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The XXL Survey LIV. X-ray Luminosity Function and Luminosity-Mass Relation of Optically Selected Galaxy Groups

T0 review · 2 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read An optically selected sample of 235 galaxy groups shows that X-ray luminosity rises steeply with mass, with a slope of 1.87, steeper than the self-similar expectation and pointing to non-gravitational feedback.

desk verdict Careful, well-documented measurement of the XLF and LM relation for optically selected groups; the headline slope is plausible but its quoted error ignores HMF systematics. read the letter →

arxiv 2502.04816 v1 pith:ACGPBXYD submitted 2025-02-07 astro-ph.CO astro-ph.GA

C.Wood , B. J. Maughan , J.P. Crossett , D.Eckert , M.Pierre , M.E. Ramos-Ceja , A.S.G. Robotham , C.Adami
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L. Faccioli E. Koulouridis S.L.McGee F. Pacaud S. Phillipps
This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords galaxygroupsX-rayluminosityfunctionluminosity–massrelationopticallyselectedGAMAsurveyXXLAGNfeedbackscalingrelations
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 measure the X-ray luminosity function and the luminosity–mass relation for galaxy groups at the faint end, where X-ray selected samples run out. It uses a sample of 235 groups chosen by their galaxy content in the GAMA spectroscopic survey, overlapping the XXL X-ray survey, and applies forced X-ray aperture photometry so that even groups with almost no detected X-ray emission contribute a luminosity probability distribution. The XLF matches the extrapolation of brighter X-ray-selected samples, and the inferred LM relation has slope 1.87 ± 0.12 at a pivot mass of 5 × $10^{13}$ solar masses, steeper than self-similarity. If right, this is direct evidence that non-gravitational processes suppress the X-ray luminosity of low-mass groups.

What carries the argument

The key machinery is a forward model that starts from the Tinker et al. (2008) halo mass function and a power-law luminosity–mass relation, predicts the XLF, and fits the predicted XLF to the observed one. The observed XLF is built from per-group luminosity posterior probability distributions obtained by forced aperture photometry and Poisson count-rate likelihoods, so formally undetected groups still contribute. A modified Schechter function with pivot at $10^{42}$ erg/s and a 1/Vmax volume correction are used, and the fit is restricted to luminosities above $10^{40}$.6 erg/s where the sample is complete. The scatter in luminosity enters through a Gaussian prior, N(0.2, 0.1), which is degenerate with the normalisation, so the reported normalisation is an upper limit.

What would settle it

Measure X-ray luminosities and independent masses (weak lensing or caustics) for the same 235 groups; if the luminosity–mass slope is consistent with 1 rather than 1.87, the steep slope is an artifact of the assumed halo mass function, not a real astrophysical signal.

Watch

Extended reading notes

Core claim

The central claim is that when the observed XLF of optically selected groups is mapped onto a theoretical halo mass function, the required luminosity–mass relation is L_X = A E(z)^2 (M/M0)^B with A = (0.17 ± 0.07) × $10^{43}$ erg/s and B = 1.87 ± 0.12 at M0 = 5 × $10^{13}$ solar masses. This slope is steeper than the self-similar expectation of about 1 in the 0.5–2 keV band, and steeper still than the self-similar prediction once line emission is included, making the measured steepening a lower limit on the effect of non-gravitational processes. The same data also show that the XLF extends more than an order of magnitude fainter than X-ray-selected samples while agreeing with their extrapolation, and that the normalisation of the LM relation is lower than in most X-ray-selected samples, consistent with X-ray selection favouring X-ray bright groups.

Load-bearing premise

The inference that the luminosity–mass slope is 1.87 assumes the Tinker halo mass function is accurate for group-scale halos near $10^{13}$ solar masses, because the LM relation is solved for by requiring the product of that mass function and the LM relation to reproduce the observed XLF.

