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arxiv: 2512.06138 · v2 · submitted 2025-12-05 · 🌌 astro-ph.CO

The eROSITA Final Equatorial-Depth Survey (eFEDS): X-ray stacking analysis of Subaru's optically selected clusters spanning low richness regime

N. T. Nguyen-Dang , N. Ota , N. Okabe , M. Oguri , I. Mitsuishi , T. H. Reiprich , F. Pacaud , E. Bulbul
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J. S. Sanders M. Br\"uggen A. Liu Y. Tsujita I. Chiu V. Ghirardini S. Grandis M. Klein K. Migkas H. Miyatake S. Miyazaki M. E. Ramos-Ceja
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Pith reviewed 2026-05-17 00:07 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords x-rayclustersscalingopticallyselectedefedserositaevolution
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The pith

Optically selected galaxy clusters show an X-ray luminosity-mass scaling slope of 1.56, slightly steeper than self-similar predictions.

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

This paper stacks X-ray observations of 997 optically selected galaxy clusters spanning richness above 15 and redshifts from 0.1 to 1.3. The analysis derives the luminosity-mass and richness-mass scaling relations using weak-lensing calibrated masses while accounting for selection effects and redshift evolution. The results indicate that the L-M slope is 1.56 with uncertainties, consistent with earlier work, and the N-M slope is about 0.77, matching theoretical expectations. No additional redshift evolution beyond self-similar is required by the data. This work matters because it probes lower mass clusters than typical X-ray samples, helping to understand selection biases in cluster cosmology.

Core claim

The authors establish that the best-fit L-M slope is 1.56^{+0.14}_{-0.12}, slightly steeper than the self-similar value of 1, yet consistent with previous findings from similar samples. The N-M slope is 0.766^{+0.070}_{-0.060}, in broad agreement with theory. X-ray detected clusters show marginally steeper L-M slopes and more centrally concentrated surface brightness profiles compared to undetected ones. The data do not require extra redshift evolution terms.

What carries the argument

The stacking analysis of X-ray count rates to obtain bolometric luminosities for weak-lensing mass calibrated clusters, used to fit scaling relations while modeling selection effects.

Load-bearing premise

The weak-lensing mass calibration is unbiased across the full richness and redshift range studied.

What would settle it

An independent measurement of the L-M slope using a different mass calibration method on a similar sample of optically selected clusters that yields a value inconsistent with 1.56 at high significance.

Figures

Figures reproduced from arXiv: 2512.06138 by A. Liu, E. Bulbul, F. Pacaud, H. Miyatake, I. Chiu, I. Mitsuishi, J. S. Sanders, K. Migkas, M. Br\"uggen, M. E. Ramos-Ceja, M. Klein, M. Oguri, N. Okabe, N. Ota, N. T. Nguyen-Dang, S. Grandis, S. Miyazaki, T. H. Reiprich, V. Ghirardini, Y. Tsujita.

Figure 1
Figure 1. Figure 1: Distribution of the CAMIRA clusters in the richness-redshift plane. Each point represents a cluster. Colors indicate the stacked groups used in the X-ray stacking analysis, defined by similar richness and redshift ranges (see Sects. 2 and 3.2). 3. X-ray data analysis 3.1. Data reduction We processed the eFEDS data from the seven telescope modules (TMs) using version eSASSusers_201009 of the eROSITA Sci￾enc… view at source ↗
Figure 2
Figure 2. Figure 2: Scaling relations of the CAMIRA optically selected clusters. Each circle represents a stacked bin described in Sect. 3.2, color-coded by its weighted average redshift. Solid lines show the best-fitting power-law models from the simultaneous fit: blue and magenta correspond to relations with respect to the WL masses and to the true masses, respectively. The shaded blue region indicates the 1σ uncertainty of… view at source ↗
Figure 3
Figure 3. Figure 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Radial surface brightness profiles of stacked CAMIRA clusters with and without X-ray detections are shown in blue and red circles, respectively. Arrows indicate upper limits. The richness bins are 15 ≤ N < 25 (top), 25 ≤ N < 40 (middle), and 40 ≤ N < 60 (bottom). The left, middle, and right columns correspond to redshift ranges 0.1 ≤ z < 0.3, 0.3 ≤ z < 0.6, and 0.6 ≤ z < 1.2, respectively. Best-fitting PSF… view at source ↗
Figure 5
Figure 5. Figure 5: Scaling relations of richness (left) and luminosity (right) with respect to true masses. The magenta solid lines and shaded regions show the best-fit relations and their uncertainties from this work. The green lines represent the results for individual CAMIRA clusters with N > 40 (Ota et al. 2023). The orange line shows the eRASS1 result (Okabe et al. 2025). The brown and gray dashed lines denote the stack… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the slopes of the N − M (left) and L − M (right) relations. Solid vertical lines mark the posterior medians from this work, with blue shaded bands indicating the 1σ credible intervals. Dashed vertical lines show the slopes expected from self-similar models. Literature values from [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

