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Modelling the selection of galaxy groups with end to end simulations

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The X-GAP galaxy-group selection is now quantified: a flux-driven detection probability, 50% completeness at 450 km/s, and 93% purity in the parent sample.

desk verdict First end-to-end selection function for the X-GAP parent sample, delivered with a robust conditional fit and a useful sigma_v-M calibration, but the headline 450 km/s completeness claim is stress-tested more weakly than the paper's own admitted LX model offset. read the letter →

arxiv 2506.04757 v1 pith:RCUV6TVN submitted 2025-06-05 astro-ph.CO astro-ph.GAastro-ph.HE

R. Seppi , D. Eckert , A. Finoguenov , S .Shreeram , E. Tempel , G. Gozaliasl , M. Lorenz , J. Wilms
show 8 more authors
G. A. Mamon F. Gastaldello L. Lovisari E. O'Sullivan K. Kolokythas M. A. Bourne M. Sun A. Pillepich
This is my paper · ORCID
classification astro-ph.COastro-ph.GAastro-ph.HE
keywords Galaxies:groupsX-rays:clustersclusters:intraclustermediumSurveysCosmology:large-scalestructureofUniverseMethods:dataanalysisselectionfunctionmockobservations
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 tries to establish exactly how the X-GAP sample of 49 galaxy groups is selected from its parent X-ray and optical catalogues, so that comparisons of the groups' gas properties to simulations are not biased by which systems were detectable. The authors build a simulated sky — dark matter haloes from Uchuu, galaxies from an SDSS mock, X-ray emission assigned by a neural network trained on hydrodynamical simulations — and run the same X-ray wavelet detection and optical friends-of-friends grouping used on real data. They find the X-GAP selection is set mostly by X-ray flux, with weaker dependence on velocity dispersion and redshift; in the X-GAP redshift range 50% completeness is reached at a velocity dispersion of 450 km/s, and after X-ray matching the parent sample is 93% pure. If correct, this selection model lets X-GAP comparisons with hydrodynamical simulations be made on an unbiased subset of the group population.

What carries the argument

The load-bearing machinery is a normalising-flow neural network (a generative model that learns a complex distribution from a chain of invertible transformations) trained on TNG300 hydrodynamical clusters plus HIFLUGCS and SPT cluster data to predict self-similar emission measure profiles and X-ray temperatures from halo mass and redshift. These profiles, together with an AGN model and real RASS background maps, are turned into X-ray photons with the SIXTE simulator; a wavelet detector finds extended sources and a friends-of-friends algorithm on the UchuuSDSS galaxy mock finds optical groups; a three-way match connects both detections to the input dark matter haloes. The matched versus unmatched haloes give the detection ratio from which the selection function is fitted.

What would settle it

Reduce all mock group luminosities by a factor of two — the offset acknowledged in Appendix A — and rerun the end-to-end detection; if the fitted 50% completeness velocity dispersion shifts noticeably from 450 km/s, the claimed selection function is not robust to the known luminosity bias. Empirically, a complete spectroscopic census of every ROSAT extended source in the X-GAP sky area would give the observed completeness curve to compare directly with the mock prediction.

Watch

Extended reading notes

Core claim

The central claim of this paper is that the X-GAP selection function — the probability that a galaxy group of given X-ray flux $F_X$, redshift $z$, and velocity dispersion $\sigma_{v,T}$ enters the sample — can be written as a single logistic curve, $P_{\rm det}(F_X,z,\sigma_{v,T}) = (1 + \exp[-\alpha_{F_x}(\log_{10} F_X - F_{X,0}) - \alpha_{\sigma_v}\,\log_{10}\sigma_{v,T} + \alpha_z\,\log_{10} z])^{-1}$, with parameters fitted to an end-to-end mock that reproduces the observed $L_X$--$\sigma_v$ distribution of the real AXES parent sample. The fit says the selection is dominated by X-ray flux, with weaker dependences on velocity dispersion and redshift; in the X-GAP redshift range $0.02<z<0.06$ the 50% completeness lies at $\sigma_{v,T}\simeq450$ km/s, and the X-ray match raises purity to 93% in the parent sample. The paper also claims a calibrated velocity dispersion--halo mass relation with a slope and normalisation consistent with the literature and an intrinsic scatter of about 0.06 dex, and that measurement scatter, not intrinsic scatter, dominates the observed velocity dispersion distribution in an SDSS-like setup.

