a

    work page doi:10.3847/psj/abf04a 2021

  16. [16]

    C., Porter, S

    Fraser, W. C., Porter, S. B., Peltier, L., et al. 2024, PSJ, 5, 227, doi: 10.3847/PSJ/ad6f9e Gárate, M., Birnstiel, T., Stammler, S. M., & Günther, H. M. 2019, ApJ, 871, 53, doi: 10.3847/1538-4357/aaf4fc

    doi:10.3847/psj/ad6f9e 2024

  17. [17]

    2021, ARA&A, 59, 203, doi: 10.1146/annurev-astro-120920-010005

    Gladman, B., & Volk, K. 2021, ARA&A, 59, 203, doi: 10.1146/annurev-astro-120920-010005

    doi:10.1146/annurev-astro-120920-010005 2021

  18. [18]

    P., & Hollenbach, D

    Gorti, U., Dullemond, C. P., & Hollenbach, D. 2009, ApJ, 705, 1237, doi: 10.1088/0004-637X/705/2/1237

    doi:10.1088/0004-637x/705/2/1237 2009

  19. [19]

    Gulbis, A. A. S., Elliot, J. L., & Kane, J. F. 2006, Icarus, 183, 168, doi: 10.1016/j.icarus.2006.01.021

    work page doi:10.1016/j.icarus.2006.01.021 2006

  20. [20]

    2026, A&A, 705, A196, doi: 10.1051/0004-6361/202556450

    Han, Y., Mansell, E., Jennings, J., et al. 2026, A&A, 705, A196, doi: 10.1051/0004-6361/202556450

    doi:10.1051/0004-6361/202556450 2026

  21. [21]

    2022a, ApJL, 938, L23, doi: 10.3847/2041-8213/ac9480

    Huang, Y., Gladman, B., Beaudoin, M., & Zhang, K. 2022a, ApJL, 938, L23, doi: 10.3847/2041-8213/ac9480

    doi:10.3847/2041-8213/ac9480 2041

  22. [22]

    2022b, ApJS, 259, 54, doi: 10.3847/1538-4365/ac559a

    Huang, Y., Gladman, B., & Volk, K. 2022b, ApJS, 259, 54, doi: 10.3847/1538-4365/ac559a

    doi:10.3847/1538-4365/ac559a

  23. [23]

    Hunter, J. D. 2007, Computing in Science Engineering, 9, 90, doi: 10.1109/MCSE.2007.55 CCKB Backstory15

    doi:10.1109/mcse.2007.55 2007

  24. [24]

    1992, Icarus, 96, 107, doi: 10.1016/0019-1035(92)90008-U

    Ida, S., & Makino, J. 1992, Icarus, 96, 107, doi: 10.1016/0019-1035(92)90008-U

    doi:10.1016/0019-1035(92)90008-u 1992

  25. [25]

    R., Krivov, A

    Jankovic, M. R., Krivov, A. V., Pearce, T. D., et al. 2026, submitted to A&A

    2026

  26. [26]

    2001, SciPy: Open source scientific tools for Python

    Jones, E., Oliphant, T., Peterson, P., et al. 2001, SciPy: Open source scientific tools for Python. http://www.scipy.org/

    2001

  27. [27]

    J., Petit, J.-M., Gladman, B., et al

    Kavelaars, J. J., Petit, J.-M., Gladman, B., et al. 2021, ApJL, 920, L28, doi: 10.3847/2041-8213/ac2c72

    doi:10.3847/2041-8213/ac2c72 2021

  28. [28]

    2021, ApJ, 909, 109, doi: 10.3847/1538-4357/abdb2a

    Kunitomo, M., Ida, S., Takeuchi, T., et al. 2021, ApJ, 909, 109, doi: 10.3847/1538-4357/abdb2a

    doi:10.3847/1538-4357/abdb2a 2021

  29. [29]

    K., & Inutsuka, S.-i

    Kunitomo, M., Suzuki, T. K., & Inutsuka, S.-i. 2020, MNRAS, 492, 3849, doi: 10.1093/mnras/staa087

    doi:10.1093/mnras/staa087 2020

  30. [30]

    J., Fuentes, J

    Lee, E. J., Fuentes, J. R., & Hopkins, P. F. 2022, ApJ, 937, 95, doi: 10.3847/1538-4357/ac8cfe

    work page doi:10.3847/1538-4357/ac8cfe 2022

  31. [31]

    Li, R., Chen, Y.-X., & Lin, D. N. C. 2022, MNRAS, 510, 5246, doi: 10.1093/mnras/stab3677

    doi:10.1093/mnras/stab3677 2022

  32. [32]

    2025, ApJ, 995, 214, doi: 10.3847/1538-4357/ae18c3

    Li, R., & Chiang, E. 2025, ApJ, 995, 214, doi: 10.3847/1538-4357/ae18c3

    doi:10.3847/1538-4357/ae18c3 2025

  33. [33]

    2021, arXiv e-prints, arXiv:2105.06042

    Li, R., & Youdin, A. 2021, arXiv e-prints, arXiv:2105.06042. https://arxiv.org/abs/2105.06042

