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REVIEW 3 major objections 5 minor 99 references

LIGHTS. A robust technique to identify galaxy edges

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper proposes that a galaxy's edge is the outermost minimum of the second derivative of its logarithmic stellar mass density profile, and shows that for NGC 3486 this criterion places the edge at 205 arcsec ± 5 arcsec with a stellar…

desk verdict A clear, well-tested edge-detection method for ultra-deep galaxy images, but the NGC 3486 edge sits suspiciously close to the model splice, so the quoted radius and ~1 M_sun/pc2 threshold should be treated as preliminary. read the letter →

arxiv 2507.01085 v2 pith:MWB2PRWQ submitted 2025-07-01 astro-ph.GA

Giulia Golini , Ignacio Trujillo , Dennis Zaritsky , Mireia Montes , Raúl Infante Sainz , Garreth Martin , Nushkia Chamba , Ignacio Ruiz Cejudo
show 14 more authors
Andrés Asensio Ramos Chen Yu Chuang Mauro D'Onofrio Sepideh Eskandarlou S. Zahra Hosseini ShahiSavandi Ouldouz Kaboud Carlos Marrero de la Rosa Minh Ngoc Le Samane Raji Javier Román Nafise Sedighi Zahra Sharbaf Richard Donnerstein Sergio Guerra Arencibia
This is my paper · ORCID
classification astro-ph.GA
keywords galaxyedgesstellarmassdensityprofilessecondderivativeedgedetectionWiener-Huntdeconvolutionpointspreadfunctionremovalstarformationthresholddeepimagingsurveyssizes
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 proposes that a galaxy's edge can be defined objectively as the outermost minimum of the second derivative of the logarithmic stellar surface mass density profile—the radius where the mass profile bends most sharply outward. The authors argue this is a physically motivated location because a disk that stops forming stars beyond a critical gas density should show exactly such a break. Applying the method to deep imaging of NGC 3486, after removing the point-spread function with Wiener-Hunt deconvolution, they identify the edge at 205 arcsec ± 5 arcsec. At that radius the stellar surface mass density is 1.3 ± 0.1 solar masses per square parsec, consistent with the predicted threshold for in situ star formation, and a two-dimensional wedge analysis finds only about 5 percent asymmetry. If correct, the method turns galaxy size into a reproducible, physically grounded measurement that can be automated for the coming ultra-deep surveys.

What carries the argument

The central object is the second derivative of the logarithmic stellar surface mass density, $\partial^2 \log \Sigma_*(r)/\partial r^2$; the paper's criterion is that its outermost minimum marks the galaxy edge. The argument is that a disk whose star formation is regulated by a gas-density threshold should have a broken-exponential mass profile, and for such a profile the outer minimum of the second derivative lands exactly on the break. The derivative is evaluated twice, numerically with a five-point stencil on the azimuthally averaged profile and analytically from a high-degree polynomial fit, and the two minima are averaged. To make the outer profile trustworthy, the point-spread function is removed with Wiener-Hunt deconvolution, a Fourier-space filter that suppresses noise with a regularization parameter, and the region beyond $R_{\rm PSFeff}\approx190''$—where deconvolution leaves too little signal—is replaced by a single exponential model with scale length $h_2=18.8''$, with residuals from a PSF-convolved version of the model added back so that real asymmetries survive.

What would settle it

Re-run the pipeline on the same data without the outer-exponential replacement, or with a different PSF-removal scheme; if the second-derivative minimum near 205 arcsec moves by more than 5 arcsec or disappears, the edge is an artifact of the data-to-model transition. As an independent check, map H-alpha or ultraviolet emission beyond 205 arcsec: detectable star formation there would contradict the claim that the edge is the limit of in situ star formation.

Watch

Extended reading notes

Core claim

The paper's central claim is that the end of in situ star formation imprints a break in the stellar mass distribution, and that the minimum of $\partial^2 \log\Sigma_*(r)/\partial r^2$ locates that break, defining the galaxy edge. On simulated broken-exponential disks, the method recovers the input edge whether the derivative is computed numerically or from a polynomial fit. For NGC 3486, after PSF removal, the numerical and polynomial minima sit at $213''\pm5''$ and $198''$, giving an adopted edge of $205''\pm5''$ ($13.8\pm0.6$ kpc). The mean stellar surface mass density at the edge is $1.3\pm0.1\,M_\odot/\mathrm{pc}^2$, the wedge-by-wedge values range from 0.75 to $4.5\,M_\odot/\mathrm{pc}^2$, and the global asymmetry is about 5%. At the same radius the neutral gas surface density is near $5\,M_\odot/\mathrm{pc}^2$, implying a star formation efficiency around 25%; the paper takes this as support for the idea that galaxy edges trace the threshold for in situ star formation, not just a visual brightness cutoff.