Load-bearing premise

The result rests on the trained network's X-ray luminosities being correct on average; the paper reports that the model overpredicts $L_X$ by about a factor of two near $10^{13}\,M_\odot$ relative to a stacking analysis, yet the robustness test rescales luminosities by only 10%.

Editorial extensions

If this is right

  • X-GAP is effectively flux-limited: detection probability is mainly a function of 0.5--2 keV flux, so undetected systems are mostly faint ones rather than low-mass ones at fixed flux.
  • Any comparison of X-GAP thermodynamic properties or gas fractions to hydrodynamical simulations must weight each mock group by Eq. 15 (or the 6-arcmin-aperture version), otherwise the comparison is biased toward bright systems.
  • Velocity dispersion measurements are reliable only for rich systems: accuracy within 10% requires about 20 recovered members, and groups with fewer than 10 members are biased by more than 20%.
  • The X-ray follow-up acts as a cleaning step: purity reaches 90% already at 280 km/s with the X-ray match, compared to 600 km/s for the optical FoF catalogue alone.
  • The velocity dispersion--mass relation is recovered unbiasedly only when measurement scatter is modelled separately; intrinsic scatter is about 0.06--0.07 dex and measurement scatter about 0.10 dex in an SDSS-like survey.

Reading between the lines

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

  • Because the selection function is expressed in observed quantities (flux, redshift, velocity dispersion) rather than halo mass, it should transfer to other RASS+SDSS selected group samples without re-simulating baryons; the ratio definition also absorbs part of the X-ray modelling uncertainty.
  • The 20-member accuracy threshold is a strong statement about galaxy population rather than halo mass: a massive cluster that is poor in observed members will still give a biased velocity dispersion, so mass calibration priors should depend on richness, not just mass.
  • The same pipeline, re-run with eROSITA exposure and background instead of RASS, would produce a direct comparison selection function; the paper's comparison with eRASS1 suggests the 50% flux limit would drop roughly fivefold.
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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 / 4 minor

Summary. This paper constructs an end-to-end forward model of the joint X-ray and optical selection of the X-GAP galaxy-group sample. Starting from the Uchuu dark-matter light cone, the authors assign X-ray emissivity profiles and temperatures with a normalising-flow network trained on TNG300 plus HIFLUGCS/SPT data, add a phenomenological AGN population, generate events with SIXTE using real ROSAT background maps, and run the wavelet and FoF detection schemes of Damsted et al. (2024) and Tempel et al. (2017). The mock is validated against the real AXES sample in the L_X-sigma_v plane (Fig. 6). The authors then fit the detection probability with the sigmoid model of Eq. (15), report 50% completeness at sigma_v about 450 km/s in the X-GAP redshift range, estimate 93% purity after X-ray matching, and calibrate the velocity dispersion-halo mass relation separating intrinsic and measurement scatter.

Significance. If the central result is robust, this is a valuable framework for using X-GAP as a benchmark for hydrodynamical simulations. The selection function is expressed in terms of observables, the purity estimate of 93% is directly actionable, and the sigma_v-M calibration with separate intrinsic and measurement scatter is useful for forward-modelling. The paper's strengths include the end-to-end nature of the pipeline, the use of public high-resolution simulations and standard public tools, a direct comparison to the real AXES sample (Fig. 6), and a formal goodness-of-fit check (chi2_r = 0.97) for the selection-function model. The main threat to the headline numbers is the acknowledged factor-of-two overprediction of L_X near 10^13 M_sun relative to eROSITA stacking results, which is tested only with a much smaller 10% luminosity rescale.

