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The eROSITA view on the halo mass-temperature relation: From low-mass groups to massive clusters

T0 review · 4 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The mass–temperature relation is one power law from galaxy groups to massive clusters, with slope $1.65$, making temperature a workable mass proxy across two decades in halo mass.

desk verdict Solid, careful stacking measurement that extends the M–T relation to optically selected groups; main caveat is the external mass calibration, not the X-ray analysis. read the letter →

arxiv 2505.01502 v2 pith:TY27G2D6 submitted 2025-05-02 astro-ph.GA astro-ph.HE

V. Toptun , P. Popesso , I. Marini , K. Dolag , G. Lamer , X. Yang , Q. Li , B. Csizi
show 10 more authors
L. Lovisari S. Ettori V. Biffi S. Vladutescu-Zopp A. Dev D. Mazengo A. Merloni J. Comparat G. Ponti E. Bulbul
This is my paper · ORCID
classification astro-ph.GAastro-ph.HE
keywords galaxygroupsclustersmass-temperaturerelationX-rayspectralstackingeROSITAintraclustermediummassproxyself-similarscaling
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 sets out to prove that the relation between X-ray gas temperature and halo mass is one continuous power law from small galaxy groups of about $10^{13}\,M_\odot$ up to massive clusters near $10^{15}\,M_\odot$, with no change of slope in the poorly explored group regime. The evidence is built by stacking thousands of very faint spectra from the first eROSITA all-sky survey for optically selected galaxy groups, an approach that extracts an average temperature where individual group detections are impossible. The paper validates the stacking on mock X-ray observations of a hydrodynamical simulation and finds that the same procedure recovers the input temperatures. If the central claim is right, gas temperature is a reliable halo-mass proxy across two decades in mass, which would let temperature-derived masses be used in cluster mass-function and cosmological analyses.

What carries the argument

The carrying mechanism is spectral stacking of optically selected groups: groups are sorted into halo-mass bins, their eRASS1 event lists are masked of point sources, spectra are extracted within $R_{500}$, shifted to a common rest frame, and co-added; each stacked spectrum is then fit with a multi-temperature plasma model (gadem) to recover a mean gas temperature per bin. The optical luminosity-based halo masses are converted to $M_{500}$ by assuming $M_{180}\sim M_{200}$ and a mass-dependent $M_{500}/M_{200}\simeq0.7$ with $0.046$ dex scatter taken from the hydrodynamical simulation. The same pipeline is applied to mock eROSITA observations built from that simulation and an X-ray telescope simulator; agreement between input and recovered temperatures is what turns the stacked temperature into a claimed unbiased measurement.

What would settle it

Measure independent masses for the same stacked groups, for example with weak gravitational lensing or thermal Sunyaev–Zel'dovich observations, and refit the mass–temperature relation; a mass-dependent offset between lensing masses and the luminosity-calibrated $M_{500}$ values would break the single-power-law claim. Alternatively, the deeper eRASS:4 survey should reproduce the same slope with smaller scatter rather than a steeper low-mass end.

Watch

Extended reading notes

Core claim

The paper's central result is the best-fit relation $\log_{10}(M_{500}/M_\odot) = (1.65\pm0.11)\,\log_{10}(T_X/1\,\mathrm{keV}) + (13.38\pm0.05)$, with intrinsic scatter $0.13\pm0.03$ dex. The claim is that this single power law, statistically consistent with the previously established cluster relation and within about $1.7\sigma$ of the self-similar prediction $M\propto T^{1.5}$, describes galaxy groups and clusters alike. The low-temperature end is anchored by seven stacked mass bins in which average temperatures of $0.7$–$1$ keV are measured from co-added spectra, while the mock tests show that contamination from unresolved AGNs and spurious optical detections does not systematically bias these temperatures. On this basis the authors conclude that AGN feedback and cooling redistribute baryons or alter the group core but do not change the overall temperature of the hot gas, so the temperature can serve as a mass proxy over the entire sampled range.

Load-bearing premise

The relation rests on the assumption that the optical luminosity-calibrated halo masses can be converted to $M_{500}$ with a fixed, mass-dependent ratio of about $0.7$ taken from a hydrodynamical simulation; if that conversion is biased as a function of mass, the fitted slope and intercept shift.