Load-bearing premise

The result depends on the assumption that the galaxy's outer disk beyond about 190 arcsec is faithfully represented by one smooth exponential decline fitted to the deconvolved image; because the reported edge at 205 arcsec lies just beyond this radius, a wrong outer model could create the sharp drop the method then finds.

Editorial extensions

If this is right

  • Galaxy sizes can be measured automatically and reproducibly from deep two-dimensional images, without visual inspection or ellipse-averaged profiles alone.
  • The ~1 solar mass per square parsec stellar density at the edge, alongside a gas density near 5 solar masses per square parsec, supports the view that the edge is the place where in situ star formation shuts off.
  • Wedge-based edge mapping makes asymmetry a measurable quantity; for NGC 3486 the edge varies by only about 5 percent around the ellipse, with neighboring sectors coherent.
  • Because stellar migration smooths edges with time, the sharpness of the detected break can be used as a rough clock for when star formation was truncated.
  • The automated recipe is designed to scale to the large, ultra-deep galaxy samples expected from next-generation sky surveys, where visual edge detection would be impractical.

Reading between the lines

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

  • If the stellar edge density is close to 1 solar mass per square parsec across disk galaxies, then edge radii measured this way become a nearly model-independent size definition; a natural next step is to measure the distribution of edge densities across galaxy mass and Hubble type.
  • Because the outer profile beyond ~190 arcsec is replaced by an exponential model, part of the sharpness at 205 arcsec may be imposed by the data-to-model transition; comparing against a deconvolution that does not replace the outer profile would isolate the intrinsic contribution.
  • The observed ~5 percent edge asymmetry and the asymmetric HI distribution of NGC 3486 both hint at a recent interaction; a testable extension is to correlate wedge-by-wedge edge radius with HI column density to see whether the edge is distorted where gas is disturbed.
  • Shallower images will make the second-derivative minimum noise-dominated; the method will likely need adaptive wedge widths or smoothing when applied to surveys that do not reach ~31 magnitudes per square arcsecond, trading angular resolution for reach.
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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 / 5 minor

Summary. The paper proposes a quantitative method for detecting the outer edges of disk galaxies by locating the outermost minimum of the second radial derivative of the logarithmic stellar surface mass density profile, in both one-dimensional elliptical-averaged profiles and two-dimensional wedge-based maps. The method is first demonstrated on a noise-free simulated broken-exponential disk, where the second-derivative minimum recovers the input edge radius. The authors then apply the method to the LIGHTS imaging of NGC 3486. After Wiener-Hunt deconvolution and a PSF-removal step in which the region beyond R_PSFeff ≈ 190 arcsec is replaced by an exponential model with h2 = 18.8 arcsec, they report an edge at R_edge = 205 arcsec ± 5 arcsec, a mean stellar surface mass density at the edge of 1.3 ± 0.1 M_sun/pc^2, and an edge asymmetry of about 5 percent. They interpret the result as supporting a connection between galaxy edges and the threshold for in situ star formation, and they argue the technique is well suited for automated edge measurement in upcoming deep surveys such as LSST, Euclid, and Roman.

Significance. If the method holds up, it offers a reproducible, automatable alternative to visual edge identification and can be extended to two-dimensional morphological analysis. The paper's strengths are the clean mathematical motivation, the explicit simulation test, and the multi-wavelength consistency checks (NUV/FUV drop, HI profile, earlier infrared break) that support the existence of an outer transition in NGC 3486. The code is presented as modular and automated, and the appendices document tests of the Wiener-Hunt deconvolution against noise, saturation, and an alternative wavelet-regularized method. However, the load-bearing NGC 3486 application has a potential circularity: the PSF-removed image contains a model exponential spliced at 190 arcsec, and the reported edge at 205 arcsec is close enough to that boundary that the measured edge location and the derived density threshold are not yet demonstrated to be independent of the chosen splice. The quantitative claims therefore require additional validation before the method can be considered robust.

