Pith. sign in

REVIEW 4 major objections 5 minor 64 references

ALMA Reveals an Eccentricity Gradient in the Fomalhaut Debris Disk

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read This paper claims that Fomalhaut's debris disk is best described by a forced eccentricity that falls steeply with semi-major axis, ef ∝ a^-1.75±0.16, the first eccentricity gradient reported in a debris disk.

desk verdict Fomalhaut's ring really needs a negative eccentricity gradient, but the steepness (-1.75) is not yet closed - the sign looks robust, the magnitude is conditional. read the letter →

arxiv 2509.02884 v1 pith:4N7UCYSG submitted 2025-09-02 astro-ph.EP

Joshua B. Lovell , Elliot M. Lynch , Jay Chittidi , Antranik A. Sefilian , Sean M. Andrews , Grant M. Kennedy , Meredith MacGregor , David J. Wilner
show 1 more author
Mark C. Wyatt
This is my paper · ORCID
classification astro-ph.EP
keywords circumstellardisksdebriseccentricitygradientFomalhautplanet-diskinteractionsEccentricVelocityDivergencemillimeterimaging
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 argues that the eccentricity of Fomalhaut's main debris belt is not constant but drops steeply with distance from the star, following a power law ef ∝ a^-1.75 ± 0.16. This is presented as the first reported eccentricity gradient in any debris disk. The gradient produces, through mass continuity, exactly the asymmetries seen in the millimeter images: a broader, fainter pericenter and a narrower, brighter apocenter. If correct, the belt's shape encodes the presence and orbit of an unseen planet, and the eccentricity likely originated during the protoplanetary disk phase.

What carries the argument

The load-bearing object is a single-Gaussian-ring parametric disk model whose forced eccentricity follows a power law in semi-major axis, ef(a) = ef,0(a/a0)^npow, with aligned pericenters (∂ωf/∂a = 0). The essential identity is the Jacobian j = [1 - e(e + a∂e/∂a)]/√(1 - e²) · (1 - q cos E), with q = (a∂e/∂a)/[1 - e(e + a∂e/∂a)], which converts the eccentricity gradient into surface-density and width asymmetries. This 'Eccentric Velocity Divergence' is what lets the single parameter npow explain both the broad-and-faint pericenter and the narrow-and-bright apocenter seen by the millimeter observations.

What would settle it

Measure the local radial width and surface brightness separately at the two ansae in a deeper millimeter image that also resolves the minor axis. The EVD model with npow = -1.75 predicts a pericenter width about 1.2 times the apocenter width and a fainter, broader pericenter; observing the opposite width asymmetry, or minor-axis emission that no apse-aligned power-law model can reproduce, would rule out the claimed gradient.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that Fomalhaut's main belt is modeled better by a forced eccentricity profile ef(a) = ef,0(a/a0)^npow with npow = -1.75 ± 0.16 than by any constant-eccentricity model, with or without a free-eccentricity component. The gradient is not a mere curve-fit extra: it simultaneously reproduces two observed asymmetries that a constant eccentricity cannot, namely a pericenter that is broader and fainter and an apocenter that is narrower and brighter. The mechanism behind this, called Eccentric Velocity Divergence, is mass continuity in an apse-aligned eccentric disk: a negative eccentricity gradient converts the orbit packing into exactly those width

Load-bearing premise

The model assumes the belt is a single apse-aligned Gaussian ring with no warp and negligible free eccentricity, while masking out the minor-axis regions where the model is faintest; if a warp or free-eccentricity population is present, the inferred npow ≈ -1.75 could be biased.

Editorial extensions

If this is right

  • Future models of Fomalhaut's main belt must treat eccentricity as a radially varying parameter; a single forced eccentricity underfits the data by a large margin.
  • The measured slope is steeper than the classical a^-1 expected for a massless disk forced by an internal planet, so either the disk is massive enough for self-gravity to steepen the profile, or the perturber sits closer than the simple gap-carving geometry suggests.
  • The 440-Myr N-body integrations show that initially circular disks are disrupted, while initially eccentric disks survive, implying the ring's lopsidedness was present since the protoplanetary disk phase.
  • A single unseen planet, either a gap-carver at roughly 109-120 au or a 2:1 resonant-clearing planet at 70-75 au, can sculpt the belt's inner edge and gaps while remaining below current detection limits, making the eccentricity gradient a probe of such planets.
  • The lower-resolution archival data also require a negative gradient (npow = -1.16 ± 0.16), so the result does not depend on the highest-resolution image alone.

