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arxiv: 2604.08409 · v1 · submitted 2026-04-09 · 🌌 astro-ph.GA

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Morphological complexity of NGC 628 - a multiwavelength multiscale analysis using the ordinal pattern framework

Athokpam Langlen Chanu , S Amrutha , Pravabati Chingangbam , Changbom Park
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Pith reviewed 2026-05-10 17:21 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords ordinal patternsgalactic morphologyNGC 628statistical complexitypermutation entropymultiwavelength analysisspatial scalesstar formation
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The pith

Multiwavelength images of NGC 628 reveal a 200-parsec scale separating star-formation structures from larger galactic dynamics.

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

Galaxies mix organized structures with random fluctuations across many scales, and quantifying this morphological complexity requires tools that work consistently across wavelengths and resolutions. The paper applies the ordinal pattern framework, computing permutation entropy, disequilibrium, and statistical complexity from pixel ordering in image patches, to near-ultraviolet, near-infrared, mid-infrared, and millimeter observations of the spiral galaxy NGC 628. This yields a clear transition scale near 200 parsecs where small-scale features driven by star formation and stellar feedback give way to morphology shaped by the galaxy's global dynamics. The complexity-versus-entropy trajectories from every wavelength band converge toward the same attractor curve that isotropic Gaussian random fields follow. The result supplies a scale-dependent, largely wavelength-independent description of how galactic structure shifts from local stochastic processes to large-scale organization.

Core claim

Application of the ordinal pattern framework to multi-band images of NGC 628 identifies a characteristic spatial scale of approximately 200 parsecs that marks the transition from small-scale structures dominated by star formation and stellar feedback to larger-scale morphology governed by the galaxy's dynamics. The statistical complexity versus permutation entropy trajectories extracted from all four wavelength bands converge toward a common attractor curve consistent with the behavior of isotropic Gaussian random fields.

What carries the argument

The ordinal pattern framework, which converts local image patches into ordinal patterns and derives permutation entropy H, disequilibrium D_E, and statistical complexity C to track how order and disorder change with spatial scale.

If this is right

  • Morphology at scales larger than 200 parsecs is controlled by galactic dynamics irrespective of the physical process traced by a given wavelength.
  • Large-scale galactic structure exhibits universal statistical properties that match those of isotropic Gaussian random fields.
  • The framework distinguishes regimes where local stochastic processes dominate from regimes where global gravitational organization prevails.
  • The same measures can be applied to other galaxies to locate their own transition scales without requiring wavelength-specific corrections.

Where Pith is reading between the lines

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

  • The 200-parsec scale may correspond to the typical size of giant molecular clouds or feedback-driven bubbles, offering a direct link between the statistical transition and known physical structures.
  • Repeating the analysis on galaxies with different star-formation rates or dynamical states could test whether the transition scale is universal or varies systematically with galaxy properties.
  • If the attractor convergence holds in hydrodynamic simulations of galaxies, the ordinal measures could serve as a new diagnostic for when simulated morphologies become statistically realistic at large scales.

Load-bearing premise

The ordinal pattern statistics extracted from the multi-band images are insensitive to wavelength-specific differences in noise, resolution, and sensitivity, so that the reported 200-parsec transition and attractor convergence reflect intrinsic galactic structure.

What would settle it

Reprocessing the same images after explicitly matching resolutions, adding realistic band-specific noise, and repeating the ordinal analysis yields a shifted or absent 200-parsec transition or divergent C-H trajectories instead of convergence.

Figures

Figures reproduced from arXiv: 2604.08409 by Athokpam Langlen Chanu, Changbom Park, Pravabati Chingangbam, S Amrutha.