major comments (3)
  1. [Sect. 3.4 and Appendix A] The robustness test applied to the acknowledged factor-of-two overprediction of L_X near 10^13 M_sun is too weak. The text reduces input luminosities by only 10% (0.04 dex), roughly seven times smaller than the 0.3 dex discrepancy quoted against Zhang et al. (2024). Because the headline 50%-completeness threshold at sigma_v = 450 km/s is obtained after marginalizing over the mock flux distribution at fixed sigma_v (right-hand panel of Fig. 10), a parent L_X-M relation that is biased high by 0.3 dex will populate high-flux bins with low-mass haloes and bias the marginalized completeness upward, with the parameters alpha_sigma_v and F_X,0 of Eq. (15) absorbing part of the bias. The Appendix A statement that the selection function is 'not affected by this particular prescription' holds for the conditional detection probability at fixed flux, not for the marginalized completeness as a function of sigma_v. Please rerun the end-to-end pipeline with a factor-of-two (0.3 dex) luminosity rescaling, or provide a semi-analytic propagation of the L_X-M uncertainty into Eq. (15) and into the quoted 450 km/s completeness threshold.
  2. [Sect. 4.3 and Fig. 6] The validation against the real AXES sample in Fig. 6 is performed after applying the X-ray plus optical selection, which preferentially retains high-L_X objects at fixed velocity dispersion (Appendix C, Fig. C.1). This makes the agreement mostly sensitive to the L_X-sigma_v correlation and to the detection pipeline, and only weakly constraining for the absolute L_X-M normalization near the flux limit, where the factor-two tension with the eROSITA stacking result resides. Please show the same comparison for an unbiased parent population, or quantify what fraction of the 0.3 dex offset in L_X at M around 10^13 M_sun survives the selection and could be hidden by Fig. 6.
  3. [Sect. 5.2 and Eq. (15)] The selection function in Eq. (15) is written in terms of the true velocity dispersion sigma_v,T, which is not directly observable, while the abstract quotes the 450 km/s 50%-completeness threshold without this qualifier. Given that Fig. 13 shows measured velocity dispersions are biased low by more than 20% for groups with fewer than 10 members, an observer who applies Eq. (15) to measured sigma_v will obtain incorrect completeness estimates. The paper should state explicitly that Eq. (15) is for forward-modelling true sigma_v, and should either provide the corresponding fit in terms of measured sigma_v,M or show how the measurement-scatter model of Section 6 converts between the two.
minor comments (4)
  1. [Abstract] The abstract states that 'the 50% completeness is reached at a velocity dispersion of 450 km/s' without specifying that this refers to the true (simulation) velocity dispersion, for the X-ray plus optical selected sample, in the redshift range 0.02 < z < 0.06; please add these qualifiers.
  2. [Eq. (1)] In Eq. (1), 'DEC = theta - 90' mixes radians and degrees if theta is computed with arccos in the standard convention; please clarify the units and the conversion to degrees.
  3. [Eq. (17)] The last line of Eq. (17) writes P(sigma_v,M | M, z, theta) as a product that includes the detection-probability factor P(I | sigma_v,T, z), but the left-hand side is not explicitly conditioned on detection; please define the selected-sample likelihood and its normalization.
  4. [Fig. 9 caption] The caption refers to green and violet contours for the base model and the six-arcminute aperture model, but the color coding is not obvious from the printed figure; please make the colors unambiguous or add panel labels.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the selection function is an empirical fit to mock completeness validated against external data; the acknowledged LX-model caveat is a calibration risk rather than a circular step.