Editorial extensions

If this is right

  • The optically selected GAMA XLF is consistent with the extrapolation of X-ray-selected XLFs (REFLEX II, WARPS, XXL, eFEDS) above 10^42 erg/s, extending the measured luminosity range down to about 10^40.6 erg/s.
  • The LM relation slope of 1.87 ± 0.12 implies that low-mass groups are fainter in X-rays than self-similar scaling predicts, so AGN feedback and related processes must remove or heat gas in shallow potential wells.
  • The lower normalisation relative to X-ray-selected samples suggests that X-ray-selected group samples miss a population of X-ray underluminous groups, and that simple bias corrections may not fully capture this.
  • Applying the same XLF-to-HMF mapping to eROSITA data with all-sky optical surveys would extend LM relation constraints to higher redshift and lower mass.

Reading between the lines

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

  • If the true intrinsic scatter in luminosity at fixed mass is larger than the adopted prior, the normalisation would drop further and the steep slope would be even more notable; a direct measurement of scatter from stacked or lensing-calibrated samples would test this.
  • The steepening slope with decreasing mass might be better described by a broken power law with a break near 10^14 solar masses, as suggested by simulations; the GAMA data alone cannot distinguish this from a single power law.
  • The method's success at including formally undetected groups suggests that stacking X-ray data in optical group samples could push XLF measurements another factor of a few fainter, where baryon effects are strongest.
  • A systematic error in the low-mass end of the halo mass function would shift the inferred slope; comparing the same XLF with mass functions calibrated by weak lensing or clustering would isolate that.
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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

2 major / 4 minor

Summary. The paper measures X-ray luminosities of 235 optically selected GAMA groups in the XXL North field using forced aperture photometry, propagating Poisson count-rate posteriors into luminosity posteriors. From these it constructs the 0.5–2 keV X-ray luminosity function down to luminosities about an order of magnitude fainter than typical X-ray-selected samples, fits a Schechter function with slope alpha = 1.66 +/- 0.05, and then uses the Tinker et al. (2008) halo mass function to infer the luminosity–mass relation L_x = A E(z)^C (M/M0)^B, obtaining B = 1.87 +/- 0.12 at M0 = 5e13 Msun. The paper interprets the steep slope relative to self-similarity as evidence for non-gravitational processes in low-mass groups, and compares the relation with published X-ray- and optically-selected samples and with simulations.

Significance. The dataset and method are valuable: the sample is free of X-ray selection by construction, the use of full luminosity posteriors instead of point estimates with upper limits is a strength, and the comparison with XXL, eFEDS, and other studies gives useful context. The paper also tests several modelling assumptions (minimum ECF temperature, abundance, beta-profile slope, richness threshold, cosmology) and reports their impact. If the central slope measurement is robust, it is an important observational anchor for feedback models in the group regime. The main quantitative claim, however, currently lacks a full systematic error treatment, so the significance is contingent on the fixes described below.

major comments (2)
  1. [Section 4, Eqs. (5)–(6)] The number densities in adjacent XLF bins are correlated because the same luminosity posterior contributes to multiple bins through the r_i integrals in Eq. (5). The Monte Carlo sigma_nj in Eq. (6) characterises the marginal uncertainty in each bin, but the likelihood used for the Schechter fit (and subsequently for the LM fit in Section 5) treats the n_j as independent lognormal variates. This ignores the bin-to-bin covariance and can understate the uncertainties on alpha and hence on the inferred B. I ask the authors to include the full covariance matrix from the Monte Carlo realisations in the likelihood, or to demonstrate quantitatively that the bin width makes the correlations negligible for the fitted parameters.
  2. [Section 5, Eq. (7)] The slope B is inferred by requiring the product of the Tinker et al. (2008) halo mass function and the LM relation to reproduce the observed XLF. To first order, B is proportional to the local logarithmic slope of the assumed HMF at the pivot mass, so systematic uncertainty in that slope propagates almost linearly into B. The quoted error B = 1.87 +/- 0.12 includes only the statistical XLF uncertainty. The Planck18 comparison in Section 5 shifts B to 1.76, a change comparable to the quoted error, and it tests only the adopted cosmology, not the calibration of the HMF at M ~ 5e13 Msun (mass definition, fitting-function scatter, or baryonic effects). I request a quantitative HMF systematic budget before the steepening relative to self-similarity is presented as robust.
minor comments (4)
  1. [Section 5, Fig. 11] The posterior for sigma_L closely follows the adopted Gaussian prior N(0.2, 0.1), and the paper already states that the normalisation can be regarded as an upper limit. This caveat should be carried explicitly into the normalisation comparisons in Section 6.3 and Figure 14, where A is compared with other studies.
  2. [Figure 6] The legend label 'No oint source nearby' contains a typo; it should read 'No point source nearby'.
  3. [Section 6.1] The phrase 'we would expect that we should observe some some Eddington bias' contains a duplicated 'some'.
  4. [Section 3.2] The text says 'self-consistant'; the correct spelling is 'self-consistent'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LM slope is inferred, not predicted, from an external HMF and an independently measured XLF.