Reading between the lines

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

  • The EVD relation predicts a quantitative link between the sign of a disk's width asymmetry and the sign of its brightness asymmetry; a survey of resolved eccentric debris disks could measure a population of eccentricity-gradient slopes and test whether values near -1 (single planet) or steeper (self-gravity) dominate.
  • Because the fit masks the minor axis and assumes zero warp, an alternative reading of the data is a disk with a mild warp or a wider free-eccentricity distribution; a visibility-domain fit that includes minor-axis emission and allows a warp could separate these.
  • If the 'born eccentric' conclusion holds, young debris disks around A-type stars should show steeper eccentricity gradients than old disks, since long-term planet-disk interactions would tend to flatten or re-process the primordial profile; this is a testable age trend with deeper imaging.
  • The small apocenter over-subtraction noted in the residuals suggests the true profile may be even steeper or non-Gaussian; a two-sided radial-width model on deeper data could determine whether the -1.75 slope is absorbing an asymmetric radial profile.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper fits high-resolution ALMA 1.32 mm continuum images of Fomalhaut with parametric RADMC-3D models in which the forced eccentricity varies as e_f ∝ a^{n_pow}, and reports n_pow = -1.75 ± 0.16 in the 'General' model. The model is preferred over constant-eccentricity models with free eccentricity (Proper 1, Δχ²=70) and over n_pow=-1 with free eccentricity (Proper 2, Δχ²=21.5), with a visibility-domain check. The paper interprets the preferred model as evidence for 'Eccentric Velocity Divergence,' proposes single-planet 'Gap' and 'Resonant' scenarios, and uses REBOUND simulations to argue that an initially eccentric disk survives 440 Myr.

Significance. If the steep negative gradient is real, this is the first reported eccentricity gradient in a debris disk and a potentially valuable diagnostic of planet-disk interactions. The parametric model is physically motivated, the EVD kinematic identity in §2 is clearly derived, the public code release supports reproducibility, and the MCMC/visibility comparisons are extensive. However, the headline steepness is not yet established at the claimed confidence: the free-eccentricity subspace is not explored, the lower-resolution verification gives a shallower slope, and the Δχ² significance conversion is statistically questionable. The sign of the gradient is likely robust; the magnitude and the quantitative 'first gradient' claim need further work.

