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REVIEW 3 major objections 4 minor 137 references

Gal3D: Superellipsoid Modeling of Radial 3D Galaxy Structure in IllustrisTNG and EAGLE Simulations

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Gal3D fits superellipsoids to simulated galaxies' density surfaces, and its shape indices $S_a$, $S_b$, $S_c$ separate disks, bars, bulges, and triaxial components, exposing a TNG–EAGLE difference in box/peanut bulge prevalence.

desk verdict Gal3D is a genuine methodological step forward for measuring 3D boxiness/diskiness in simulated galaxies; the TNG-EAGLE comparison is plausible but presently under-supported by statistics. read the letter →

arxiv 2608.12933 v1 pith:ABRBAKHL submitted 2026-08-13 astro-ph.GA

Shuai Lu , Min Du This is my paper · ORCID
classification astro-ph.GA
keywords galaxystructuresuperellipsoidthree-dimensionalshapebox/peanutbulgeIllustrisTNGEAGLEcosmologicalhydrodynamicalsimulationsstellarmorphology
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 intrinsic three-dimensional shapes of galaxies are normally hidden behind projection effects; Gal3D sidesteps this by working on simulated particle data, reconstructing a smooth density field, and fitting superellipsoids to surfaces of constant density. The central claim is that the shape indices $S_a$, $S_b$, and $S_c$, which the fit returns alongside the usual axis ratios and orientations, quantify boxiness and diskiness that standard ellipsoidal fits miss, so a single radial profile can separate disks, bars, bulges, and triaxial spheroids. Applying the method to the IllustrisTNG and EAGLE simulations, the paper finds that the radial extent of flattened disk structure grows with stellar mass up to roughly $10^{11}\,M_\odot$ and then drops sharply, that bar-related elongation strengthens above $10^{10.5}\,M_\odot$ but is weaker in EAGLE, and that box/peanut bulge signatures are common in TNG but weak or absent in EAGLE. If these measurements are right, Gal3D offers a practical, open-source tool for comparing intrinsic morphology across cosmological simulations and for connecting three-dimensional structure to projected observables.

What carries the argument

The load-bearing object is the superellipsoid isodensity surface $f(x,y,z)=[(x/a)^2]^{S_a}+[(y/b)^2]^{S_b}+[(z/c)^2]^{S_c}=1$, with semi-axes $a\ge b\ge c$ and shape indices $S_a$, $S_b$, $S_c$ controlling boxiness ($S>1$) versus diskiness/pointedness ($S<1$). The paper constructs the density field with adaptive kernel density estimation, samples it along a golden-ratio Fibonacci lattice of rays, forces each ray's radial density profile to be monotonic via envelope interpolation, inverts to get one isodensity point per ray, and fits the superellipsoid by minimizing an area-weighted surface-radius-ratio mismatch $(r'^2 (D-1)^2)$. This parameterization allows each density level to have its own center, orientation, and higher-order shape, which is what lets one radial profile separate nuclear disks, bulges, main disks, bars, box/peanut bulges, and triaxial spheroids.

What would settle it

Build a synthetic galaxy whose density is a known superellipsoid plus an X-shaped or ring-like perturbation, run Gal3D's ray-inversion pipeline on it, and check whether the fitted $S_a$ and $S_c$ recover the input values; if they are systematically biased when the radial density profile is non-monotonic, the box/peanut claims derived from TNG would be called into question.

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Extended reading notes

Core claim

The central discovery is that superellipsoid fitting of isodensity surfaces recovers higher-order, non-ellipsoidal structure that iterative shape-tensor methods miss, and that this structure is physically informative. Fitting the implicit surface $(x/a)^{2S_a} + (y/b)^{2S_b} + (z/c)^{2S_c} = 1$ to each density level returns axis ratios, Euler angles, center offsets, and shape indices; values $S>1$ correspond to boxy surfaces and $S<1$ to pointed, disky ones. In the TNG and EAGLE samples, the method shows the outer parts of TNG bars carry elevated $S_a$ and $S_c$, the signature of box/peanut bulges, while EAGLE bars do not, and it traces the expansion and collapse of disk regions with stellar mass. The paper presents these results as evidence that Gal3D can serve as a practical standard for quantifying intrinsic radial 3D structure in simulations.