full rationale

The paper's central results do not reduce to their inputs by construction. The selection function in Eq. 15 is fitted to the mock completeness ratio defined in Eq. 14, which is a forward-modelled quantity computed from simulated X-ray and optical detections; it is not a parameter hidden inside the definition of the input. The headline 50% completeness at 450 km/s and the 93% purity estimate are outputs of this forward model, and the purity estimate in Eq. 16 explicitly weights the simulated purity by the observed AXES velocity-dispersion distribution, providing an external anchor. The mock is validated against independent data in Fig. 6 (AXES LX-sigma_v relation), Fig. 4 (LX-M and TX-M relations compared to multiple observational samples), and Fig. 11 (sigma_v-M relation compared to Munari et al. 2013 and Ferragamo et al. 2022). The self-citations present, such as Seppi et al. (2022) for the X-ray matching scheme and Seppi et al. (2024) for an eRASS1 comparison, are methodological or comparative and are not load-bearing for the main claim. Appendix A honestly discloses that the TNG-based luminosity model overpredicts LX by about a factor of two near 10^13 Msun, and the 10% rescale robustness test is a sensitivity check rather than a circular validation; the possibility that the marginalized 450 km/s completeness is sensitive to the LX-M normalization is a calibration uncertainty, not a derivation that assumes its own conclusion. Overall, the derivation chain is self-contained and externally benchmarked, so no circular step can be exhibited.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

No new physical entities are introduced; the neural network, mock light cones, and selection function fits are methods and empirical models, not postulates of new phenomena. The free parameters are all fitted to mock data or chosen as hyperparameters of the pipeline.

free parameters (8)
  • Base selection function parameters (alpha_Fx, F_X,0, alpha_sigma_v, alpha_z) = 4.78, -11.03, 0.83, 1.73
    Fitted to the mock completeness ratio in Eq. 14 using UltraNest; this is the central model of the paper (Table 2, base model F500c).
  • 6-arcmin aperture selection function parameters = 4.76, -10.84, 1.01, 2.19
    Same sigmoid fit but with flux measured in a fixed 6-arcmin aperture; reported in Table 2.
  • Velocity dispersion-halo mass normalisation A = 1145.1 +/- 3.9 km/s (M200c, full sample)
    Posterior from the hierarchical model Eq. 17 applied to true sigma_v,T (Table 3).
  • Velocity dispersion-halo mass slope alpha = 0.330 +/- 0.001 (M200c)
    Posterior from Eq. 17; comparable to Munari et al. (2013) and Ferragamo et al. (2022).
  • Intrinsic scatter of true sigma_v at fixed mass = 0.073 +/- 0.001 dex (full sample); 0.057 dex for X-ray selected
    Fitted in Eq. 17; decreases when optical and X-ray selections are applied (Table 3).
  • Measurement scatter between measured and true sigma_v = 0.102 +/- 0.001 dex (optical); 0.106 +/- 0.002 (optical+X-ray)
    Fitted in the full calibration of Eq. 17; dominates the total scatter in the SDSS-like setup.
  • Detection probability sigmoid in Eq. 17 = slope 6.4 (optical), 10.8 (opt+X); normalisation 2.64 and 2.68
    Fitted selection probability P(I|sigma_v,T,z) used as the selection term in the mass calibration.
  • Assumed log-normal scatter in optical-to-halo matching = 0.08 dex
    Chosen by hand in Eq. 13 to define the matching statistic; later measured sigma_meas ~ 0.10 dex in Sect. 6, so the matching assumption is only approximately correct.
assumptions (7)
  • domain assumption TNG300 hydrodynamical simulation provides realistic X-ray emissivity and temperature profiles for galaxy groups and clusters
    The neural network is trained on TNG300 (plus HIFLUGCS and SPT data); hydro simulations are approximate, and Appendix A reports a factor ~2 overprediction of LX near 1e13 Msun, so the assumption is imperfect but used as the basis for all mock X-ray fluxes.
  • domain assumption The normalizing flow transfers TNG profiles to Uchuu halos with correct covariances in mass and redshift
    Sect. 3.3; the flow generates profiles conditional on M and z, and the resulting LX-M and TX-M relations are compared to observations in Fig. 4.
  • domain assumption UchuuSDSS mock reproduces SDSS galaxy positions, magnitudes, and redshifts needed for FoF group finding
    Sect. 4.2; the mock overproduces galaxies near z~0.2 but matches SDSS counts below z<0.14, the range used for X-GAP.
  • domain assumption Comparat et al. (2019) AGN model and RASS background maps describe the X-ray sky seen by ROSAT
    Sect. 2.2 and 2.3; AGN model calibrated to the hard X-ray luminosity function; background is resampled from real RASS maps, assuming the modelled spectral components are correct.
  • domain assumption Wavelet detection on mock images and FoF with Tempel et al. (2017) linking reproduce the real AXES/X-GAP detection
    Sect. 4; validation via comparison of LX-sigma_v in mock and real AXES (Fig. 6).
  • domain assumption Measured velocity dispersion follows a log-normal distribution around the true value
    Used in Eq. 17; Fig. 13 shows a systematic bias for poor systems and the alternative fit in Eq. 18 gives m=0.85, q=0.06, so the assumption is only approximate; the paper shows the scaling relation parameters are robust to it.
  • standard math Poisson statistics for photon counts and background
    Used for source matching thresholds in Sect. 4.3.1 and error bars throughout.