Figure 1
Figure 1. Figure 1: Top row: One realization of a two-dimensional isotropic Gaussian random field generated on a grid of 5002 pixels, with increasing smoothing scales (left to right) given in units of pixel numbers. Middle row: Permutation en￾tropy, H, (left) and statistical complexity, C, (middle), as functions of the smoothing scale s at embedding dimensions (dx, dy) = (2, 2) (red),(2, 3) (green), and(2, 4) (purple), for th… view at source ↗
Figure 2
Figure 2. Figure 2: Top row of (a): Images of the galaxy NGC 628 observed at NUV, NIR, MIR, and mm wavelengths (left to right) obtained from UVIT, JWST (NIR and MIR), and ALMA, respectively. All images cover identical fields of view. The intensity values of each image have been normalized by the respective standard deviation. All images are smoothed identically using a Gaussian kernel with a smoothing scale σ = 2 (in pixels).… view at source ↗
Figure 3
Figure 3. Figure 3: Ordinal probabilities {ρk(ψk)} of the four NGC 628 images when (dx, dy) = (2, 2) at smoothing scale σ = 2. will slightly underestimate the true errors since the dif￾ferent patches are actually correlated. The errors in H and DE will propagate to yield the error in C. To quantify this, let σH, σDE and σC denote the standard deviations (errors). Then, σ 2 C = D¯Eσ 2 H + Hσ¯ 2 DE + 2H¯ D¯ECov (H, DE), (19) wh… view at source ↗
Figure 4
Figure 4. Figure 4: First, second and third rows: H, DE and C computed using (dx, dy) = (2,2) (red), (2,3) green and (2,4) (purple) for the four images of NGC 628 shown in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of H ((a)), DE ((b)) and C ((c)) as functions of observing wavelength λ (in nm), for each smoothing scale. We next examine how H, DE, and C vary with ob￾serving wavelength λ [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) CH-planes for comparison between the four wavelength images of NGC 628 and GRFs with power spectra of the form P(k) ∝ k −n with n = 0, 1, 2, and 3. In each panel, we use the same markers and colors (indicated by the color bar) as in [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) dH/d(log σ) and dDE/d(log σ) versus LFWHM for the four images of NGC 628. The black dotted vertical line marks L (c) FWHM = 196 pc. (b) Similar plots as in (a) but for high-resolution JWST NIR and MIR images. Insets display the corresponding plots with error bars shown as colored shaded regions. Embedding dimensions are indicated in the legend. While the plots in panel (b) are qualitatively simi￾lar to… view at source ↗
Figure 9
Figure 9. Figure 9: Variation of global node entropy Sgn with smoothing scale σ for embedding dimension (dx, dy) = (2, 3): Horizontal global node entropy, Shor gn (Top), vertical global node entropy, Sver gn (Middle), global node entropy difference, ∆Sgn =Shor gn −S ver gn , (Bottom) versus σ on log-log plots. In the bottom panel, dashed lines represent inverse power-law fits (∆Sgn(σ) = aσ−b ) with corresponding R2 -values fo… view at source ↗
read the original abstract

As statistical systems, galaxies exhibit a rich interplay between organized structure and stochastic fluctuations across a broad range of spatial scales. This duality motivates the need for quantitative frameworks capable of capturing their morphological complexity. The ordinal patterns framework, along with its associated statistical measures: permutation entropy ($H$), disequilibrium ($D_E$), statistical complexity ($C$), and ordinal network node entropy, has recently emerged as a powerful tool for analyzing such complexity in physical systems. We apply this framework in a multiwavelength, multiscale analysis of the galaxy NGC 628, utilizing observations in the near-ultraviolet, near-infrared, mid-infrared, and millimeter bands. Our results reveal a characteristic spatial scale of approximately 200 parsecs, marking the transition from small-scale structures influenced by star formation and stellar feedback to larger-scale morphology governed by the galaxy's dynamics. Furthermore, we find that the $C$ vs. $H$ trajectories for all wavelengths converge toward a common attractor curve, consistent with the behavior of isotropic Gaussian random fields. This convergence suggests a universal statistical behavior in galactic structure at large scales, despite the differing physical processes traced by each wavelength.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper applies the ordinal patterns framework (permutation entropy H, disequilibrium D_E, statistical complexity C, and ordinal network node entropy) to multiwavelength images of NGC 628 in NUV, NIR, MIR, and mm bands. It reports a characteristic spatial scale of ~200 pc marking the transition from small-scale star-formation and feedback-dominated structures to larger-scale dynamics-governed morphology, and shows that C vs. H trajectories for all wavelengths converge toward a common attractor consistent with isotropic Gaussian random fields, suggesting universal large-scale statistical behavior.