Load-bearing premise

The method assumes that every ray from the galaxy center hits any given density level exactly once, so non-monotonic structures like X-shaped box/peanut bulges are forced into a single radius per direction and the fitted $S_a$ and $S_c$ could be biased.

Editorial extensions

If this is right

  • A single Gal3D radial profile can flag the presence of a bar, a box/peanut bulge, a disk, and a spheroid without separate component-by-component decompositions.
  • The result that flattened disk extent peaks near $M_* \sim 10^{11}\,M_\odot$ and then declines sets a quantitative benchmark that galaxy formation models should reproduce.
  • The systematic TNG–EAGLE difference in box/peanut bulge strength implies that subgrid feedback implementations shape the vertical structure of bars, a prediction that can be compared with edge-on observations of barred galaxies.
  • Because Gal3D can project its 3D models, it offers a route to translating intrinsic shape indices into predicted isophotal boxiness/diskyness, linking simulations to observable quantities.

Reading between the lines

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

  • One could test whether the same superellipsoid indices, applied to dark matter or gas components, trace assembly history more directly than the stellar shapes alone.
  • The monotonicity regularisation used in ray inversion could be relaxed (e.g., allowing two radii per direction for X-shaped bulges) to see whether the TNG box/peanut signatures become even stronger.
  • If Gal3D were applied to observed galaxies via deprojection of edge-on images, the inferred $S_c$ might serve as a new observational discriminator between boxy and disky bulges.
  • The resolution dependence seen within TNG (thinner disks at higher resolution) warns that the EAGLE–TNG differences could be partly numerical; a resolution-matched EAGLE run would settle this.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper presents Gal3D, an open-source framework that reconstructs a smoothed stellar density field from particle data using adaptive kernel density estimation and fits superellipsoids to iso-density surfaces, extracting radial profiles of axis ratios, orientation angles, center offsets, and superellipsoid shape indices S_a, S_b, S_c. The method is applied to z=0 galaxy samples from IllustrisTNG (TNG50-1, TNG50-2, TNG100-1) and EAGLE100, and the resulting mean profiles are used to compare disk extents, bar strengths, box/peanut bulge signatures, and outer triaxiality as functions of stellar mass. The paper also includes numerical sensitivity tests for the fitting objective and for the smoothing and angular-sampling parameters, and makes the code and shape-profile data publicly available.

Significance. If the method performs as claimed, Gal3D offers a substantially more flexible description of intrinsic 3D galaxy structure than the standard iterative inertia tensor, with the potential to separate boxiness and diskiness in a single radial profile. The reported TNG versus EAGLE differences in box/peanut bulge signatures and outer triaxiality are of direct interest for galaxy formation comparisons. Strengths of the paper include the public code and data releases, the careful sensitivity analysis in Appendix A, and the explicit acknowledgment in Section 2.5 of the limitation imposed by the single-valued isodensity assumption. However, the absence of synthetic recovery tests and the lack of uncertainties on the population maps currently leave the central quantitative claims under-supported.