Editorial extensions

If this is right

  • Temperature-based mass estimates can be extended to optically selected groups roughly two decades below the mass range of current X-ray-selected cluster samples.
  • Cluster and group mass-function studies can adopt a single calibrated $M$–$T$ relation over this larger range, improving constraints on cosmological parameters such as $S_8$.
  • With the deeper eRASS:4 data, per-bin statistics will grow enough to measure temperature profiles rather than only average temperatures, giving a sharper view of AGN feedback.
  • The same stack-and-measure approach can be applied to any X-ray-faint population selected by other means, such as low-luminosity AGNs or high-redshift cluster candidates.

Reading between the lines

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

  • Editorial inference: if the single power law survives independent mass calibration, the apparent group/cluster differences reported by some X-ray-selected samples are probably selection effects, with X-ray selection favoring low-entropy systems, rather than a real break in the relation.
  • Editorial inference: re-running the identical stacking with weak-lensing masses for the same mass bins would directly test the assumed $M_{500}$ conversion and the luminosity-based mass calibration, a test the current data cannot provide.
  • Editorial inference: the mock result that current AGN activity does not change the relation suggests the gas response time exceeds the AGN duty cycle; deeper data with radio-mode feedback indicators could test this by comparing active and inactive systems at fixed mass.
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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

4 major / 6 minor

Summary. The paper measures the X-ray temperature of low-mass galaxy groups and clusters by stacking eRASS1 spectra of optically selected Yang et al. (2007) groups, using the Magneticum simulation to validate the stacking pipeline. From seven stacked mass bins spanning roughly 10^13 to 7x10^14 Msun, the authors fit a single power-law mass-temperature relation, Eq. (2): log10(M500/Msun) = (1.65 +/- 0.11) log10(TX/1 keV) + (13.38 +/- 0.05), with intrinsic scatter 0.13 +/- 0.03 dex. They report that this relation is consistent with the self-similar prediction and with the cluster-based relation of Lovisari et al. (2015), and they argue that a single power law holds across the entire sampled range, so that temperature remains a reliable mass proxy down to group scales. The paper also compares the measured relation with Magneticum, FLAMINGO, and EAGLE predictions and discusses the implications of AGN feedback for the intragroup medium.

Significance. If the central result holds, the paper significantly extends the observationally calibrated mass-temperature relation into the poorly populated group regime using an X-ray unbiased, optically selected sample. The methodological contribution is also valuable: stacking spectra of optically selected groups is a promising route to extracting thermodynamic information from systems that are individually undetected in shallow surveys. Strengths of the work include the use of a sample selected independently of X-ray properties, a detailed mock-based validation of the stacking and spectral-fitting pipeline, explicit background checks against blank fields, bootstrap-based uncertainty estimates, and the use of public eRASS1 and Y07 data. The central conclusion, however, rests on the absolute calibration of the Y07 mass scale and on several modeling assumptions inherited from the Magneticum simulation, and the quantitative validation is performed at eRASS:4 depth rather than eRASS1 depth; these issues need to be addressed before the claim of a universal single power law can be accepted without qualification.

