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REVIEW 5 major objections 3 minor 25 references

AXES-SDSS: Solving the puzzle of X-ray emission of optical galaxy groups via a modified Hausdorff distance

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

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Pith's one-line read A modified Hausdorff distance of 0.631 Mpc matches optical galaxy groups to X-ray sources at 90% purity, revealing that over half of nearby groups, even low-mass ones, emit X-rays.

desk verdict The MHD matching idea is a genuine improvement for optical-X-ray group matching, but the headline purity and low-σ detection claims are not yet backed by a reproducible measurement. read the letter →

arxiv 2507.06377 v1 pith:XBFGPZQW submitted 2025-07-08 astro-ph.HE astro-ph.CO

J. Kosowski , A. Finoguenov , E. Tempel , G. A. Mamon This is my paper · ORCID
classification astro-ph.HEastro-ph.CO
keywords galaxygroupsX-rayemissionclustersmodifiedHausdorffdistanceROSATAll-SkySurveySDSSgroupcatalogpurityandcompletenessvelocitydispersion
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

This paper establishes a reproducible way to identify which optical galaxy groups correspond to X-ray sources, using a modified Hausdorff distance between the group's galaxy positions and X-ray contours. The authors claim that a distance cutoff of 0.631 Mpc yields 90% purity, and that over half of nearby groups have X-ray emission, including groups with velocity dispersions as low as 200 km/s. If correct, this overturns the view that low-mass groups often lack X-ray emission because of feedback. Instead, previous non-detections would be explained by over-merging in optical group catalogs and source confusion in X-ray data. This matters because clean group identifications are a prerequisite for cluster cosmology, especially at low redshift where projection effects are strongest.

What carries the argument

The load-bearing tool is a modified Hausdorff distance, in which the directed distance from one set to another is the median, rather than the maximum, of the nearest-neighbor distances between points, and the two directed distances are averaged rather than maximized. This variant is robust to interloper galaxies and to unrelated X-ray sources contaminating the contours. The X-ray contours are extracted from ROSAT All-Sky Survey data by combining wavelet scales of 12 and 24 arcminutes after removing smaller-scale emission, drawn at a fixed surface brightness level of 2e-5 counts per second per pixel. The optical side uses volume-limited friends-of-friends group catalogs with a constant linking length, chosen so that the group membership traces a similar baryonic overdensity as the X-ray contour level.

What would settle it

Use a hydrodynamical simulation to generate synthetic X-ray maps at the same 0.5-2 keV band and wavelet scales, then check whether the 2e-5 counts per second per pixel contour that encloses 1266 square degrees of the all-sky RASS maps actually sits at baryonic overdensity about 500; alternatively, point a deeper X-ray telescope at dozens of the matched 200-300 km/s groups and check whether the majority show independent X-ray emission, as the paper's central claim requires.

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Extended reading notes

Core claim

The central claim is that two-way matching between X-ray contours drawn at a fixed surface brightness level and the projected positions of optical group members, measured with a modified Hausdorff distance (MHD), identifies galaxy groups far more completely than earlier methods that rely on optical counterpart distance and richness. Using volume-limited SDSS group catalogs, the paper finds an MHD cutoff of 0.631 Mpc gives 90% purity, with completeness of 50% for groups with velocity dispersions around 200 km/s at low redshift, degrading toward higher redshift in a way that indicates flux-limited rather than surface-brightness-limited detection. More than half of nearby groups are matched to X-ray emission, and the matched low-velocity-dispersion groups follow the same velocity-dispersion–X-ray-luminosity scaling relation as groups with small optical/X-ray center separations. The paper concludes that large optical/X-ray center offsets are not signs of unassociated systems or different feedback levels, but are artifacts of over-merging in the optical group catalog and source confusion in the X-ray maps.

Load-bearing premise

The X-ray contour level chosen by experimentation is assumed to correspond to roughly the same baryonic overdensity, about 500 times the mean, as the optical group finder's membership, so that the two tracers probe the same physical region; if that correspondence is wrong, all the matching distances and the purity and completeness estimates are systematically biased.