    Pith/arXiv arXiv 2021

  34. [34]

    N., & Simon, J

    Li, R., Youdin, A. N., & Simon, J. B. 2019, ApJ, 885, 69, doi: 10.3847/1538-4357/ab480d

    doi:10.3847/1538-4357/ab480d 2019

  35. [35]

    B., Li, R., et al

    Lim, J., Simon, J. B., Li, R., et al. 2026, ApJ, 1000, 156, doi: 10.3847/1538-4357/ae47e9

    doi:10.3847/1538-4357/ae47e9 2026

  36. [36]

    S., Rumpl, W., & Nordsieck, K

    Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425, doi: 10.1086/155591

    doi:10.1086/155591 1977

  37. [37]

    2020, Kuiper belt: formation and evolution, ed

    Morbidelli, A., & Nesvorný, D. 2020, Kuiper belt: formation and evolution, ed. D. Prialnik, M. A. Barucci, & L. Young, 25–59, doi: 10.1016/B978-0-12-816490-7.00002-3

    doi:10.1016/b978-0-12-816490-7.00002-3 2020

  38. [38]

    J., Lin, H

    Napier, K. J., Lin, H. W., Gerdes, D. W., et al. 2024, PSJ, 5, 50, doi: 10.3847/PSJ/ad1528 Nesvorný, D. 2018, ARA&A, 56, 137, doi: 10.1146/annurev-astro-081817-052028 Nesvorný, D., Li, R., Youdin, A. N., Simon, J. B., & Grundy, W. M. 2019, Nature Astronomy, 3, 808, doi: 10.1038/s41550-019-0806-z Nesvorný, D., & Vokrouhlický, D. 2019, Icarus, 331, 49, doi:...

    doi:10.3847/psj/ad1528 2024

  39. [39]

    M., Nesvorný, D., & Thirouin, A

    Noll, K., Grundy, W. M., Nesvorný, D., & Thirouin, A. 2020, Trans-Neptunian binaries (2018), ed. D. Prialnik, M. A. Barucci, & L. Young, 201–224, doi: 10.1016/B978-0-12-816490-7.00009-6

    doi:10.1016/b978-0-12-816490-7.00009-6 2020

  40. [40]

    2017, in Proceedings of Workshop on Machine Learning Systems (LearningSys) in The Thirty-first Annual Conference on Neural Information Processing Systems (NIPS)

    Okuta, R., Unno, Y., Nishino, D., Hido, S., & Loomis, C. 2017, in Proceedings of Workshop on Machine Learning Systems (LearningSys) in The Thirty-first Annual Conference on Neural Information Processing Systems (NIPS). http: //learningsys.org/nips17/assets/papers/paper_16.pdf

    2017

  41. [41]

    W., & Cuzzi, J

    Ormel, C. W., & Cuzzi, J. N. 2007, A&A, 466, 413, doi: 10.1051/0004-6361:20066899

    doi:10.1051/0004-6361:20066899 2007

  42. [42]

    E., Ercolano, B., Clarke, C

    Owen, J. E., Ercolano, B., Clarke, C. J., & Alexander, R. D. 2010, MNRAS, 401, 1415, doi: 10.1111/j.1365-2966.2009.15771.x

    arXiv 2010

  43. [43]

    L., Cabrit, S., et al

    Pascucci, I., Beck, T. L., Cabrit, S., et al. 2025, Nature Astronomy, 9, 81, doi: 10.1038/s41550-024-02385-7

    doi:10.1038/s41550-024-02385-7 2025

  44. [44]

    2011, ApJ, 735, 8, doi: 10.1088/0004-637X/735/1/8

    Perez-Becker, D., & Chiang, E. 2011, ApJ, 735, 8, doi: 10.1088/0004-637X/735/1/8

    doi:10.1088/0004-637x/735/1/8 2011

  45. [45]

    J., et al

    Petit, J.-M., Gladman, B., Kavelaars, J. J., et al. 2023, ApJL, 947, L4, doi: 10.3847/2041-8213/acc525

    doi:10.3847/2041-8213/acc525 2023

  46. [46]

    B., Armitage, P

    Simon, J. B., Armitage, P. J., Li, R., & Youdin, A. N. 2016, ApJ, 822, 55, doi: 10.3847/0004-637X/822/1/55

    doi:10.3847/0004-637x/822/1/55 2016

  47. [47]

    M., & Birnstiel, T

    Stammler, S. M., & Birnstiel, T. 2022, ApJ, 935, 35, doi: 10.3847/1538-4357/ac7d58 Van Laerhoven, C., Gladman, B., Volk, K., et al. 2019, AJ, 158, 49, doi: 10.3847/1538-3881/ab24e1

    doi:10.3847/1538-4357/ac7d58 2022

  48. [48]

    N., & Goodman, J

    Youdin, A. N., & Goodman, J. 2005, ApJ, 620, 459, doi: 10.1086/426895

    doi:10.1086/426895 2005