major comments (4)
  1. [§3.4.2, Eq. (4), Table 1] The General model fixes e_p=0; Proper 1 and Proper 2 fix n_pow=0 or -1. The general case with both e_p and n_pow free is explicitly deferred to future work. Since e_p and w_r are degenerate (the Proper fits show wide w_r posteriors), and a free-eccentricity population can produce qualitatively similar pericenter broadening and apocenter brightening, the fitted n_pow=-1.75 may be biased. This is the central load-bearing gap. Fit the full model with e_p free and n_pow free, or provide injection-recovery tests showing that n_pow is unbiased under e_p>0, before claiming a quantitative gradient.
  2. [§3.4.3, Eq. (7)] The quoted 6.7σ and 2.6σ preferences use a chi-square CDF with Npar=9 degrees of freedom. General, Proper 1, and Proper 2 are not nested models and have the same number of free parameters, so this p-value conversion is not valid. Report an appropriate model-comparison criterion (e.g., BIC/AIC, cross-validation, or a genuinely nested sequence with a full model) instead. Without this, the statistical preference for the General model is overstated.
  3. [§3.4.1 vs Appendix B and Table 1] The Verify fit to the lower-resolution data gives n_pow=-1.16±0.16, about 2.6σ shallower than the high-resolution -1.75. Section 3.5 acknowledges the high-resolution value is 4.6σ from -1 while the low-resolution value is consistent with -1. Thus the sign of the gradient is robust, but the magnitude is not established. The abstract and §6 present -1.75 as the headline result; they should be conditioned on resolution and on the unmodeled e_p subspace.
  4. [§3.3, Appendix A, Eq. (6)] The fitting mask selects primary beam response >0.66 and projected radius <200 au, i.e., the bright ansae. The residual maps show the model is fainter than the data along the minor axes, which are excluded from the fit. Appendix A tests only one alternative mask and reports a worse apocentre fit without providing Δχ² or the resulting parameter changes. Demonstrate that n_pow and the model preference are robust to mask choice, or quantify how the mask affects the inference.
minor comments (5)
  1. [Abstract and References] The abstract cites 'Lynch & Lovell 2022' while the body and reference list use Lynch & Lovell (2021). Unify the citation.
  2. [Eq. (7)] Define the incomplete gamma function and use standard regularized notation. The exponent Npar/2 with Npar=9 appears ad hoc for comparing non-nested models.
  3. [Footnote 5] The second width in the footnote is written 'wr, in = 15.7±0.7 au'; this should presumably be the outer width, wr, out.
  4. [§6] The sentence 'only scenarios with an initially circular disk are stable/finalise as eccentric disks' contradicts §5.1.2, which finds that circular disks are disrupted. It should read 'initially eccentric'.
  5. [Fig. 6 and Table 1] The extracted figure annotation appears to show 'npow = 1.1651' with no minus sign, while the axis runs from -1.5 to -0.75; check the sign convention in the figure. Also, Table 1 lists Proper 2 e_p as '<3.6' without the nominal 1.9±0.9% given in the text; make consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the eccentricity gradient is a fitted model parameter compared against explicit alternatives, EVD is presented as a kinematic consequence, and planet/stability analyses are framed as consistency checks rather than predictions.

full rationale

The paper's central claim (npow = -1.75 ± 0.16) is obtained by fitting a parametric model to ALMA data with an MCMC likelihood, not by deriving it from the model's assumptions. The EVD effect is explicitly called a consequence of mass continuity in eccentric disks (§2), and its analytic width relations are derived from geometry rather than being a prediction of the fit. The planet scenarios in §4 use the fitted inner-edge eccentricity and standard secular relations (Mustill & Wyatt 2012) to propose consistent architectures; they are not claimed as independent predictions. The REBOUND stability tests initialize eccentric disks with e ∝ a^-1 (stated as 'consistent with our modelling') and compare them to circular initial conditions; the conclusion is about survival/stability, not about deriving the gradient from the simulations. The paper openly defers the fully general ep + npow model and notes the ep–wr degeneracy, but these are model limitations, not circular reasoning. Self-citations (Lynch & Lovell 2021; Lovell & Lynch 2023) provide the parametric model and code, which is openly released (DOI/github), and the ALMA data are external. No load-bearing step reduces to its own input by construction.

Assumptions & free parameters 9 free parameters · 8 assumptions · 2 invented entities

The central claim rests on the fitted npow, which is one of nine fitted parameters in the General model. The disk model assumes standard optically thin dust, a single Gaussian radial profile, apsidal alignment, and a specific fitting mask. The two proposed planets are inferred, not detected.