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Cite this review

Pith. "Pith review of Modelling the selection of galaxy groups with end to end simulations." pith.science (2026). https://pith.science/paper/RCUV6TVN

@misc{pith2026250604757,
  author       = {Pith},
  title        = {Pith review of: Modelling the selection of galaxy groups with end to end simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RCUV6TVN}},
  note         = {Machine review of arXiv:2506.04757}
}
read the original abstract

Feedback from supernovae and AGN shapes galaxy formation and evolution, yet its impact remains unclear. Galaxy groups offer a crucial probe, as their binding energy is comparable to that available from their central AGN. The XMM-Newton Group AGN Project (X-GAP) is a sample of 49 groups selected in X-ray (ROSAT) and optical (SDSS) bands, providing a benchmark for hydrodynamical simulations. In sight of such a comparison, understanding selection effects is essential. We aim to model the selection function of X-GAP by forward modelling the detection process in the X-ray and optical bands. Using the Uchuu simulation, we build a halo light cone, predict X-ray group properties with a neural network trained on hydro simulations, and assign galaxies matching observed properties. We compare the selected sample to the parent population. Our method provides a sample that matches the observed distribution of X-ray luminosity and velocity dispersion. The 50% completeness is reached at a velocity dispersion of 450 km/s in the X-GAP redshift range. The selection is driven by X-ray flux, with secondary dependence on velocity dispersion and redshift. We estimate a 93% purity level in the X-GAP parent sample. We calibrate the velocity dispersion-halo mass relation. We find a normalisation and slope in agreement with the literature, and an intrinsic scatter of about 0.06 dex. The measured velocity dispersion is accurate within 10% only for rich systems with more than about 20 members, while the velocity dispersion for groups with less than 10 members is biased at more than 20%. The X-ray follow-up refines the optical selection, enhancing purity but reducing completeness. In an SDSS-like setup, velocity dispersion measurement errors dominate over intrinsic scatter. Our selection model will enable the comparisons of thermodynamic properties and gas fractions between X-GAP groups and hydro simulations.

Figures

Figures reproduced from arXiv: 2506.04757 by the authors.