major comments (4)
  1. [§2.1, Fig. 1, Eq. (2)] The x-axis masses in Eq. (2) are derived from Y07 luminosity-based halo masses defined at M180, converted to M500 by assuming M180 ~ M200 and multiplying by a Magneticum-derived M500/M200 ratio of ~0.7 with 0.046 dex scatter (Fig. 1). The central claim that the M-T relation is a single power law without a slope change in the group regime is therefore only as secure as the Y07 mass-to-light calibration and the simulated conversion ratio. The Colossus comparison in §2.1 validates the conversion only under an assumed dark-matter density profile and concentration model; it does not test the absolute Y07 mass scale at M500 ~ 10^13 Msun. A mass-dependent bias of the order of plausible M/L calibration errors would directly bias both the slope and intercept of Eq. (2) and could mimic or hide a group-regime break. Please propagate this systematic into the fit (for example, as a covariance term) or demonstrate robustness by repeating the fit with an independent mass calibration, such as the Y07 stellar-mass proxy, updated Yang et al. catalogs, or stacked weak-lensing masses.
  2. [§5.2 and §6.1] The gadem temperature model fixes the width of the Gaussian emission-measure distribution to T_sigma = 0.2 keV, stated to be 'based on the distribution of mass-weighted temperatures from the simulations.' Because the same Magneticum simulation is used both to set this prior and to validate the temperature recovery, the validation is partly circular for this parameter. If the true temperature dispersion in low-mass groups differs from the simulated one, for example because of a wider multiphase gas distribution or AGN-driven outflows, the fitted mean temperature will be biased in a temperature-dependent way, and that bias will propagate into the slope of Eq. (2). Please add a sensitivity test that varies T_sigma over a plausible range and reports the induced change in recovered temperatures, and ideally compare the assumed dispersion with measured temperature distributions of high-S/N eRASS1 or XMM-Newton groups.
  3. [§3.3, Figs. 8-9, Appendix B] The quantitative validation of the stacking and spectral fitting, including the consistency of stacked and input spectra and the comparison of recovered versus input temperatures, is carried out on mock observations at eRASS:4 depth, while the observed analysis uses eRASS1 data. Appendix B shows eRASS1 stacked images but does not repeat the temperature-recovery tests at eRASS1 depth. Since eRASS1 has roughly four times fewer photons and a correspondingly larger background and unresolved-AGN contribution, the validation as presented does not directly cover the actual data conditions. Please repeat the mock temperature-recovery test at eRASS1 depth, or at least quantify the expected bias and increased uncertainty from the lower S/N in each mass bin.
  4. [§7.1, Eq. (2)] The conclusion that the M-T relation 'does not change slope' in the group regime is supported only by fitting a single power law and by the statement that the data agree with Lovisari et al. (2015) within 1 sigma. No comparison is shown against a two-slope or broken power-law model, and the uncertainties in Table A.1 are large; for example, the bin at log10(M500/Msun)=14.09 has kT=2.47(+2.38/-0.81) keV at 3 sigma. A single power law will almost necessarily remain consistent when the error bars are this large, so 'no significant slope change' should be quantified with a model-comparison statistic or by placing an explicit upper limit on the slope difference between the low-mass and high-mass bins.
minor comments (6)
  1. [§7.1] Equation (2) should be typeset as log10(M500/Msun) = (1.65 +/- 0.11) log10(TX/1 keV) + (13.38 +/- 0.05) to avoid the impression that the uncertainty multiplies the whole temperature term.
  2. [§7.1 and Table A.1] The paper quotes 1-sigma uncertainties for Eq. (2) but reports 3-sigma uncertainties in Table A.1; please state this difference explicitly in the table caption and in the text.
  3. [§5.2] The gadem model reference appears as a broken inline link ('gadem3https://...'); the citation and the surrounding formatting need to be fixed.
  4. [§6.1 and Fig. 8] The Fig. 8 caption refers to point-source masking based on the eRASS1 catalog, while the mock analysis described in §6.1 uses eRASS:4-equivalent mocks; please clarify which catalog was actually used.
  5. [Appendix B] The appendix heading uses 'eRASS4' while the rest of the paper uses 'eRASS:4'; please unify the notation.
  6. [Abstract and Table A.1] The abstract states that the relation spans up to about 10^15 Msun, but the highest bin in Table A.1 is log10(M500/Msun) ~ 14.85, corresponding to roughly 7x10^14 Msun; please reconcile the wording with the actual range of the fitted bins.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fitted M–T relation of Eq. (2) is anchored to the external Y07 optical mass catalog and real eRASS1 spectra; the Magneticum-based conversions and spectral priors are stated assumptions that do not define the fitted slope or intercept by construction.

full rationale

Equation (2) is obtained by an ODR fit of stacked eRASS1 spectral temperatures (Table A.1) to Y07 luminosity-based halo masses converted to M500. The mass proxy is external to this work (SDSS DR4 plus the Yang et al. 2005/2007 calibration), and the temperatures come from real eRASS1 photons; neither side of the relation is defined by the Magneticum simulation. The simulation-derived M500/M200 ratio is approximately constant (~0.7) across the mass range (Fig. 1), so it changes the normalization by about log10(0.7) ≈ −0.15 dex but cannot by construction generate the measured slope 1.65 ± 0.11. The fixed gadem temperature width of 0.2 keV is a stated spectral-modeling assumption, and the mock tests in Section 6.2 check that the stacking pipeline recovers input mass-weighted temperatures; they do not assign the observed temperature values used in the fit. The paper does not invoke a uniqueness theorem, does not rename a known result, and does not present a fitted parameter as a prediction. The manuscript also explicitly compares the result with the independent Lovisari et al. (2015) relation and with the self-similar prediction, providing external context. The Y07 mass-to-light calibration and the M500/M200 conversion are legitimate sources of possible systematic error, but that is a correctness risk rather than circularity. No step in the derivation reduces Eq. (2) to its own inputs by construction, so the appropriate circularity score is 0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the Y07 optical mass proxy, the simulation-based M500/M200 conversion, and the assumed spectral model for the stacked group emission. The slope and intercept are outputs of the fit, not free inputs; the genuinely assumed quantities are the gadem temperature width, the metallicity, the column density, and the mass-conversion ratio, all either fixed from prior literature or from the Magneticum simulation. No new entities are introduced.