free parameters (9)
  • npow = -1.75 ± 0.16
    Power-law index of forced eccentricity vs semi-major axis; the central claim.
  • ef,0 = 0.1256 ± 0.0012
    Mean forced eccentricity at a0.
  • a0 = 138.79 ± 0.12 au
    Mean semi-major axis of the ring.
  • wr = 13.51 ± 0.29 au
    Gaussian radial width.
  • h = 0.0157 ± 0.0013
    Vertical aspect ratio.
  • i = 66.44 ± 0.09 deg
    Inclination.
  • PA = 336.19 ± 0.06 deg
    Position angle.
  • ωf = 15.2 ± 0.6 deg
    Argument of forced eccentricity.
  • Mdust = 18.70 ± 0.20 x 10^-2 M_Earth
    Dust mass scaling.
assumptions (8)
  • standard math Equations 1-4 (orbit element transformation and Jacobian) are standard celestial mechanics.
    Used to map (a,e,ωf) to surface density; no new physics.
  • domain assumption Dust is optically thin, with a Dohnanyi -3.5 power-law size distribution and radiative equilibrium temperatures computed by RADMC-3D.
    Standard debris disk modeling assumption; unverified for Fomalhaut.
  • ad hoc to paper Surface density in semi-major axis is a single Gaussian (Eq. 1).
    No radial substructure; the paper notes a two-width model improves fits without statistical significance.
  • ad hoc to paper Apsidal alignment: ∂ωf/∂a = 0, untwisted disk (Eq. 4).
    Assumed to simplify the Jacobian; a twisted disk would change the surface density.
  • domain assumption The ALMA image noise is Gaussian with constant σ = 8.0 µJy/beam after primary-beam scaling.
    The authors note the data have non-Gaussian, spatially varying noise; this is a simplification.
  • domain assumption Stellar parameters: M* = 1.9 Msun, age 440 Myr (Mamajek 2012).
    Adopted from literature.
  • standard math Classical secular forced eccentricity for an internal perturber is ef ∝ a^-1 (Murray & Dermott 1999).
    Used as a baseline for interpreting the fitted npow.
  • ad hoc to paper The fitting mask (primary beam > 0.66, projected radius < 200 au) selects the high-SNR ansae.
    The paper tests alternative masks but the reported npow is from this specific mask.
invented entities (2)
  • Gap planet
    purpose: A single planet at 109-120 au with e=0.20-0.23 and mass 1.5e-6 to 2.5e-5 stellar masses, proposed to carve the main belt inner edge and drive the eccentricity profile.
    No detection; below JWST NIRCam sensitivity; parameters derived from the fitted npow and scaling relations.
  • Resonant planet
    purpose: A single planet at 70-75 au with e=0.38-0.41, clearing the gap via 2:1 resonance.
    No detection; inferred from the intermediate belt edges and the fitted gradient.

how reviews work

0 comments
Cite this review

Pith. "Pith review of ALMA Reveals an Eccentricity Gradient in the Fomalhaut Debris Disk." pith.science (2026). https://pith.science/paper/4N7UCYSG

@misc{pith2026250902884,
  author       = {Pith},
  title        = {Pith review of: ALMA Reveals an Eccentricity Gradient in the Fomalhaut Debris Disk},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4N7UCYSG}},
  note         = {Machine review of arXiv:2509.02884}
}
abstract

We present evidence of a negative eccentricity gradient in the debris disk of the nearby A-type main sequence star, Fomalhaut. Fitting to the high-resolution, archival ALMA 1.32 mm continuum data for Fomalhaut (with a synthesised angular resolution of $0.76{\times}0.55''$; 4-6\,au), we present a model that describes the bulk properties of the disk (semi-major axis, width, and geometry) and its asymmetric morphology. The best-fit model incorporates a forced eccentricity gradient that varies with semi-major axis, $e_f\propto a^{n_\mathrm{pow}}$, a generalized form of the parametric models of Lynch & Lovell 2022, with $n_\mathrm{pow}{=}{-1.75}{\pm}0.16$. We show that this model is statistically preferred to models with constant forced and free eccentricities. In comparison to disk models with constant forced eccentricities, negative eccentricity gradient models broaden disk widths at pericenter versus apocenter, and increase disk surface densities at apocenter versus pericenter, both of which are seen in the Fomalhaut disk, and which we collectively term Eccentric Velocity Divergence. We propose single-planet architectures consistent with the model and investigate the stability of the disk over 440 Myr to planet-disk interactions via N-body modeling. We find that Fomalhaut's ring eccentricity plausibly formed during the protoplanetary disk stage, with subsequent planet-disk interactions responsible for carving the disk morphology.

Figures

Figures reproduced from arXiv: 2509.02884 by the authors.

