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

The paper presents 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 (Sa, Sb, Sc), 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 ∼ 1011 M⊙ and then declines sharply, with EAGLE galaxies showing a saturation at M∗,30 ∼ 1010.5 M⊙. The bar-related εab ≡ 1 − b/a strengthens above M∗,30 ∼ 1010.5 M⊙ in both simulations, but remains systematically weaker in EAGLE. In TNG, outer bar regions are commonly associated with elevated Sa and Sc, 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.

The paper details the methodology: The method first reconstructs a continuous stellar mass density field with adaptive kernel density estimation, and then provides two complementary approaches: an iterative shape-tensor method that refines a trial ellipsoidal shell on the density field, and a ray-based superellipsoid fit that matches a superellipsoid surface to extracted isodensity contours. The shape tensor provides an ellipsoidal reference measurement of axis ratios and orientations, while the superellipsoid fit is our fiducial method for capturing non-ellipsoidal structure through additional shape parameters. The fitted 3D models can also be projected and compared directly with simulated stellar surface-density maps.

The superellipsoid parameterization is given by f (x, y, z) = (x/a)(2Sa) + (y/b)(2Sb) + (z/c)(2Sc) = 1, where a ≥ b ≥ c > 0 are the semi-axes, and Sa, Sb, and Sc are the superellipsoid shape indices. The standard ellipsoid is recovered when Sa = Sb = Sc = 1, whereas S 1 produces boxier shapes. Each fitted iso-density surface is allowed to have its own center and orientation in the simulation coordinate system, with 12 free parameters: the semi-axes (a, b, c), the superellipsoid indices (Sa, Sb, Sc), the center offsets (∆xc, ∆yc, ∆zc), and the Euler angles (α, β, γ).

The paper applies Gal3D to four simulation samples: TNG50-1, TNG50-2, TNG100-1 from IllustrisTNG, and EAGLE100 from EAGLE. The final samples contain 4333, 1088, and 6519 galaxies for TNG50-1, TNG50-2, and TNG100-1, respectively, and 3043 galaxies for EAGLE100.

The main results are summarized in two stellar-mass regimes:

At stellar masses (10.0 ≲ log(M∗,30 /M⊙) ≲ 11.0):

• The radial extent of flattened disk regions increases with stellar mass up to ∼ 1011 M⊙. Over this mass range, EAGLE galaxies have less radially extended and less vertically thinner disk structures than TNG galaxies and show a saturation of disk extent at log(M∗,30 /M⊙) ∼ 10.5, while the TNG runs continue to increase up to ∼ 1011 M⊙. Higher TNG resolution is associated with thinner disk structures.

• The bar-related ⟨εab ⟩ signal strengthens above log(M∗,30 /M⊙) ∼ 10.5 in all four simulations, but remains systematically weaker in EAGLE100 than in the TNG runs. Within the TNG suite, higher resolution is associated with a less radially extended bar-related region.

• Box/peanut-shaped bulges are more prominent in TNG than in EAGLE100.

Across the transition interval 11.0 ≲ log(M∗,30 /M⊙) ≲ 11.1, the radial extent of flattened disk regions declines sharply, from tens of kiloparsecs to less than ∼ 10 kpc.

At the highest stellar masses (log(M∗,30 /M⊙) ≳ 11.1):

• Prolate or triaxial stellar structures remain common in the inner regions of massive galaxies in both simulations.

• The outer bodies of massive EAGLE galaxies are, on average, more prolate or triaxial than their TNG counterparts.

The paper also demonstrates that Gal3D can distinguish nuclear disks, bulges, main disks, bars, box/peanut bulges, stellar halos, and early-type envelopes, while also quantifying higher-order features such as boxiness and diskiness. The superellipsoid indices provide an efficient discriminator between boxy and disky isodensity structures that are degenerate in axis-ratio profiles.

Improvement 1: Morphology-Aware Galaxy Classification System

• What it does: An AI system can now classify simulated galaxies into fine-grained 3D structural types (e.g., disk+bulge, box/peanut bulge, triaxial early-type, nuclear disk) using the full superellipsoid parameter set (a, b, c, Sa, Sb, Sc, center offsets, Euler angles) instead of relying on 2D projected images or simple axis ratios.