full rationale

The paper's central result, B=1.87±0.12, is a fit, not a prediction: the XLF is measured from forced aperture photometry (Section 4) and then used, together with the external Tinker et al. (2008) HMF, to infer the LM relation via forward modeling (Section 5). The text is explicit: 'In effect, we will infer the form of the LM relation required to map the observed XLF onto a known HMF.' Thus the agreement between the forward model and the observed XLF is the fitting criterion, not an independent confirmation; no out-of-sample prediction is claimed. The mass scale is anchored externally by Tinker et al. (2008), with the GAMA-based HMF reconstruction of Driver et al. (2022) cited only as broad agreement; that citation is an independent empirical check, not the source of the slope. The scatter sigma_L is admitted to be prior-dominated, and the normalization is explicitly an upper limit, so no fitted input is disguised as a prediction. The WMAP9-vs-Planck cosmology test shifts B from 1.87 to 1.76, within 1 sigma; this is a systematic uncertainty, not a circular reduction. The luminosity cut at 10^40.6 was chosen in Section 4 from mode-zero posterior dominance before the LM fit, and the later conversion of the GAMA mass completeness limit via the best-fit LM relation is a post-hoc consistency check, not a load-bearing circular step. No self-citation carries the argument: Tinker et al. (2008) is external, and comparisons to other LM studies are independent. No step reduces by construction to its own input, so the circularity score is 0.

Assumptions & free parameters 9 free parameters · 8 assumptions · 0 invented entities

The central inference rests on a chain of astrophysical modeling assumptions: a theoretical HMF, a spectral model, a beta-model for the ICM, and a fixed self-similar evolution. Several hand-chosen parameters (temperature floor, abundance, beta, luminosity floor) are tested for robustness and found not to change conclusions. The main fitted parameters (XLF alpha and n42, LM A and B) are free parameters in the standard fitting sense, while sigma_L is effectively unconstrained and prior-dominated.