major comments (3)
  1. [Section 5 / Figure 7] The population conclusions in Sections 5.1-5.3 rest on the mean maps in Figure 7, which are shown without any estimate of the uncertainty in the mean (for example, bootstrap or jackknife over galaxies) or a significance test for the TNG versus EAGLE differences. Please add per-bin uncertainties and perform a two-sample significance test in the relevant mass-radius bins, especially for the claims that EAGLE has less extended disks, weaker bars, and weaker box/peanut signatures; without these, the reported offsets may be within sampling noise.
  2. [Appendix A] The numerical tests in Appendix A compare the two objective functions and vary k and N_ray, but they never test whether the fitting recovers known input parameters. Because the core claim of the paper is that the superellipsoid indices S_a, S_b, S_c are recovered from simulated galaxies, the manuscript should include synthetic recovery tests in which density fields with known superellipsoid shape parameters (including S<1 and S>1, and with additional particle noise) are fitted and the input values are recovered. This would directly support the interpretation of S_a>1 and S_c>1 as box/peanut signatures and S_c<1 as a vertically disky morphology used in Sections 4.3 and 5.2.
  3. [Section 2.4.1 / 2.5] The monotonic regularization of the radial density profile in Section 2.4.1 enforces a single isodensity radius per ray, which suppresses genuine non-monotonic structures such as X-shaped box/peanut bulges. The paper acknowledges this in Section 2.5, but the comparison in Section 5.2 between TNG and EAGLE box/peanut signatures relies on the S_a and S_c values obtained from these regularized profiles. Please quantify the impact of this approximation on the fitted indices for representative X-shaped or multi-component morphologies, or add an explicit caveat that the measured box/peanut differences refer to the regularized single-valued description.
minor comments (4)
  1. [Section 2.3 / Equation (5)] The statement that the eigenvalues scale as lambda_i proportional to a^2, b^2, c^2 is made for a uniform ellipsoidal shell; please state the assumed surface density and the normalization convention so that readers can reproduce the relationship.
  2. [Section 2.4.3 / Equation (10)] The area-weighting factor (r'_i)^2 in the objective function is described as approximate; a brief derivation of why this factor corresponds to an equal-area weighting for the Fibonacci-sampled rays would improve transparency.
  3. [Section 4.3] The terms 'boxiness' and 'diskiness' are used to describe the superellipsoid shape indices, but these could be confused with the standard isophotal shape coefficients a_4/a; please add a sentence clarifying that S>1 and S<1 refer to the superellipsoid's departure from a purely ellipsoidal surface, not to Fourier isophote coefficients.
  4. [Section 3.3] The iterative shrinking-sphere centering method is cited but not described; adding a one-sentence summary of the algorithm and its convergence criterion would aid reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the shape indices are direct measurements from the reconstructed density field, and the TNG versus EAGLE trends are empirical summaries of those measurements.

full rationale

The central derivation chain is self-contained. Gal3D reconstructs a density field, extracts iso-density points along Fibonacci-sampled rays, and fits a 12-parameter superellipsoid to those points. The parameters a, b, c, S_a, S_b, S_c, center offsets, and Euler angles are all fitted from the particle data in a bounded least-squares problem (Section 2.4), so there is no quantity that is first fitted to a subset of data and then predicted as a closely related output. The TNG versus EAGLE comparisons in Section 5 are mean radial profiles of these fitted parameters; they are observational summaries of the measurements, not derivations that re-enter their own inputs. The interpretation of S_a > 1 and S_c > 1 as boxiness is a semantic reading of Equation (7) and Figure 2, but the paper does not claim to derive boxiness from the definition; it measures the indices and then interprets them, with one galaxy cross-checked against an external box/peanut identification (Anderson et al. 2023). Similarly, the bar-related quantity epsilon_ab = 1 - b/a is a direct ratio of fitted semi-axes, and the claim that it strengthens with stellar mass is an empirical trend, not a forced consequence of the fitting procedure. The self-citations to Zhao et al. (2020) and Lu et al. (2025) appear only as corroborative context for bar fraction trends in the same simulations and are not load-bearing for the method or for the new shape-index results. The acknowledged limitation in Section 2.5 that a single superellipsoid cannot exactly represent strongly X-shaped box/peanut bulges is an honest scope statement and is weighed as such; it flags a modeling approximation, not a circular step. Numerical sensitivity tests in Appendix A establish stability of the fitted profiles to the objective function, smoothing length, and ray number, and the code and data are publicly released. No step in the paper reduces to its own input by construction, and no prediction is equivalent to a fitted parameter renamed.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The method rests on standard numerical tools and domain assumptions about galaxy density structure. There are no invented physical entities. Free parameters are procedural choices; the S-index range and edge thresholds directly shape the reported trends.