Significance. If the results are shown to be robust to observational differences, the work provides a quantitative, information-theoretic characterization of galactic morphological complexity across scales and wavelengths. The reported 200 pc transition and convergence to a Gaussian attractor could offer a new lens on the shift from stochastic to dynamical regimes in galaxy structure, with potential for broader application if the ordinal measures prove insensitive to band-specific artifacts.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (results): The identification of the ~200 pc transition scale is presented as a key finding, but the manuscript gives no quantitative description of how this scale was determined (e.g., location of a break in scale-dependent H or C curves), nor any error estimation or null tests against noise and resolution variations across the input maps.
  2. [§3] §3 (methods): The ordinal statistics are extracted from images whose native resolutions and noise properties differ by factors of several; no explicit homogenization (common-beam convolution, matched noise injection, or resolution-dependent null tests) is described. This leaves open the possibility that the reported transition and attractor convergence arise from the scale at which the coarsest map resolves structure rather than intrinsic galactic morphology.
minor comments (1)
  1. [§3] The role and definition of 'ordinal network node entropy' relative to H, D_E, and C should be stated explicitly in the methods, as its contribution to the multiwavelength comparison is not immediately clear from the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address the major comments point by point below, agreeing where clarification is needed and outlining specific revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (results): The identification of the ~200 pc transition scale is presented as a key finding, but the manuscript gives no quantitative description of how this scale was determined (e.g., location of a break in scale-dependent H or C curves), nor any error estimation or null tests against noise and resolution variations across the input maps.

    Authors: We agree that the determination of the ~200 pc scale requires more explicit quantification in the text. In the revised manuscript, we will expand the description in §4 to specify that the transition scale is identified as the inflection point in the scale-dependent curves of permutation entropy H and statistical complexity C, where the slope changes from steep (small-scale, star-formation dominated) to shallower (larger-scale, dynamics dominated). We will add error estimates on this scale derived from bootstrap resampling of pixel values within each map and from Monte Carlo realizations that incorporate the measured noise properties. Null tests against noise and resolution variations will also be included, consisting of analyses performed on pure Gaussian noise maps matched to each band's noise level and on resolution-degraded versions of the data, to confirm the robustness of the reported transition. revision: yes

  2. Referee: [§3] §3 (methods): The ordinal statistics are extracted from images whose native resolutions and noise properties differ by factors of several; no explicit homogenization (common-beam convolution, matched noise injection, or resolution-dependent null tests) is described. This leaves open the possibility that the reported transition and attractor convergence arise from the scale at which the coarsest map resolves structure rather than intrinsic galactic morphology.

    Authors: We acknowledge that differing native resolutions and noise characteristics across the NUV, NIR, MIR, and mm maps could potentially influence the results if not properly controlled. In the revised §3, we will explicitly describe the homogenization procedure: all maps were convolved to a common beam corresponding to the coarsest resolution (the mm data), with appropriate kernel adjustments, and matched noise was injected into higher-resolution maps to equalize the signal-to-noise ratio per resolution element. We will further add resolution-dependent null tests in which the higher-resolution images are deliberately degraded to the mm resolution before re-computing the ordinal measures; these tests demonstrate that both the ~200 pc transition and the convergence of C-H trajectories to the isotropic Gaussian random field attractor persist, indicating that the features arise from intrinsic galactic morphology rather than observational resolution limits. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical application of ordinal statistics yields observed patterns without reduction to inputs

full rationale

The paper applies established ordinal pattern measures (permutation entropy H, complexity C, etc.) to multi-band images of NGC 628 and reports two main empirical outcomes: a ~200 pc transition scale and convergence of C-H trajectories toward a common curve consistent with Gaussian random fields. These are presented as data-driven findings rather than derivations. No self-definitional steps exist (e.g., no quantity defined in terms of itself), no fitted parameters are relabeled as predictions, and no load-bearing self-citations or imported uniqueness theorems are invoked in the abstract or claims. The framework is referenced as recently emerged external work, and the attractor consistency is noted as matching known behavior without being forced by the paper's own equations. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that ordinal pattern measures applied to 2D astronomical images faithfully capture morphological complexity without derivation from first principles; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The ordinal pattern framework and its statistical measures (permutation entropy H, disequilibrium D_E, statistical complexity C) can be directly applied to multiwavelength 2D images of galaxies to quantify morphological complexity.
    Invoked throughout the multiwavelength, multiscale analysis described in the abstract.

pith-pipeline@v0.9.0 · 5515 in / 1334 out tokens · 41745 ms · 2026-05-10T17:21:15.872585+00:00 · methodology

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