This is the second paper in a series exploring the X-ray properties of galaxy clusters optically selected by the Subaru Hyper Suprime-Cam (HSC) survey, using data from the SRG/eROSITA Final Equatorial-Depth Survey (eFEDS). We aim to investigate scaling relations between observable cluster properties and mass, and to study the radial X-ray profiles of a large sample of optically selected clusters. We analyze a sample of 997 CAMIRA clusters with richness $N > 15$ and redshifts of $0.1 < z < 1.3$. Using bolometric luminosities derived from count rates and a weak-lensing mass calibration, we study the $L-M$ and $N-M$ scaling relations through stacking analysis, while accounting for selection effects and redshift evolution. We also compare clusters with and without X-ray counterparts in the eFEDS catalog in terms of their scaling relations and surface brightness profiles. The best-fit $L-M$ slope ($1.56^{+0.14}_{-0.12}$) is slightly steeper than the self-similar prediction, yet remains consistent with our previous findings. The $N-M$ slope ($0.766^{+0.070}_{-0.060}$) broadly agrees with theoretical expectations and other optical samples. The data do not require any additional redshift evolution beyond the standard self-similar scaling, although current constraints on evolution remain weak. X-ray detected clusters exhibit a marginally steeper $L-M$ slope, higher central surface brightness, and more centrally concentrated X-ray profiles than undetected systems. Our results highlight systematic differences in the X-ray properties between optically and X-ray selected cluster samples. This study extends scaling relation analyses into lower mass and luminosity regimes, demonstrating the value of combining deep X-ray and optical surveys like eROSITA and Subaru HSC.

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

1 major / 2 minor

Summary. The manuscript reports X-ray stacking analysis of 997 CAMIRA clusters (N>15, 0.1<z<1.3) from Subaru HSC in the eFEDS field. Using bolometric luminosities from count rates and weak-lensing mass calibration, it derives the L-M scaling relation with best-fit slope 1.56^{+0.14}_{-0.12} (slightly steeper than self-similar) and N-M slope 0.766^{+0.070}_{-0.060} (consistent with expectations). The analysis accounts for selection effects and redshift evolution, finds no requirement for additional evolution beyond self-similar scaling, and compares X-ray detected versus undetected clusters, noting steeper L-M slopes and more centrally concentrated profiles for detected systems.

Significance. If the central results hold, this work meaningfully extends cluster scaling-relation studies into the low-richness regime by combining deep eROSITA X-ray data with optical selection and external weak-lensing calibration. The stacking methodology, explicit comparison of detected/undetected subsamples, and consistency checks on redshift evolution are strengths that help quantify selection biases between optical and X-ray samples, with direct relevance to cosmological analyses using large optical surveys.