major comments (3)
  1. [§4.2.2–§4.4, Fig. 4] The reported edge for NGC 3486 is not demonstrated to be independent of the PSF-removal model. Section 4.2.2 constructs the PSF-corrected image by splicing a single exponential with h2 = 18.8 arcsec into the region R > R_PSFeff ≈ 190 arcsec, while the inner region is the Wiener-Hunt deconvolved image. The edge-detection step in §4.4 then finds the minimum of the second derivative at 205 arcsec ± 5 arcsec, only one 10 arcsec bin outside the model boundary at R_PSFeff. Because the splice itself inserts a slope break in the logarithmic profile, the second-derivative minimum could be localizing the model transition rather than an intrinsic property of the galaxy; the 15 arcsec offset is comparable to the adopted bin width. The original profile in Fig. 4 does show a steepening near 200 arcsec, and the independent NUV/FUV and HI data support a real outer transition, so the edge may well be genuine. Nevertheless, the quantitative location and the derived 1.3 ± 0.1 M_sun/pc^2 threshold are not robustly measured unless the analysis is repeated without the splice. Please (a) compute the second derivative on the original background-subtracted profile and on the Wiener-Hunt deconvolved profile before the exponential is spliced in, (b) vary R_PSFeff and h2 over their plausible ranges and show that R_edge is stable, and (c) quantify the curvature contribution of the model boundary. The wavelet-deconvolution comparison in Appendix F tests the deconvolution step, not the edge-detection step against the splice location.
  2. [§4.4] The quoted uncertainty on R_edge does not reflect the actual spread between the two estimators used. The text reports R_edge,num = 213 arcsec ± 5 arcsec from the numerical derivative and R_edge,fit = 198 arcsec from the polynomial fit, a difference of 15 arcsec, which is three times the quoted error of ±5 arcsec. Adopting R_edge = 205 arcsec ± 5 arcsec as the mean of these two values underestimates the systematic uncertainty unless the two estimators are highly correlated, which is not argued. Given that the stellar mass density profile is steep at this radius, the claimed density 1.3 ± 0.1 M_sun/pc^2 depends on this choice. The authors should either report the full 198–213 arcsec range as the systematic uncertainty or provide a principled way of combining the two estimates.
  3. [§2.3 and Appendix F] The robustness of the method is not yet quantified for realistic data. The proof-of-concept simulation in §2.3 is noise-free with a known broken-exponential edge, and the deconvolution tests in Appendix F evaluate profile recovery, not the accuracy of the edge location. A central claim of the paper is that the technique is robust for deep imaging and suitable for survey pipelines, but no recovery test reports the bias and scatter of R_edge and Sigma*(R_edge) as a function of S/N, PSF shape, radial binning, wedge width, or model mismatch (for example, a disk with a faint stellar halo). A minimal addition would be to run the full edge-detection pipeline on the Noisy and Noisy2 models of Fig. F.1 and on a model with a halo like Model2, and to report how often and how accurately the input edge is recovered. Without such a test, the generality of the method across the varied data qualities of LSST, Euclid, and Roman is asserted rather than demonstrated.
minor comments (5)
  1. [Abstract] The abstract says 'removing the effect of the PSF by the galaxy itself'; the intended wording is 'from the galaxy itself'.
  2. [§4.5] Section 4.5 describes 60-degree wedges shifted by 30 degrees, which produces overlapping wedges; the text should clarify whether the wedges overlap and why this was chosen.
  3. [Equation (1)] Equation (1) contains a typesetting artifact ('h' before the bracket); please ensure the broken-exponential expression is typeset correctly.
  4. [Acknowledgements / Data availability] The paper does not provide a data/code availability statement despite emphasizing that the code is modular; for a methods paper, a repository link would help reproducibility.
  5. [Fig. 6] The statement that 'neighboring angular sectors exhibit similar R_edge,theta' is not quantitatively supported; a correlation test or at least a numeric summary would make the claim concrete.

Circularity Check

1 steps flagged · score 4.0 of 10

The NGC 3486 edge at 205″ is partly determined by the PSF-removal model boundary at R_PSFeff≈190″, although the second-derivative method itself is independently validated on simulations and by external gas/NUV data.