Figure 1
Figure 1. Forward modelling of the X-GAP selection. We start from a dark matter halo light cone generated from the Uchuu simulation, we build a novel method to assign cluster and groups X-ray profiles and temperatures as a function of halo mass and redshift, we use abundance matching schemes to simulate galaxies and AGN. We generate X-ray events accounting for the telescope response. Finally, we reproduce the detection scheme… view at source ↗
Figure 2
Figure 2. Dark matter halo light cone generated from individual Uchuu snapshots. This panel shows a slice within ±50 Mpc along the z-axis, up to redshift of 0.4. Haloes more massive than 1012.5 M⊙ are shown, each one is colour coded by its redshift. The shaded areas denote the various snapshots used to generate the light cone. 2.1. Halo light cone Uchuu is a large dark matter only simulation with high resolution (Ishiyama et … view at source ↗
Figure 3
Figure 3. Emission measure profiles with self similar scaling, colour coded for temperature, as a function of radius in units of R500c. The units on the y-axis are Mpc keV−1/2 cm−6 . The bottom part of the panel shows the evolution of the profile intrinsic scatter at different radii. For reference it is compared to the model from Comparat et al. (2020) and profiles of X-COP clusters (Ghirardini et al. 2019). the only scatter … view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Scaling relation between X-ray luminosity and measured veloc￾ity dispersion. The result from our simulation (the real AXES) is shown in blue (orange). We find excellent agreement between the mock and real data in Damsted et al. (2024). (Böhringer et al. 2000; Ebeling e…
Figure 7
Figure 7. Figure 7: Two dimensional probability of detection for X-ray plus opti￾cally selected haloes in our simulation (see Sect. 5.1). The panels shows the completeness fraction as a function of three combinations of X-ray flux, velocity dispersion, and true velocity dispersion. the ra…
Figure 9
Figure 9. Figure 9: Marginalized posterior distribution of the best fit model of the X￾ray plus optical selection function (see Eq. 15). The filled 2D contours show the 1-σ and 2-σ confidence levels of the posteriors after convolu￾tion with the uniform priors. The green contours denote th…
Figure 8
Figure 8. Figure 8: Probability of detection for X-GAP selected haloes as a func￾tion of observables. The three panels show different combination of flux measured within R500c, redshift, and velocity dispersion on the x-axis, in different colours, and symbols. The various line styles deno…
Figure 10
Figure 10. Figure 10: Trade-off between completeness and purity as a function of velocity dispersion. Left hand panel: Fraction of objects with a corresponding real input dark matter halo as a function of measured velocity dispersion. The blue line shows the fraction of objects detected in…
Figure 11
Figure 11. Figure 11: Scaling relation between velocity dispersion and halo mass. Top panel: Scaling relation for the true velocity dispersion (Eq. 3). The orange and green lines show the results from Munari et al. (2013) and Ferragamo et al. (2022). Bottom panel: Scaling relation for the …
Figure 12
Figure 12. Figure 12: Marginalized posterior distributions of the best fit scaling re￾lation parameters between velocity dispersion and M200c. The filled 2D contours show the 1-σ and 2-σ confidence levels of the posteriors after convolution with the uniform priors. The model is given by Eq…
Figure 13
Figure 13. Figure 13: Ratio between measured and true velocity dispersion as a func￾tion of number of recovered galaxy members. The red line shows the gapper velocity dispersion measured by the CLEAN algorithm, while the blue one refers to the direct estimate from the FoF finder. The black…
Figure 14
Figure 14. Figure 14: Probability of detection as a function of core properties. The dashed lines represent the normalised distribution of the full population. Top panel: completeness fraction as a function of emissivity profile ratio measured at R500c and in the inner most bin. Different …
Figure 15
Figure 15. Figure 15: Selection of relaxed and unrelaxed groups from the dark matter halo point of view, using the spin and offset parameters. file. On the opposite, a large ratio means that the profile is flatter and the system is closer to a non cool core. The result is shown in [PITH_F…
Figure 17
Figure 17. Figure 17: Average galaxy members’ distance from the halo center as a function of halo mass. The blue line denoted relaxed haloes, the red line refers to disturbed ones. To investigate this discrepancy, we measure the average dis￾tance of the recovered galaxy members from the ha…

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Forward citations

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    astro-ph.HE 2025-07 conditional novelty 6.0 of 10

    A modified Hausdorff distance between X-ray contours and optical galaxy positions identifies matches with 90% purity and reveals X-ray emission in over half of nearby low-velocity-dispersion groups.

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