major comments (1)
  1. [Weak-lensing mass calibration and L-M fitting] § on weak-lensing mass calibration and L-M fitting: The headline L-M slope of 1.56^{+0.14}_{-0.12} is obtained by dividing stacked X-ray luminosities by weak-lensing masses for the N>15 sample. At the low-richness end the WL S/N is low; the manuscript must demonstrate (via simulation or jackknife test) that shape noise, miscentering, or residual selection-function modeling do not introduce a mass-dependent bias that artificially steepens the recovered slope. Without such a test the central claim that the slope is only mildly steeper than self-similar remains vulnerable.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'consistent with our previous findings' should include an explicit citation to the prior paper in the series.
  2. [Figures and captions] Figure captions and text: ensure all stacked surface-brightness profiles and scaling-relation panels are labeled with the exact richness and redshift cuts used, and that error bars on the fitted slopes are stated in the figure legends as well as the text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback, which has helped us identify areas to strengthen the manuscript. We address the major comment on weak-lensing mass calibration below and will incorporate the suggested robustness tests in the revised version.

read point-by-point responses

  1. Referee: [Weak-lensing mass calibration and L-M fitting] § on weak-lensing mass calibration and L-M fitting: The headline L-M slope of 1.56^{+0.14}_{-0.12} is obtained by dividing stacked X-ray luminosities by weak-lensing masses for the N>15 sample. At the low-richness end the WL S/N is low; the manuscript must demonstrate (via simulation or jackknife test) that shape noise, miscentering, or residual selection-function modeling do not introduce a mass-dependent bias that artificially steepens the recovered slope. Without such a test the central claim that the slope is only mildly steeper than self-similar remains vulnerable.

    Authors: We agree that explicit validation of the weak-lensing masses at low richness is important to confirm that the reported L-M slope is not artificially steepened by noise or modeling effects. In the revised manuscript we will add a new subsection presenting jackknife resampling tests on the shear profiles and mock simulations that inject shape noise, miscentering offsets, and the optical selection function. These tests demonstrate that any mass-dependent bias in the stacked luminosities or derived masses remains smaller than the statistical uncertainties on the slope and does not shift the best-fit value outside the quoted 1-sigma errors. We will also show that the L-M slope recovered from the higher-richness (N>30) subsample, where WL S/N is higher, is statistically consistent with the full N>15 result. These additions will directly address the referee's concern while preserving the central conclusion that the slope is only mildly steeper than self-similar. revision: yes

Circularity Check

1 steps flagged

Minor self-citation for consistency check; central L-M and N-M slopes independently fitted from stacking analysis with external WL calibration

specific steps
  1. self citation load bearing [Abstract]
    "The best-fit L-M slope (1.56^{+0.14}_{-0.12}) is slightly steeper than the self-similar prediction, yet remains consistent with our previous findings."

    The slope value is presented alongside a consistency claim referencing prior work by overlapping authors, but the slope itself is obtained from an independent fit to the current stacked luminosities and WL masses rather than being forced by that citation.

full rationale

The paper derives its primary results—the L-M slope of 1.56^{+0.14}_{-0.12} and N-M slope of 0.766^{+0.070}_{-0.060}—directly from stacked X-ray count rates converted to bolometric luminosities, divided by weak-lensing masses for the N>15 CAMIRA sample, while modeling selection effects and redshift evolution. This is an observational fit to new eFEDS data and does not reduce by construction to prior inputs or self-citations. The sole self-reference ('consistent with our previous findings') is a non-load-bearing consistency note in the abstract; the measurement itself relies on external WL mass calibration and explicit accounting for biases rather than any self-definitional loop, fitted-input prediction, or ansatz smuggled via citation. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Central results rest on weak-lensing mass calibration (external but assumed unbiased), self-similar redshift evolution model, and assumptions about X-ray surface-brightness profiles and selection functions; no new particles or forces postulated.

free parameters (2)
  • L-M slope
    Fitted parameter from stacked data; central claim reports its value and uncertainty.
  • N-M slope
    Fitted parameter from stacked data; central claim reports its value and uncertainty.
axioms (2)
  • domain assumption Weak-lensing masses provide unbiased calibration across 0.1 < z < 1.3 and N > 15
    Invoked to convert observables to mass; appears in the scaling-relation fitting description.
  • domain assumption Self-similar redshift evolution applies with no additional terms required
    Stated as consistent with data; used to interpret lack of extra evolution.

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