  1. fitted input called prediction [Sections 4.2.1, 4.2.2, and 4.4]
    "Compared to the original (background-subtracted) profiles, the deconvolved profiles exhibit a steeper outer slope beyond R=190''. We visually define this transition point as R_PSFeff. ... We modeled the Wiener-Hunt deconvolved profile in the range between R_PSFeff ... This results in an outer exponential scale length (h2) of 18.8'' in both filters. ... an outer region (R>R_PSFeff) that transitions to an exponential declining profile."

    The reported edge, R_edge=205''±5'', is the minimum of the second derivative of the PSF-removed stellar-mass profile. That profile is built by splicing an exponential model (h2=18.8'') fitted to the deconvolved data at R>R_PSFeff onto the deconvolved inner image, where R_PSFeff≈190'' was itself visually defined as the radius at which the deconvolved profile steepens. A second-derivative minimum is therefore expected near the splice location regardless of the galaxy's intrinsic structure, and the recovered 205'' lies only ~15'' (one to two radial bins) from the model boundary. Consequently the quantitative edge and the associated Sigma*(R_edge)=1.3 M_sun/pc2 are not fully independent of the PSF-removal assumption.

full rationale

The central methodological claim—that the minimum of the second derivative of the logarithmic stellar mass density locates a galaxy edge—is not circular: it is derived from a broken-exponential model and validated on a simulated disk in Section 2.3, where the true edge is known and recovered. The application to NGC 3486, however, contains a partially circular step. The PSF-removed image used for edge detection is constructed by fitting an outer exponential to the Wiener-Hunt deconvolved profile beyond R_PSFeff, a radius visually defined as the steepening point of that same profile, and then splicing this model onto the inner data. The second-derivative minimum at 205''±5'' therefore largely tracks the model transition at ~190'' rather than being an independent measurement. This is mitigated by the fact that the original, unmodified profile already shows a slope change near 200'', and by independent agreement with gas, NUV, and infrared indicators, so the edge is not purely an artifact. Still, the quantitative edge location and the ~1 M_sun/pc2 threshold are not fully model-independent. No load-bearing self-citation or uniqueness import was found; the many self-citations are to prior data-reduction and edge-measurement work and do not by themselves force the result.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The central measurement rests on fitted profile parameters (h2, R_PSFeff, polynomial degree, wedge width) and on standard assumptions about galaxy profile shapes, PSF removal, and mass-to-light conversion.

free parameters (4)
  • Outer exponential scale length h2 = 18.8 arcsec (both g and r bands)
    Fitted to the Wiener-Hunt deconvolved surface brightness profile between R_PSFeff and the 0.1 mag uncertainty radius (Section 4.2.2); used to build the PSF-removed model of the outer disk, from which the edge profile is derived.
  • R_PSFeff (PSF-effective radius) = ~190 arcsec (visually defined)
    The radius beyond which the PSF is deemed to affect the profiles; visually set from Fig. 4 (Section 4.2.2). The outer model starts here, so this choice influences where the edge can be found.
  • Polynomial degree for profile fitting = 30 (stated as a high-degree polynomial)
    A 30-degree polynomial is fit to the averaged stellar mass density profile to compute analytical second derivatives (Sections 2.3.1 and 4.4); the edge estimate is averaged between numerical and polynomial results.
  • Wedge width for 2D analysis = 60 degrees (12 wedges)
    Chosen as a compromise between S/N and azimuthal resolution (Section 4.5); affects the recovered per-wedge edge radii.
assumptions (5)
  • domain assumption Disk galaxy stellar mass profiles are well described by a broken exponential with two scale lengths (Eq. 1); the transition point defines the galaxy edge.
    Adopted in Section 2.2 and used to justify that the minimum of the second derivative of log Sigma* locates the edge; real galaxies may deviate.
  • standard math The second derivative of log Sigma*(r) has a minimum at the transition radius for a broken exponential.
    Mathematically true for the functional form in Eq. 1 with a sufficiently sharp transition; used throughout Section 2.
  • domain assumption The LIGHTS PSF model (Sedighi et al. 2025) and the Wiener-Hunt deconvolution with automatic regularization accurately recover the intrinsic light distribution.
    Relied on in Section 4.2.1 to remove PSF effects; tests in Appendix F show edge preservation but not for the full model-subtraction pipeline.
  • domain assumption The stellar mass density map derived from g and r band imaging via the Roediger and Courteau (2015) M/L-color relation and a Chabrier IMF traces the true stellar mass distribution.
    Used in Section 4.3 to build Sigma* maps; uncertainties in M/L and IMF affect absolute Sigma*(R_edge) but not the shape strongly, as the paper notes.
  • domain assumption The distance to NGC 3486 is 13.6 Mpc (Kourkchi et al. 2020).
    Converts the edge radius from arcsec to kpc and affects the absolute mass densities and comparisons with literature.