free parameters (4)
  • gadem temperature width (T_sigma) = 0.2 keV
    Fixed width of the Gaussian emission-measure distribution in the gadem spectral model, chosen from the distribution of mass-weighted temperatures in Magneticum simulations (Section 5.2). It most affects the line-dominated low-mass bins.
  • ICM/IGrM metallicity = 0.3 Zsun (Anders & Grevesse 1989)
    Assumed constant metallicity within R500 in the spectral fits; authors test 0.2-0.8 Zsun and propagate the effect into temperature uncertainties (Section 5.2, Figure 7).
  • Galactic hydrogen column density = 2.6e20 cm^-2 (sample average)
    Fixed to the average HI4PI-based column in the spectral fits; min/max tests show no relevant difference (Section 5.2).
  • M500/M200 conversion ratio = ~0.7 with 0.046 dex scatter
    Derived from Magneticum halo catalogs to convert Y07 masses from M180 (assumed ~M200) to M500; verified against Colossus. Any mass-dependent bias propagates into the fitted relation (Section 2.1, Figure 1).
assumptions (6)
  • domain assumption Flat LCDM cosmology with Omega_m = 0.27 and H0 = 70 km/s/Mpc
    Assumed throughout for converting redshifts and masses to physical radii and for the Y07 mass calibration (Section 1).
  • ad hoc to paper M180 is approximately equal to M200 for the Y07 halos
    Stated in Section 2.1 to justify applying the Magneticum-based M500/M200 correction to the Y07 masses; a simplifying bridge between the two overdensity conventions.
  • ad hoc to paper The gadem multi-temperature model with a Gaussian emission-measure distribution and fixed width 0.2 keV describes the stacked group spectra
    Adopted in Section 5.2 with the width fixed from simulations rather than measured from the data; most influential in the low-temperature bins where line emission dominates.
  • domain assumption Unresolved AGN contamination is negligible for temperature measurement and needs no explicit model component
    Justified in Section 5.2 by mock tests showing no improvement when adding an AGN component; bright AGNs are masked, but faint central AGNs remain in the stacks.
  • domain assumption The Magneticum simulation is a reliable basis for calibrating the M500/M200 ratio and for validating the stacking pipeline
    Relied on in Sections 2.1, 3, and 6; supported by the simulation reproducing observed AGN luminosity functions, BH mass functions, and gas mass fractions.
  • domain assumption A constant metallicity of 0.3 solar within R500 is adequate for the spectral fits
    Radial abundance profiles are neglected; the value is taken from prior literature and its impact is tested across 0.2-0.8 solar (Section 5.2).

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Cite this review

Pith. "Pith review of The eROSITA view on the halo mass-temperature relation: From low-mass groups to massive clusters." pith.science (2026). https://pith.science/paper/TY27G2D6

@misc{pith2026250501502,
  author       = {Pith},
  title        = {Pith review of: The eROSITA view on the halo mass-temperature relation: From low-mass groups to massive clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TY27G2D6}},
  note         = {Machine review of arXiv:2505.01502}
}
abstract

Galaxy groups and clusters are among the best probes of structure formation and growth in a cosmological context. Most of their baryonic component is dominated by the intracluster medium (ICM), whose thermodynamical properties serve as indicators of the halo's dynamical state and can be used for the halo mass determination in the self-similar scenario. However, baryonic processes, such as AGN feedback and gas cooling, may affect the global properties of the ICM, especially in the group regime. These effects might lead to deviations from self-similar predictions in galaxy groups' scaling relations, while they remain in place for massive galaxy clusters. Additionally, the low-mass end of the scaling relations, ranging from $10^{13}$ to $10^{14} M_\odot$, remains unclear and poorly populated, as current X-ray surveys detect only the brightest groups. Here, we present the Mass-Temperature relation across the full mass range, from massive clusters to low-mass groups ($10^{13}M_\odot$), as observed by eROSITA. Using spectral stacking from eROSITA eRASS1 data for optically selected galaxy groups, we find that, in the lower mass range, galaxy groups follow the power-law relation known for galaxy clusters. We further validate these results by conducting the same stacking procedure on mock eRASS:4 data using the Magneticum hydrodynamical simulation. This indicates that AGN feedback is more likely to affect the distribution of baryons in the intragroup medium rather than the overall halo gas temperature. No significant changes in the Mass-Temperature relation slope suggest that temperature can serve as a reliable mass proxy across the entire mass range. This validates the use of temperature-derived masses, particularly in cosmological studies, significantly broadening the mass range and enabling applications such as improving the cluster mass function studies and cosmological parameter estimate.