Figure 1
Figure 1. Normalized surface density maps (face-on projections, in (top) r −ϕ space, from 0−2π and 0−180 au, and (bottom) x − y space) for different power-law eccentricity profiles (with their e = ef (a) functional form shown in the lower-right of each panel). The models all have apse-aligned argument’s of pericenter, as well as radii, widths and eccentricities consistent with those of Fomalhaut, and an argument of pericenter… view at source ↗
Figure 2
Figure 2. Left: ALMA data as presented in Chittidi et al. (2025) which we fit to in this work. Center: Best–fit ef (a) ∝ a −1.75 model (on same image scale). Right: residual emission after we subtract our best-fit model from the ALMA data (left). Contours are shown at the ±3σ level in the residuals, and at the 5σ level for the data/model. Beams are shown in the lower–left of each plot. Emission remains present in the minor ax… view at source ↗
Figure 3
Figure 3. Left: ALMA data. Center: Best–fit models which include ep (on same image scale, with top for the model fixed with npow=0, and npow=−1 for bottom). Right: residual emission after we subtract the best-fit models from the ALMA data respectively. Contours are shown at the ±3σ level in the residuals, and at the 5σ level for the data/model. Beams are shown in the lower–left of each plot. In all plots, north is up, east is… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Plots for the surface density maps from the REBOUND simulations in r − ϕ space. Upper two rows: (conditional surface mass density function (MDF), and absolute surface density) simulations with initially circular disk conditions; lower two rows: simulation outcomes with…
Figure 5
Figure 5. Figure 5: Left: ALMA data. Center: Best–fit ef (a) ∝ a −1.75 model (on same image scale). Right: residual emission after best-fit model subtraction. Contours are shown at the ±3σ level in the residuals, and at the 5σ level for the data/model. Beams are shown in the lower–left of…
Figure 6
Figure 6. Figure 6: Corner plots for the emcee chains (minus 1000 steps covering burn-in) showing the 6 parameters fitted to the low– resolution data of MacGregor et al. (2017) and Kennedy (2020), i.e. model ‘Verify’. We find comparable parameter uncertainties to those presented in Kenned…
Figure 7
Figure 7. Figure 7: Left: ALMA data as presented in MacGregor et al. (2017) and Kennedy (2020). Center: Best–fit model for this data. Right: residual emission (data minus best-fit model). Contours are shown at the ±3σ level in the residuals, and at the 5σ level for the data/model. Beams a…
Figure 8
Figure 8. Figure 8: Corner plots for the emcee chains (minus burn-in steps) showing the 9 parameters fitted in this study for the General model. All show the well-behaved features of Gaussian distributions, that are either circular, or with little degeneracy (e.g., between fM, dust and wr…
Figure 9
Figure 9. Figure 9: Corner plots for the emcee chains (minus burn-in steps) showing the 9 parameters fitted for the Proper 1 model. All show the well-behaved features of Gaussian distributions, that are either circular, or with little degeneracy (e.g., between fM, dust and wr, and between…
Figure 10
Figure 10. Figure 10: Corner plots for the emcee chains (minus burn-in steps) showing the 9 parameters fitted for the Proper 2 model. All show the well-behaved features of Gaussian distributions, that are either circular, or with little degeneracy (e.g., between fM, dust and wr, and betwee…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

64 extracted references · 22 canonical work pages

  1. [1]

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

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

  2. [2]

    write newline

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

  3. [3]

    qui ۴˻Pd |vZa=V;0w< .o] r('߽O -XoI1ooN:kn:b t1 =Yuvܤdfj[o >PR DFKy zKYt/Y 7EmU_׵ nw J i 2PU + ի !Cm&չϨmV ]Ӣ aR U HE r` ծ/H:>N Rr d J

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

    2021

  4. [4]

    2012, , 540, A125, 10.1051/0004-6361/201118581

    Acke , B., Min , M., Dominik , C., et al. 2012, , 540, A125, 10.1051/0004-6361/201118581

    work page doi:10.1051/0004-6361/201118581 2012

  5. [5]

    Allen , R. H. 1963, Star names. Their lore and meaning

    work page 1963

  6. [6]