Editorial extensions

If this is right

  • Previous non-detections of X-ray emission from low-mass galaxy groups should be attributed to over-merging in optical group catalogs and source confusion in X-rays, not to feedback suppressing the gas.
  • Groups with large separations between their optical and X-ray centers are genuine associations, since they obey the same velocity-dispersion–X-ray-luminosity scaling relation as groups with well-centered emission.
  • An MHD cutoff computed in physical megaparsecs yields higher completeness than an angular cutoff while preserving comparable purity, so it is the preferable matching criterion for nearby groups.
  • Cleaning group membership with the MHD cutoff produces a shallower velocity-dispersion–X-ray-luminosity scaling relation, indicating that interloper removal changes the derived scaling properties of groups.
  • The identification procedure is reproducible and not tuned to a specific pair of surveys, so it can be applied to future optical and X-ray data that reach similar group outskirts.

Reading between the lines

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

  • Deeper X-ray surveys such as eROSITA should recover the same low-velocity-dispersion groups at higher redshift if the flux-limited interpretation is correct; a systematic absence there would challenge the claim that over half of nearby groups emit X-rays.
  • Hydrodynamical simulations can turn the asserted correspondence between the chosen X-ray contour level and a baryonic overdensity of about 500 into a measured calibration, which would place the purity and completeness numbers on firmer footing.
  • The MHD matching rule could also be applied to Sunyaev-Zeldovich sources from CMB surveys, where projection and source confusion similarly complicate the identification of optical counterparts.
  • Because the method tolerates large center offsets, it may be used to detect and even dissect over-merged groups, potentially splitting blended systems into their constituent halos.
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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

5 major / 3 minor

Summary. The manuscript presents a method for identifying X-ray emission from optically selected galaxy groups by matching RASS X-ray contours to SDSS spectroscopic group member positions with a modified Hausdorff distance (MHD) defined as the mean of two directed median distances. The authors apply the method to two volume-limited group catalogs (v180 and v195), calibrate the MHD cutoff from the 5% confusion limit of candidate matches, estimate purity by matching a scrambled group catalog, and estimate completeness from the ratio of chance to total matches. They report that an MHD of 0.631 Mpc provides 90% purity, that over half of nearby groups, including those with velocity dispersions near 200 km/s, are detected in X-rays, and that large optical/X-ray center offsets follow the same scaling relations as small offsets, which they interpret as evidence against a feedback explanation for prior non-detections.

Significance. The proposed method is potentially valuable: it uses fixed-linking-length volume-limited catalogs, releases machine-readable X-ray property catalogs, and directly addresses a known problem of projection and source confusion in group identification. If the claims hold, the method would improve the completeness of low-mass group detections and inform interpretations of group scaling relations. The central quantitative claims, however, are not yet established because the purity estimate depends on an underspecified scrambling procedure, the 90% purity value is not derived in the main text, and the completeness definition appears misstated. These are fixable with additional analysis and clarification.