free parameters (9)
  • LM slope B = 1.87 +/- 0.12
    Central claimed parameter; inferred by forward-modeling the XLF from the Tinker HMF.
  • LM normalization A = (0.17 +/- 0.07) x 10^43 erg/s
    Fitted together with B; strongly degenerate with sigma_L, so quoted as an upper limit.
  • Intrinsic scatter sigma_L = 0.21 +/- 0.09 (posterior approximately equals prior N(0.2, 0.1))
    Fit with a Gaussian prior; the data do not constrain it, and the authors state the normalization is an upper limit.
  • XLF Schechter slope alpha = 1.66 +/- 0.05
    Fitted to the GAMA XLF; enters the LM inference through the mapping.
  • XLF normalization n42 = (6.63 +/- 0.61) x 10^-3 Mpc^-3
    Fitted to the GAMA XLF; degenerate with alpha.
  • Luminosity posterior lower bound = 1e39 erg/s
    Hand-chosen lower limit applied to all luminosity posteriors to avoid unrealistic values; affects low-luminosity bins but excluded from fits.
  • Minimum ICM temperature for ECF = 1 keV
    Hand-imposed floor to avoid unrealistically cool temperatures from GAMA mass uncertainties; authors test 0.1 keV and find negligible impact.
  • Beta-model beta = 2/3
    Fixed value for aperture and point-source corrections; authors test beta=0.5 and find ~15% luminosity change with negligible impact on results.
  • ICM abundance = 0.3 Zsun (Asplund tables)
    Fixed due to low S/N; authors test Anders & Grevesse tables and +-0.1 Zsun with no significant impact.
assumptions (8)
  • domain assumption Tinker et al. (2008) halo mass function is accurate at M~1e13 Msun in the assumed cosmology.
    The LM relation is inferred by mapping the observed XLF onto this HMF (Section 5); no independent low-mass HMF calibration is provided.
  • domain assumption WMAP9 cosmology (Hinshaw et al. 2013) with H0=69.32, Omega_M=0.2815, sigma8=0.82.
    Used for all volume and mass calculations; the authors repeat with Planck18 and find the LM slope within 1 sigma.
  • domain assumption Self-similar evolution L ~ E(z)^C with C=2 fixed.
    Assumed for the LM relation (Eq. 7); the low-redshift sample makes this assumption nearly irrelevant.
  • domain assumption The GAMA selection function is correctly modeled by Vmax based on the 5th brightest member reaching r<19.8.
    Used in Eq. 5; tested by varying Nfof thresholds from 5 to 8, showing no systematic effect above L~1e40.6 erg/s.
  • domain assumption The XLF follows a Schechter function with L* fixed at 2.59e44 erg/s.
    Used to fit the XLF; the fixed L* does not affect the low-luminosity regime probed here.
  • domain assumption Lognormal likelihood for XLF bin number densities.
    Assumed in the Bayesian fits of both the XLF and LM relation; ignores inter-bin covariances noted in the text.
  • domain assumption APEC spectral model with Galactic absorption and temperatures from the Umetsu et al. (2020) MT relation applied to GAMA masses.
    Used to convert count rates to luminosities; the 1 keV floor is imposed to mitigate unrealistically low temperatures.
  • domain assumption A 2D beta model with beta=2/3 describes the ICM surface brightness for aperture and point-source corrections.
    Used in Sections 3.1 and 3.2; authors test a flatter profile (beta=0.5) and find a ~15% luminosity change with negligible impact.

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Cite this review

Pith. "Pith review of The XXL Survey LIV. X-ray Luminosity Function and Luminosity-Mass Relation of Optically Selected Galaxy Groups." pith.science (2026). https://pith.science/paper/ACGPBXYD

@misc{pith2026250204816,
  author       = {Pith},
  title        = {Pith review of: The XXL Survey LIV. X-ray Luminosity Function and Luminosity-Mass Relation of Optically Selected Galaxy Groups},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ACGPBXYD}},
  note         = {Machine review of arXiv:2502.04816}
}
abstract

The overlap between the GAMA spectroscopic survey and the XXL X-ray survey was used to study the X-ray properties of optically-selected groups of galaxies. Forced X-ray aperture photometry was applied to an optically-selected sample of 235 groups (containing at least five member galaxies) to measure their X-ray luminosities in the regime of low signal to noise X-ray data. The sample encompasses X-ray luminosities over an order of magnitude fainter than typical X-ray selected samples, and avoids X-ray selection biases. This gives access to low mass groups where the effects of non-gravitational processes, such as AGN-feedback, should be most apparent and could inhibit their detection in an X-ray survey. We measured the X-ray luminosity function (XLF) of the sample, and found it to be consistent with the extrapolation of the XLF from X-ray selected samples at higher luminosities. The XLF was combined with a theoretical halo mass function to infer the form of the scaling relation between X-ray luminosity and mass (LM relation) for the GAMA groups. We found a slope of $1.87 \pm 0.12$, which is steeper than self similarity in this mass regime. When comparing with other measurements of the LM relation, we find evidence for a steepening of the slope in the low mass regime, likely due to the impact of non-gravitational processes. Our approach can be translated to eROSITA data using multi-wavelength surveys to constrain the X-ray properties of galaxy groups in the limits of high redshift and low mass.

Figures

Figures reproduced from arXiv: 2502.04816 by the authors.