free parameters (8)
  • k (KDE neighbor number) = 32
    Number of nearest neighbors in the adaptive kernel density estimation; profiles stable for k>=16 according to Appendix A, but value is hand-chosen for resolution/noise balance.
  • N_ray (Fibonacci directions) = 1024
    Angular sampling resolution; tests show N_ray=64 already reproduces trends, so 1024 is a hand-chosen practical value.
  • n (radial samples per ray) = 500
    Logarithmic radial sampling count; no sensitivity test reported.
  • S index bounds = 0.2 to 2
    Numerical bounds imposed on S_a, S_b, S_c; extreme shapes are clipped, which could compress measured boxiness.
  • bar threshold epsilon_ab=0.4 = 0.4
    Hand-chosen visual guide to mark bar edges and identify bar-related regions in Section 4; the population bar trends in Section 5.2 rest on this threshold.
  • disk threshold epsilon_ac=0.6 and bulge threshold 0.4 = 0.6 / 0.4
    Hand-chosen guides for disk and bulge outer boundaries used in Section 4 examples; also used in isolating radial regions.
  • outer density limit rho_outer = 100 Msun/kpc^3
    Defines the outermost radial extent of ray profiles; restricts the radial range of fitted shapes.
  • weighting parameter w_m = formula (1 + N_above)/(2 + N_m)
    Combines upper and lower monotonic envelopes in each radial interval; choice affects the regularized profile when density is non-monotonic.
assumptions (5)
  • standard math Fibonacci lattice on the sphere yields nearly uniform directions with Voronoi cell areas within about 2% of the mean.
    Section 2.2 invokes this property for angular quadrature; construction follows Caroli et al. 2009.
  • domain assumption The unweighted shape tensor (w=1) recovers the principal axes of an ellipsoidal shell.
    Section 2.3 adopts this from Zemp et al. 2011; the eigenvalue proportionality lambda_i proportional to a_i^2 is used to update the trial shell.
  • domain assumption The shrinking-sphere center is a valid origin for every fitted isodensity surface, with only small offsets.
    Section 3.3 recenters galaxies; Section 2.4.2 lets each surface have its own center offset but does not co-fit the global center.
  • domain assumption Density along each ray is monotonic once regularized, so each isodensity surface has exactly one radius per direction.
    Section 2.4.1 constructs monotonic profiles via envelope interpolation; this is the load-bearing geometric premise behind all fitted superellipsoids.
  • domain assumption The TRF solver converges to the global optimum of the bounded least-squares objective.
    Section 2.4.3 uses lmfit's TRF; no multi-start or global optimization is reported, so fit results may depend on initialization.

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Cite this review

Pith. "Pith review of Gal3D: Superellipsoid Modeling of Radial 3D Galaxy Structure in IllustrisTNG and EAGLE Simulations." pith.science (2026). https://pith.science/paper/ABRBAKHL

@misc{pith2026260812933,
  author       = {Pith},
  title        = {Pith review of: Gal3D: Superellipsoid Modeling of Radial 3D Galaxy Structure in IllustrisTNG and EAGLE Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ABRBAKHL}},
  note         = {Machine review of arXiv:2608.12933}
}
abstract

Galaxy morphology and structure are key tracers of galaxy formation and evolution, making accurate measurements of intrinsic three-dimensional (3D) shape essential for linking morphology to galaxy assembly and for comparing numerical simulations. We present Gal3D, a framework that reconstructs smoothed density fields from particle data and quantifies the radial 3D structure of simulated galaxies by fitting superellipsoids to iso-density surfaces. The method recovers axis ratios, orientations, center offsets, and superellipsoid indices ($S_a$, $S_b$, $S_c$), enabling a flexible characterization of diverse galactic structures such as disks, classical bulges, box/peanut bulges, and triaxial components. Applying Gal3D to galaxies in the IllustrisTNG and EAGLE simulations, we find that the radial extent of flattened disk regions increases with stellar mass up to $M_{*,30}\sim10^{11}\,M_\odot$ and then declines sharply, with EAGLE galaxies showing a saturation at $M_{*,30}\sim10^{10.5}\,M_\odot$. The bar-related $ \varepsilon_{ab}\equiv 1-b/a$ strengthens above $M_{*,30}\sim10^{10.5}\,M_\odot$ in both simulations, but remains systematically weaker in EAGLE. In TNG, outer bar regions are commonly associated with elevated $S_a$ and $S_c$, indicating enhanced boxiness and more prominent box/peanut-shaped bulges, whereas such higher-order signatures are weak or absent in EAGLE. At the highest stellar masses, flattened disks become less prominent, while inner prolate or triaxial structures remain common and massive EAGLE galaxies have more prolate or triaxial outer stellar bodies than their TNG counterparts. These results demonstrate that Gal3D provides a practical framework for quantifying intrinsic radial 3D structure and comparing morphology across cosmological simulations.