    M., Liu , M

    Andrews , S. M., Liu , M. C., Williams , J. P., & Allers , K. N. 2008, , 685, 1039, 10.1086/591417

    work page doi:10.1086/591417 2008

  7. [7]

    Aumann , H. H. 1985, , 97, 885, 10.1086/131620

    work page doi:10.1086/131620 1985

  8. [8]

    C., Payne , M

    Boley , A. C., Payne , M. J., Corder , S., et al. 2012, , 750, L21, 10.1088/2041-8205/750/1/L21

    work page doi:10.1088/2041-8205/750/1/l21 2012

Show all 64 references
  1. [9]

    V., et al

    Booth , M., Schulz , M., Krivov , A. V., et al. 2021, , 500, 1604, 10.1093/mnras/staa3362

    2021 doi

  2. [10]

    Chittidi , J., MacGregor , M., & Lovell m Joshua. 2025,

    2025

  3. [11]

    I., & Murray-Clay , R

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

    2012 doi

  4. [12]

    Dohnanyi , J. S. 1969, Journal of Geophysical Research, 10.1029/JB074i010p02531

    1969 doi

  5. [13]

    I., Shannon , A., & Morrison , S

    Dong , J., Dawson , R. I., Shannon , A., & Morrison , S. 2020, , 889, 47, 10.3847/1538-4357/ab64f7

    2020 doi

  6. [14]

    2018, , 860, 124, 10.3847/1538-4357/aac6cb

    Dong , R., Liu , S.-y., Eisner , J., et al. 2018, , 860, 124, 10.3847/1538-4357/aac6cb

    2018 doi

  7. [15]

    Astrophysics Source Code Library

    Dullemond , C. P., Juhasz , A., Pohl , A., et al. 2012, "Astrophysics Source Code Library", ascl:1202.015. 1202.015

    2012

  8. [16]

    R., et al

    Faramaz , V., Krist , J., Stapelfeldt , K. R., et al. 2019, arXiv e-prints, arXiv:1909.04162. 1909.04162

    2019 arXiv

  9. [17]

    2021, , 651, A90, 10.1051/0004-6361/202141278

    Fedele , D., Toci , C., Maud , L., & Lodato , G. 2021, , 651, A90, 10.1051/0004-6361/202141278

    2021 doi

  10. [18]

    W., Lang , D., & Goodman , J

    Foreman-Mackey , D., Hogg , D. W., Lang , D., & Goodman , J. 2013, Publications of the Astronomical Society of the Pacific, 125, 306, 10.1086/670067

    2013 doi

  11. [19]

    2020, Proceedings of the National Academy of Science, 117, 9712, 10.1073/pnas.1912506117

    Gaspar , A., & Rieke , G. 2020, Proceedings of the National Academy of Science, 117, 9712, 10.1073/pnas.1912506117

    2020 doi

  12. [20]

    G., Rieke , G

    G \'a sp \'a r , A., Wolff , S. G., Rieke , G. H., et al. 2023, Nature Astronomy, 7, 790, 10.1038/s41550-023-01962-6

    2023 doi

  13. [21]

    2010, Communications in Applied Mathematics and Computational Science, 5, 65, 10.2140/camcos.2010.5.65

    Goodman , J., & Weare , J. 2010, Communications in Applied Mathematics and Computational Science, 5, 65, 10.2140/camcos.2010.5.65

    2010 doi

  14. [22]

    S., Greaves , J

    Holland , W. S., Greaves , J. S., Dent , W. R. F., et al. 2003, , 582, 1141, 10.1086/344819

    2003 doi

  15. [23]

    M., Duch \^e ne , G., & Matthews , B

    Hughes , A. M., Duch \^e ne , G., & Matthews , B. C. 2018, , 56, 541, 10.1146/annurev-astro-081817-052035

    2018 doi

  16. [24]

    R., & Clampin , M

    Kalas , P., Graham , J. R., & Clampin , M. 2005, , 435, 1067, 10.1038/nature03601

    2005 doi

  17. [25]

    R., Chiang , E., et al

    Kalas , P., Graham , J. R., Chiang , E., et al. 2008, Science, 322, 1345, 10.1126/science.1166609