major comments (5)
  1. [Abstract and Section 5] The abstract states that an MHD of 0.631 Mpc provides 90% purity, but this number does not appear in the main text. Section 5 reports purity as binned values and states that purity remains above 60% for most velocity-dispersion bins; no global or weighted purity of 90% is derived. Please state how 90% is obtained, or revise the abstract to match the reported binned purities.
  2. [Section 4.2] The MHD matching limit is defined as the weighted 5% confusion limit of matches. If the limit admits 5% random matches, the expected purity is about 95%, not 90%; if the 5% refers to a different quantity, the definition is incomplete. The relation between the threshold choice and the purity estimated in Section 5 must be stated explicitly.
  3. [Section 5] The purity estimate is based on a scrambled catalog constructed 'with random offsets applied to each group,' but the offset distribution is not specified. Purity is sensitive to the offset scale: too-small offsets keep scrambled groups correlated with real X-ray sources and inflate the random-match count, while too-large offsets deflate it. Please specify the offset distribution and validate the procedure, for example by varying the offset scale or by scrambling the X-ray source positions instead.
  4. [Section 5] The sentence 'The final completeness was determined as the ratio of chance matches to the total potential matches (chance and excess matches)' defines completeness as the random-match fraction, which is not the usual fraction of true matches recovered. This ambiguity affects the interpretation of the completeness panels in Fig. 4 and the 50% completeness line in Fig. 3; please give the explicit formula and distinguish completeness from contamination.
  5. [Section 3] The X-ray contour level is chosen 'by experimenting' and is asserted to correspond to a baryonic overdensity of approximately 500, but the paper states that the effect of this choice will be modeled in future work. Because the contour extent directly changes all MHD values, the purity and completeness estimates depend on this calibration; please provide a sensitivity test against contour level or a simulation-based justification.
minor comments (3)
  1. [Fig. 2 caption] The caption says the maximum allowed MHD is 9.54 arcmin, while Section 4.2 refers to an upper limit of 9.84 arcmin; please make the threshold values consistent.
  2. [Eq. (6)] The notation $\ln \sigma\,\mathrm{km}^{-1}\mathrm{s} = \beta \ln (L_X/10^{43}\,\mathrm{erg}\,\mathrm{s}^{-1}) + N(\alpha,\sigma')$ is ambiguous; please define the distribution $N$ and clarify how $\alpha$ and $\sigma'$ are used, especially since $\alpha$ is also used for the intercept in Table 2.
  3. [Section 4.2] The implementation averages median closest distances computed against contours and against nonzero wavelet pixels, whereas Eqs. (3)-(4) define the MHD between two point sets; please clarify how the contour/pixel representation maps onto the formal definition.

Circularity Check

1 steps flagged · score 6.0 of 10

The headline 90% purity is an in-sample consequence of the 5%-confusion threshold choice, not an independent measurement; the rest of the derivation is not circular.

  1. fitted input called prediction [Sec. 4.2 (MHD match threshold) and Sec. 5 (purity estimate); Abstract]
    "For this upper MHD limit of real matches, we used the weighted 5% confusion limit of matches, scaled to the ratio of total optical groups to X-ray contours of our sample. ... We then iterated over our potential matches to determine which maximum MHD value produces the same confusion limit. That value was used as the maximum MHD limit. ... We calculated random matches from this set and the purity was calculated as one minus the ratio of random matches to true matches (ones found using the unscrambled set) for each bin."

    The MHD cutoff is not set by an independent criterion but is defined as the value at which random matches reach a predetermined '5% confusion limit.' The purity in Sec. 5 is then measured as one minus the ratio of random to true matches, i.e., it estimates the same random-match contamination that was used to choose the threshold. The abstract's statement that 'an MHD of 0.631 Mpc provides 90% purity' is therefore an in-sample restatement of the adopted 5% confusion choice (with the exact mapping left unreconciled), not an external validation of the matching. Because the scrambling offset distribution is not specified, the 90% figure is not independently reproducible from the text.

full rationale

Most of the paper is self-contained relative to external inputs: the SDSS group catalog (Tempel et al. 2014), the RASS wavelet maps, and the MHD definition from Huttenlocher et al. and Dubuisson & Jain are external, and the scaling-relation comparison between small- and large-center-offset matches is an internal but non-circular test. The claimed low-velocity-dispersion detections and the conclusion about over-merging/source confusion are consequences of applying the chosen threshold and are not by themselves circular. The one load-bearing circular element is the purity claim: the threshold is selected as a 5% confusion limit and then '90% purity' is estimated from the same random-match concept, so the headline number is substantially forced by the threshold definition rather than independently demonstrated. I do not see load-bearing self-citation, an imported uniqueness theorem, or a renamed known result; those patterns are absent. The contour-level choice is an acknowledged calibration ('By experimenting with the contour levels, we selected...') and is a limitation, not a circular step.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central claim rests on a hand-tuned X-ray contour level, a data-fit matching threshold, and an underspecified scrambling procedure for purity. The paper does not introduce new physical entities, but the matching method includes several ad hoc choices that function as free parameters. The main physical assumption is that the X-ray contour level traces the same overdensity as the optical group definition, which is asserted but not measured.