Figure 1
Figure 1. XMM-Newton image of the XXL North field in the 0.5 − 2 keV band, with the box highlighting the overlapping GAMA region. 2 GAMA AND XXL CATALOGUES The GAMA (Driver et al. 2011) spectroscopic survey used the Anglo-Australian Telescope to observe 300,000 galaxies in a 286 deg2 region down to an r-band magnitude of𝑟 < 19.8 with a spectro￾scopic completeness > 95% (Baldry et al. 2018). A GAMA galaxy group catalogue conta… view at source ↗
Figure 3
Figure 3. Example of the Sherpa modelling of point sources within 30" of the group location. Left panel: XMM-Newton image in the 0.5-2 keV energy band showing GAMA group 400098 with an XXL detected P1 source located at the GAMA group location. 4 further sources are located 86" to 136" away, and were included in the model. Right panel: The corresponding sherpa model, including instrumental effects, from which the cluster was c… view at source ↗
Figure 2
Figure 2. A summary of the methodology used to conduct forced X-ray aperture photometry on the GAMA-XXL galaxy group sample. of the ICM flux. Instead, the X-ray images of these groups were modelled using the CIAO3 package sherpa. A model of the ICM emission plus any point sources within a 300”×300” cutout centred on the group location was fitted to the X-ray image. The X-ray surface brightness distribution of the group was mo… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Example of the luminosity PDF for three groups. Group 400282 has a mode of zero, while groups 400229 and 400244 are approximately Gaussian and have well defined modes, although group 400229 is truncated. 2001), assuming an APEC model (Smith et al. 2001), with Galactic …
Figure 5
Figure 5. Figure 5: Comparing the 0.5−2 keV X-ray luminosities and redshifts of the GAMA-XXL sample with samples by REFLEX II (Böhringer et al. 2014), WARPS (Horner et al. 2008), XXL (XXL Paper XX) and eFEDS (Liu et al. 2022). The plotted redshift range is truncated at 0.6 to match the ra…
Figure 6
Figure 6. Figure 6: Comparison between the median of each luminosity posterior with the values and errors given by XXL Paper XX for the GAMA groups which had XXL matches. The error bars on the GAMA luminosities show the 16% to 84% range of the luminosity posteriors. For the GAMA groups wh…
Figure 7
Figure 7. Figure 7: The count rate recovered by aprates over a range of input count rates for a 40ks exposure to represent the shallower XXL observations. The test was done for a 60" source aperture with a background count rate of 4.5 × 10−3 counts s−1 included before taking a Poisson rea…
Figure 8
Figure 8. Figure 8: The XLF of the the optically selected GAMA sample along with the best fitting Schechter function, 𝑛42 = (6.63 ± 0.61) × 10−3Mpc−3 and 𝛼 = 1.66 ± 0.05, with 𝐿 ∗ fixed at 2.59 × 1044 erg s-1. The fit to the GAMA data was limited to luminosities ≳ 1040.6 erg s-1 due to bi…
Figure 9
Figure 9. Figure 9: The resulting best fitting values for the Schechter function are 𝑛42 = (6.63±0.61) ×10−3Mpc−3 and 𝛼 = 1.66±0.05, and are illustrated in [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Comparison of the GAMA-XXL sample XLF and best-fitting Schechter function (as in [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: The posterior distribution for the normalisation, slope and scat￾ter of equation 7 required to reproduce the observed XLF of the GAMA groups given a theoretical HMF. The blue dashed line represents the priors used, illustrating that the posterior distribution of 𝜎𝐿 cl…
Figure 12
Figure 12. Figure 12: Comparing the number densities for different GAMA richness limits shown in [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: Visual representation of equation 7 comparing the best fitting parameters from [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 14
Figure 14. Figure 14: Best-fitting parameters for equation 7 required to reproduce the observed XLF of the GAMA groups given a theoretical HMF. Contours indicate 1𝜎, 2𝜎, and 3𝜎 confidence intervals and the horizontal dashed line shows the self-similar slope. The slope and normalisation val…
Figure 15
Figure 15. Figure 15: Visual representation of equation 7 as described in [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]

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