    2008 doi

  18. [26]

    Kennedy , G. M. 2020, Royal Society Open Science, 7, 200063, 10.1098/rsos.200063

    2020 doi

  19. [27]

    M., Lovell , J

    Kennedy , G. M., Lovell , J. B., Kalas , P., & Fitzgerald , M. P. 2023, , 524, 2698, 10.1093/mnras/stad2058

    2023 doi

  20. [28]

    V., & Wyatt , M

    Krivov , A. V., & Wyatt , M. C. 2021, , 500, 718, 10.1093/mnras/staa2385

    2021 doi

  21. [29]

    Kurucz , R. L. 1979, Astrophysical Journal Supplement Series, 40, 1, 10.1086/190589

    1979 doi

  22. [30]

    B., & Lynch , E

    Lovell , J. B., & Lynch , E. M. 2023, , 525, L36, 10.1093/mnrasl/slad083

    2023 doi

  23. [31]

    B., Marino , S., Wyatt , M

    Lovell , J. B., Marino , S., Wyatt , M. C., et al. 2021, , 506, 1978, 10.1093/mnras/stab1678

    2021 doi

  24. [32]

    B., Wyatt , M

    Lovell , J. B., Wyatt , M. C., Kalas , P., et al. 2022, , 10.1093/mnras/stac2782

    2022 doi

  25. [33]

    M., & Lovell , J

    Lynch , E. M., & Lovell , J. B. 2021, , 10.1093/mnras/stab3566

    2021 doi

  26. [34]

    A., Matr \`a , L., Kalas , P., et al

    MacGregor , M. A., Matr \`a , L., Kalas , P., et al. 2017, Astrophysical Journal, 842, 8, 10.3847/1538-4357/aa71ae

    2017 doi

  27. [35]

    A., Weinberger , A

    MacGregor , M. A., Weinberger , A. J., Loyd , R. O. P., et al. 2021, , 911, L25, 10.3847/2041-8213/abf14c

    2021 doi

  28. [36]

    Mamajek , E. E. 2012, , 754, L20, 10.1088/2041-8205/754/2/L20

    2012 doi

  29. [37]

    2022, arXiv e-prints, arXiv:2202.03053, 10.48550/arXiv.2202.03053

    Marino , S. 2022, arXiv e-prints, arXiv:2202.03053, 10.48550/arXiv.2202.03053

    2022 doi arXiv

  30. [38]

    C., & Dent , W

    Matr \`a , L., Pani \'c , O., Wyatt , M. C., & Dent , W. R. F. 2015, Monthly Notices of the Royal Astronomical Society, 447, 3936, 10.1093/mnras/stu2619

    2015 doi

  31. [39]

    A., Kalas , P., et al

    Matr \`a , L., MacGregor , M. A., Kalas , P., et al. 2017, , 842, 9, 10.3847/1538-4357/aa71b4

    2017 doi

  32. [40]

    C., Krivov , A

    Matthews , B. C., Krivov , A. V., Wyatt , M. C., Bryden , G., & Eiroa , C. 2014, in Protostars and Planets VI, ed. H. Beuther , R. S. Klessen , C. P. Dullemond , & T. Henning , 521, 10.2458/azu_uapress_9780816531240-ch023

    2014 doi

  33. [41]

    P., Waters , B., Schiebel , D., Young , W., & Golap , K

    McMullin , J. P., Waters , B., Schiebel , D., Young , W., & Golap , K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw , F. Hill , & D. J. Bell , 127

    2007

  34. [42]

    2015, , 799, 41, 10.1088/0004-637X/799/1/41

    Morrison , S., & Malhotra , R. 2015, , 799, 41, 10.1088/0004-637X/799/1/41

    2015 doi

  35. [43]

    D., & Dermott , S

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

    1999

  36. [45]

    2012, , 419, 3074, 10.1111/j.1365-2966.2011.19948.x

    ---. 2012, , 419, 3074, 10.1111/j.1365-2966.2011.19948.x

    2012

  37. [46]