• Specific capability: Given a galaxy's stellar particle data, the AI can output a structured label (e.g., flattened disk with boxy bulge, Sa=1.3, Sc=0.8) and a confidence score, enabling automated large-scale morphological census across cosmological simulations.

Improvement 2: Predictive Scaling Relation for Disk Extent vs. Stellar Mass

• What it does: The AI can predict the radial extent of flattened disk regions (and its sharp decline) as a function of stellar mass, calibrated to the two-regime behavior (rise to 10 11 M⊙, then collapse).

• Specific capability: For a new simulation or observed galaxy, the AI can estimate the expected disk radius and flag outliers (e.g., galaxies with unusually extended disks at high mass), aiding in identifying feedback or merger-driven quenching events.

Improvement 3: Cross-Simulation Morphology Transfer and Bias Correction

• What it does: The AI learns the systematic differences between TNG and EAGLE (e.g., weaker bar-related ε ab, less boxy bulges, more prolate outer bodies in EAGLE) and can correct for resolution or subgrid physics biases.

• Specific capability: Given a galaxy from EAGLE, the AI can predict what its TNG-equivalent morphology would be (e.g., if this galaxy were in TNG, its bar would be 20% stronger and its disk 15% more extended), enabling apples-to-apples comparisons across simulations.

Improvement 4: Generative Model for Synthetic Galaxy Density Fields

• What it does: Using the 12-parameter superellipsoid fits as a compact latent representation, the AI can generate new, realistic 3D stellar density fields for galaxies with specified morphology (e.g., boxy bulge, Sa=1.2, Sb=1.0, Sc=0.9, with a 5 kpc disk).

• Specific capability: This enables rapid creation of mock galaxy catalogs for training other AI systems (e.g., image-based classifiers) without running expensive hydrodynamical simulations, and allows controlled experiments on how morphology affects observable properties.

Improvement 5: Automated Detection and Quantification of Bars and Box/Peanut Bulges

• What it does: The AI can automatically identify the radial range where ε ab (bar strength) and Sa/Sc (boxiness) are elevated, and output the bar length, strength, and whether a box/peanut bulge is present.

• Specific capability: For a galaxy, the AI returns a structured report: Bar detected from 2–6 kpc, ε ab=0.35, Sa=1.4 (boxy), Sc=0.7 (peanut-like). This replaces manual or threshold-based methods, enabling unbiased comparisons of bar fractions across mass and redshift.

Improvement 6: Radial Morphology Profiler

• What it does: The AI can take a galaxy and output a continuous radial profile of shape parameters (a, b, c, Sa, Sb, Sc, center offsets, orientation) at every isodensity surface, effectively compressing the full 3D structure into a 1D morphological fingerprint.

• Specific capability: This fingerprint can be used for clustering galaxies into morphological families (e.g., disk-dominated with inner triaxiality) or for tracking how a galaxy's structure evolves over time in a simulation, without manual inspection.

Improvement 7: Resolution-Aware Morphology Predictor

• What it does: The AI learns how superellipsoid parameters (especially disk thinness and boxiness) vary with simulation resolution (TNG50-1 vs. TNG50-2 vs. TNG100-1) and can correct for resolution-induced biases.

• Specific capability: Given a low-resolution galaxy, the AI can predict its high-resolution morphology (e.g., disk thickness would decrease by 20% and Sa would increase by 0.1 at TNG50-1 resolution), enabling fair comparisons across different simulation runs or observations.

Improvement 8: Anomaly Detector for Unusual 3D Structures

• What it does: Using the distribution of superellipsoid parameters across the full galaxy population, the AI can flag galaxies with extreme or rare shapes (e.g., Sa > 2, or highly offset centers) that may indicate mergers, tidal disruption, or numerical artifacts.

• Specific capability: The AI outputs a list of anomalous galaxies with a reason (e.g., Sc=0.3, unusually disky outer envelope, likely a recent accretion event), helping researchers prioritize follow-up analysis.