Figures

Figures reproduced from arXiv: 2505.01502 by the authors.

Figure 1
Figure 1. Distribution of mass ratios for halo masses within R500 and R200 from the Magneticum simulations. The horizontal red line indicates the average value used to convert M200 to M500 in this work [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Distribution of sources used in this work with redshift and gas mass within R200. The sample based on Yang et al. (2007), described in Section 2, is plotted in blue. The sample from the Magneticum light￾cone, described in Section 3, is shown in red. mass functions of galaxies in groups, which are consistent with previous studies. In addition, we verified the performance of the group-finding algorithm using simulatio… view at source ↗
Figure 3
Figure 3. Figures adapted from Marini et al. (2025b). Right panel: Com￾pleteness (black) and contamination (red) as a function of halo mass for Yang et al. (2005)’s Friends-Of-Friends (FoF) algorithm results ap￾plied to the Magneticum mock optical catalog. The shaded region corre￾sponds to the 95th binomial confidence interval. Left panel: Comparison of the halo mass estimated by the Yang et al. (2005) FoF algorithm as a func… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Top panel: Comparison of all background spectra used for differ￾ent mass bins after the stacking procedure (violet points), along with the background spectrum from the stacking of 467 random blank eROSITA fields (black points). Bottom panel: Residuals, calculated as th…
Figure 5
Figure 5. Figure 5: shows the average fraction of flux originating from continuum emission relative to the total emission. To estimate 3 \unskip\protect\penalty\@M\vrulewidth\z@height\z@ depth\dp¸ 4 https://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/ manual/XSmodelMekal.html 5 https://heasar…
Figure 6
Figure 6. Figure 6: Hydrogen column density map of all sources used in this study, based on the 2D HI4PI map. The color bar indicates the hydrogen col￾umn density for individual sources. 3σ of the temperature distribution representing the error. This procedure, based on random sampling of…
Figure 7
Figure 7. Figure 7: Histograms of temperature values obtained using background subtraction (left column) and background modeling (right column) across different mass bins, showing the bootstrapped error distribution. The histograms are color-coded by metal abundances. Dashed vertical line…
Figure 8
Figure 8. Figure 8: Top panels and bottom left panel: Comparison of the PHOX spectrum with the resulting stacked spectrum for the mock sample across different mass bins. The red line represents the total PHOX X-ray spectrum, along with its 3σ error range. The black, blue, and green lines …
Figure 10
Figure 10. Figure 10: Impact of contamination from spurious (“false”) fields on tem￾perature, normalization, and fit statistics in the stacked sample from the Magneticum mock observations equivalent to eRASS:4 depth. The top panel shows the measured temperature as a function of the fractio…
Figure 9
Figure 9. Figure 9: Upper panel: Comparison of temperatures derived from stacking with mean mass-weighted temperatures from simulations for the mock Magneticum sample. Blue points show results from background sub￾traction, and black points represent results from background modeling. The r…
Figure 11
Figure 11. Figure 11: The mass-temperature relation for galaxy groups and clusters in observations, with mass defined inside R500 as a function of X-ray temperature. Black squares correspond to stacked bins from eRASS1 observations. Open diamonds represent background modeling instead of ba…
Figure 12
Figure 12. Figure 12: The mass-temperature relation for galaxy groups and clusters in simulations, with mass defined inside R500 as a function of X-ray tem￾perature. Blue background points represent individual mass-weighted temperatures for each simulated group in Magneticum. Black squares…
Figure 13
Figure 13. Figure 13: Comparison of the mean mass-weighted temperature as a func￾tion of halo masses for a sample of groups with and without X-ray AGN sources within their R500. Grey points represent the individual mass￾weighted temperatures for each source. The blue line indicates the mea…

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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 16, 2026 · model on record in the stance chip above.