free parameters (4)
  • X-ray contour surface brightness level = 2e-5 counts/s/pixel
    Chosen by experimenting with contour levels to match the extent of X-ray sources in Khalil et al. (2024), not derived from simulations.
  • MHD matching threshold = 0.631 Mpc (and 9.54 arcmin)
    Determined from the data using a weighted 5% confusion limit; not predicted from an external model.
  • Random offset scale for scrambled groups = not specified
    Purity is estimated using scrambled groups with random offsets, but the offset scale is not stated, affecting the random match rate.
  • MHD modifications (median and mean) = N/A
    The use of the median instead of the maximum and the mean of directed distances are choices to handle contamination; they are not optimized but are ad hoc.
assumptions (3)
  • domain assumption X-ray surface brightness traces baryonic overdensity in group outskirts.
    The contour level is assumed to correspond to a baryonic overdensity of about 500, matching the optical group definition, but this is not independently verified.
  • domain assumption The modified Hausdorff distance with median and mean preserves the notion of set distance in the presence of contamination.
    The choice of the median over the best 50% and the mean of directed distances is motivated by outlier resistance, but its statistical properties are not proven in this context.
  • ad hoc to paper The scrambled group catalog provides a valid model of random coincidences.
    Purity is computed by comparing matches from the true catalog to matches from scrambled groups, which relies on the assumption that scrambling preserves the relevant distribution of group positions.

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Cite this review

Pith. "Pith review of AXES-SDSS: Solving the puzzle of X-ray emission of optical galaxy groups via a modified Hausdorff distance." pith.science (2026). https://pith.science/paper/XBFGPZQW

@misc{pith2026250706377,
  author       = {Pith},
  title        = {Pith review of: AXES-SDSS: Solving the puzzle of X-ray emission of optical galaxy groups via a modified Hausdorff distance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XBFGPZQW}},
  note         = {Machine review of arXiv:2507.06377}
}
read the original abstract

The identification of X-ray and CMB sources as galaxy groups and clusters is a prerequisite for cluster cosmology. But the identification of groups, especially nearby ones, suffers from projection effects which in turn affect the purity of the sample. In X-rays, the position of the cluster can be given either by the peak of the emission, or by the full information content of the cluster image. Similarly, the optical center, or its member galaxies, can describe the optical counterpart. With the progress of numerical simulations, it is currently feasible to reproduce both the optical group membership assignment and the behavior of the group outskirts in X-rays, and therefore there is an opportunity to define a reproducible group identification procedure. We performed two-way matching between X-ray contours, drawn at a fixed surface brightness level corresponding to a baryonic overdensity of ~500, to the projected galaxy positions using a modified Hausdorff distance (MHD). We used the volume-limited SDSS group catalog to evaluate the purity and completeness of the procedure, maintaining the constant performance of the optical group finder with redshift. We find that an MHD of 0.631 Mpc provides 90% purity. This is a clear improvement over the methods that rely on the optical counterparts' distance and richness. We study the purity versus MHD and the completeness versus redshift and velocity dispersion. Over half of nearby groups have X-ray emission, even those with velocity dispersions as low as 200km/s; this has never previously been demonstrated. The bulk of these groups follow the same scaling relations as the groups with a small separation between the optical and X-ray centers, removing feedback as an explanation for the lack of matches in previous studies. Instead, the problem is caused by over-merging in the optical group catalog construction and source confusion in X-rays.

Figures

Figures reproduced from arXiv: 2507.06377 by the authors.

Figure 1
Figure 1. Number of optical to X-ray combinations as a function [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Examples of both a matched (2a) and an unrelated (2b) pair of X-ray (red contour) and optical (black dots) group com￾ponents, determined by the MHD calculations. The maximum MHD allowed for a match is 9.54 arcmin. large overlap between contour and optical members and with the contour aligned with the region of highest member density. Con￾versely, the right panel shows an optical/X-ray pairing that our method determi… view at source ↗
Figure 4
Figure 4. Completeness (top panels) and purity (bottom panels) of the optical/ [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Four examples of group identifications with the optical and extended X-ray centers shown. Despite all of these examples [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Left panels: Scaling relations between velocity dispersion ( [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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