Figures

Figures reproduced from arXiv: 2608.12933 by the authors.

Figure 1
Figure 1. Overview of the Gal3D methodology. The central 3D rendering shows the stellar particle distribution (gray points), the spherical Voronoi cells associated with the ray directions (green mesh), and three nested fitted superellipsoid models at different density levels; the projected image beneath the rendering shows the corresponding model projection. Panels (a)–(c) show the three preprocessing steps: (a) adaptive kern… view at source ↗
Figure 2
Figure 2. Examples of generalized ellipsoids (superellipsoids) with varying ellipticities and shape indices. Left: standard ellipsoids (Sa = Sb = Sc = 1) with varying ellipticities εab ≡ 1−b/a and εbc ≡ 1−c/b, with the value of εac ≡ 1−c/a annotated in each panel. Moving upward increases flattening, while moving from left to right increases elongation. Right: models with fixed axis ratios a : b : c = 10 : 5 : 4 and varying sh… view at source ↗
Figure 3
Figure 3. Comparison of the projected stellar surface-density maps produced by the ellipsoid and superellipsoid models for a representative simulated galaxy. Rows are grouped into face-on (top two rows) and edge-on (bottom two rows) projections; within each pair, the upper row shows the wide-field view (25 kpc on a side) and the lower row shows the zoomed central region (6 kpc on a side), as indicated by the dashed rectangle … view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Distribution of the selected z = 0 galaxy samples in the κrot–M∗,30 plane. From left to right, the panels show TNG50-1, TNG50-2, TNG100-1, and EAGLE100. Points represent individual galaxies and are coloured by local number density, with the colour bar shown at the uppe…
Figure 5
Figure 5. Figure 5: Radial 3D shape profiles for three representative disk galaxies from TNG50-1. From top to bottom, the panel groups show an unbarred galaxy (SubfindID 264885), a barred galaxy (SubfindID 485056) with a face-on boxy but vertically thin bar, and a barred galaxy (SubfindID…
Figure 6
Figure 6. Figure 6: Similar to [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Two-dimensional maps of mean radial 3D shape profiles as functions of stellar mass log M∗,30 (x-axis) and radius r (y-axis) for the four simulation samples. Each column corresponds to one simulation, as labeled at the top. The five rows show, from top to bottom, the me…
Figure 8
Figure 8. Figure 8: Numerical tests of the superellipsoid fitting procedure for a representative TNG50-1 galaxy. The four rows show, from top to bottom, εac, εab, Sa, and Sc. The left column compares the radial profiles obtained with two objective functions: the fiducial surface-radius-ra…
Figure 9
Figure 9. Figure 9: Projected stellar surface-density maps of the χ 2 D and χ 2 f superellipsoid models for the test galaxy of [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Superellipsoids with fixed axis ratios a : b : c = 10 : 5 : 4 and Sc = 1, varying the shape indices Sa and Sb independently. This figure complements [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: Computation time as a function of particle number Npart for the superellipsoid fit and two implementations of the iterative shape-tensor method, measured on a single CPU core. Error bars show the mean and standard deviation of five repeated measurements at each partic…

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Reviewed August 15, 2026 · model on record in the stance chip above.