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Cite this review

Pith. "Pith review of LIGHTS. A robust technique to identify galaxy edges." pith.science (2026). https://pith.science/paper/MWB2PRWQ

@misc{pith2026250701085,
  author       = {Pith},
  title        = {Pith review of: LIGHTS. A robust technique to identify galaxy edges},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MWB2PRWQ}},
  note         = {Machine review of arXiv:2507.01085}
}
abstract

The LIGHTS survey is imaging galaxies at a depth and spatial resolution comparable to what the Legacy Survey of Space and Time (LSST) will produce in 10 years (i.e., $\sim$31 mag/arcsec$^2$; 3$\sigma$ in areas equivalent to 10$^{\prime\prime}$$\times$ 10$^{\prime\prime}$). This opens up the possibility of probing the edge of galaxies, as the farthest location of in-situ star formation, with a precision that we have been unable to achieve in the past. Traditionally, galaxy edges have been analyzed in one-dimension through ellipse averaging or visual inspection. Our approach allows for a two-dimensional exploration of galaxy edges, which is crucial for understanding deviations from disc symmetry and the environmental effects on galaxy growth. In this paper, we propose a novel method using the second derivative of the surface mass density map of a galaxy to determine its edges. This offers a robust quantitative alternative to traditional edge-detection methods when deep imaging is available. Our technique incorporates Wiener-Hunt deconvolution to remove the effect of the Point Spread Function (PSF) by the galaxy itself. By applying our methodology to the LIGHTS galaxy NGC 3486, we identify the edge at 205$^{\prime\prime}$ $\pm$ 5$^{\prime\prime}$. At this radius, the stellar surface mass density is $\sim$1 M$_\odot$/pc$^2$, supporting a potential connection between galaxy edges and a threshold for in-situ star formation. Our two-dimensional analysis on NGC 3486 reveals an edge asymmetry of $\sim$5$\%$. These techniques will be of paramount importance for a physically motivated determination of the sizes of galaxies in ultra-deep surveys such as LSST, Euclid and Roman.

Figures

Figures reproduced from arXiv: 2507.01085 by the authors.

Figure 1
Figure 1. Edge detection method. The figure presents the stellar mass density map in Cartesian and polar coordinates (top left and top central panels), and the averaged surface stellar mass density profile (bottom left panel) of a simulated disk, computed in three different cases as is explained in the main text. The first derivative of the stellar mass density profile (bottom central panel) and the second derivative in both … view at source ↗
Figure 2
Figure 2. Flowchart illustrating the steps used to account for the effect of the PSF on the outermost regions of NGC 3486 (see main text for details). The panels display LIGHTS data of NGC 3486. Each panel covers a FoV of 15.5′ × 15.5′ . Article number, page 6 of 17 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Surface stellar mass density profiles of two simulated disks. Left: Model1, consisting of a broken exponential disk only. Center: Model2, similar to Model1, but with a steeper outer disk slope (h2) and a faint stellar halo. Right: Comparison of the PSF-convolved profiles for both models. from the X axis). This choice of parameters is justified in the Appendix E and compared with previous estimates. To maintain consi… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Surface brightness profiles of NGC 3486 in the g band (up￾per panel) and r band (central panel) using LIGHTS data. The sur￾face brightness profiles shown correspond to the background-subtracted data (green), the Wiener-Hunt deconvolved data (blue), and the data for whi…
Figure 5
Figure 5. Figure 5: Edge detection in NGC 3486. Upper row: Stellar mass surface density map in Cartesian and polar coordinates (left and central panels) and polar map of its second derivative (right). Bottom row: Radial profile of averaged stellar mass surface density as a function of rad…
Figure 6
Figure 6. Figure 6: Distribution of stellar surface mass density at Redge,θ. The green box corresponds to 1.3 ± 0.1 M⊙/pc2 at Redge. The orange line corre￾sponds to the median of the Σ⋆(Redge,θ). The colored region corresponds to a 1σ dispersion. Coincidence of locations at Redge,θ occurs…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.