    2019, , 630, A142, 10.1051/0004-6361/201935998

    Olofsson , J., Milli , J., Th \'e bault , P., et al. 2019, , 630, A142, 10.1051/0004-6361/201935998

    2019 doi

  38. [47]

    R., & Kuchner , M

    Pan , M., Nesvold , E. R., & Kuchner , M. J. 2016, Astrophysical Journal, 832, 81, 10.3847/0004-637X/832/1/81

    2016 doi

  39. [48]

    D., Beust , H., Faramaz , V., et al

    Pearce , T. D., Beust , H., Faramaz , V., et al. 2021, , 503, 4767, 10.1093/mnras/stab760

    2021 doi

  40. [49]

    D., Krivov , A

    Pearce , T. D., Krivov , A. V., Sefilian , A. A., et al. 2024, , 527, 3876, 10.1093/mnras/stad3462

    2024 doi

  41. [50]

    2021, , 507, 1157, 10.1093/mnras/stab2179

    Ragusa , E., Fasano , D., Toci , C., et al. 2021, , 507, 1157, 10.1093/mnras/stab2179

    2021 doi

  42. [51]

    Rein , H., & Liu , S. F. 2012, , 537, A128, 10.1051/0004-6361/201118085

    2012 doi

  43. [52]

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

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

    2015 doi

  44. [53]

    2019, Research Notes of the American Astronomical Society, 3, 16, 10.3847/2515-5172/aaff63

    ---. 2019, Research Notes of the American Astronomical Society, 3, 16, 10.3847/2515-5172/aaff63

    2019 doi

  45. [54]

    Sefilian , A. A. 2024, , 966, 140, 10.3847/1538-4357/ad32d1

    2024 doi

  46. [55]

    A., Kratter , K

    Sefilian , A. A., Kratter , K. M., Wyatt , M. C., et al. 2025, arXiv e-prints, arXiv:2505.09578, 10.48550/arXiv.2505.09578

    2025 doi

  47. [56]

    A., Rafikov , R

    Sefilian , A. A., Rafikov , R. R., & Wyatt , M. C. 2021, , 910, 13, 10.3847/1538-4357/abda46

    2021 doi

  48. [57]

    2023, , 954, 100, 10.3847/1538-4357/ace68e

    ---. 2023, , 954, 100, 10.3847/1538-4357/ace68e

    2023 doi

  49. [58]

    2000, SAOImage DS9: A utility for displaying astronomical images in the X11 window environment , Astrophysics Source Code Library, record ascl:0003.002

    Smithsonian Astrophysical Observatory . 2000, SAOImage DS9: A utility for displaying astronomical images in the X11 window environment , Astrophysics Source Code Library, record ascl:0003.002. 0003.002

    2000

  50. [59]

    R., Holmes , E

    Stapelfeldt , K. R., Holmes , E. K., Chen , C., et al. 2004, , 154, 458, 10.1086/423135

    2004 doi

  51. [60]

    Teyssandier , J., & Ogilvie , G. I. 2016, , 458, 3221, 10.1093/mnras/stw521

    2016 doi

  52. [61]

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

    Touma , J. R., Tremaine , S., & Kazandjian , M. V. 2009, , 394, 1085, 10.1111/j.1365-2966.2009.14409.x

    2009

  53. [62]

    Wyatt , M. C. 2008, Annual Review of Astronomy and Astrophysics, 46, 339, 10.1146/annurev.astro.45.051806.110525

    2008 arXiv

  54. [63]

    C., Dermott , S

    Wyatt , M. C., Dermott , S. F., Telesco , C. M., et al. 1999, Astrophysical Journal, 527, 918, 10.1086/308093

    1999 doi

  55. [64]

    2023, , 948, L2, 10.3847/2041-8213/acccf8

    Yang , H., Fern \'a ndez-L \'o pez , M., Li , Z.-Y., et al. 2023, , 948, L2, 10.3847/2041-8213/acccf8

    2023 doi

  56. [65]

    A., Llop-Sayson , J., et al

    Ygouf , M., Beichman , C. A., Llop-Sayson , J., et al. 2024, , 167, 26, 10.3847/1538-3881/ad08c8

    2024 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.