Pith. sign in

REVIEW 2 major objections 5 minor 86 references

In Magneticum, X-ray-bright groups at fixed mass cluster ~17% more strongly than X-ray-faint ones, a baryonic form of assembly bias largely captured by formation time.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · grok-4.5

2026-07-12 00:13 UTC pith:YFHMXN2M

load-bearing objection Clean Magneticum measurement of LX- and fgas-dependent linear bias at fixed mass; formation-time matching largely kills the large-scale signal; model-dependent but well scoped. the 2 major comments →

arxiv 2607.03746 v1 pith:YFHMXN2M submitted 2026-07-04 astro-ph.CO

Baryonic assembly bias in X-ray-selected galaxy groups and clusters: insights from the Magneticum simulation

classification astro-ph.CO
keywords halo assembly biasX-ray luminositygas fractiongalaxy groups and clustershalo-matter biashydrodynamical simulationsbaryonic physicslarge-scale structure
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Galaxy groups and clusters are usually treated as if their large-scale clustering depends only on halo mass. This paper shows that, inside the Magneticum hydrodynamical simulation, that is incomplete: at fixed mass, systems with higher X-ray luminosity (and especially higher gas fraction) are more strongly clustered than fainter or gas-poorer systems. The effect is measured from the halo-matter cross-power spectrum after building mass-matched percentile samples. For the 84th-versus-16th split the linear bias difference is about 0.17 (~17%); gas-fraction splits give ~39%. The signal is strongest at group scales, already present in gas fraction from redshift ~2, and becomes clear in X-ray luminosity only at low redshift once gas thermodynamics tracks baryon retention. Matching on formation time as well as mass largely erases the large-scale bias difference, so X-ray luminosity is acting as a baryonic tracer of assembly bias. A sympathetic reader cares because flux-limited X-ray surveys preferentially select the bright end of the scatter and therefore may not sample the mass-only bias relation assumed in cosmological analyses.

Core claim

In the Magneticum simulation, mass-matched X-ray-bright (or gas-rich) halos are more strongly clustered on large scales than X-ray-faint (or gas-poor) ones. For the fiducial 84th–16th percentile split the linear bias difference is Δb_lin = 0.17 ± 0.03 (~17% enhancement relative to the faint sample); gas-fraction selection yields ~39%. The effect peaks at group masses, is already present in gas fraction from z ≃ 2, appears in X-ray luminosity mainly at z ≲ 0.3, and is reduced below 2σ once formation time is also matched. Thus X-ray luminosity traces a baryonic manifestation of halo assembly bias beyond mass.

What carries the argument

Mass-matched percentile splits of the L_X–M and gas-fraction–M relations, followed by the linear halo bias extracted as the large-scale ratio of the halo-matter cross-power spectrum to the matter power spectrum (b = P_hm(k)/P_mm(k)).

Load-bearing premise

The result depends on Magneticum’s subgrid baryonic physics producing the particular link between high X-ray luminosity (or high gas fraction) and late formation; other simulations report the opposite luminosity–formation-time trend.

What would settle it

Repeat the same mass-matched L_X and gas-fraction splits and bias measurement in an independent hydrodynamical suite that predicts the opposite L_X–formation-time correlation; if the bright/gas-rich samples no longer show higher large-scale bias (or the sign flips), the Magneticum claim does not generalise.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Mass-only halo-bias models mis-estimate the clustering of X-ray-selected samples once luminosity or gas-fraction scatter is present.
  • Flux-limited X-ray surveys that prefer bright systems at fixed mass will weight toward the higher-bias side of the Magneticum relation.
  • Gas fraction is a stronger and earlier tracer of the assembly-dependent clustering signal than X-ray luminosity.
  • Forward models used for eROSITA-like cosmological analyses need a luminosity- or gas-dependent secondary bias term at group scales.
  • Formation-time matching largely removes the large-scale signal, so residual small-scale differences must come from other correlated properties (accretion rate, concentration, feedback history).

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If competing simulation suites reverse the L_X–assembly correlation, the sign of luminosity-dependent bias becomes a clean discriminator among AGN-feedback and baryon-retention models.
  • Observational tests will need mocks that fold in surface-brightness selection and mass-proxy scatter, because those effects can dilute or enhance the intrinsic Magneticum signal.
  • Group-scale samples, not massive clusters, are where secondary baryonic bias is most likely to matter for next-generation X-ray clustering constraints.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper measures large-scale halo bias for mass-matched X-ray-bright vs X-ray-faint (and gas-rich vs gas-poor) groups and clusters in the Magneticum Box2/hr hydrodynamical simulation. Using percentile ranking of LX,200 (and fgas) within narrow M200 bins, the authors compute the linear bias from the halo–matter cross-power spectrum Phm(k)/Pmm(k). For the 84th–16th LX split they report Δblin = 0.17 ± 0.03 (~17% enhancement of the bright sample), with a consistent but weaker 67th–33rd signal; the gas-fraction split is stronger (~39% and ~26%). The effect peaks at group scales, is already present for fgas from z ≃ 2, and becomes significant for LX only at z ≲ 0.3. Simultaneous matching on M200 and formation time z50 reduces the large-scale bias difference below 2σ. The authors conclude that, within Magneticum, X-ray luminosity is a baryonic tracer of assembly bias beyond mass.

Significance. If the Magneticum result holds, it supplies a concrete, observationally relevant secondary bias for X-ray-selected group samples that dominate eROSITA-like catalogues. The analysis is carefully scoped to one simulation suite, uses standard estimators (mass-matched percentiles, Phm/Pmm, jackknife, dual percentile cuts, redshift evolution, and formation-time matching), and includes a useful k_lin robustness check (Appendix A). The explicit comparison with Hyenas/Flamingo (opposite LX–formation-time trend) correctly frames the result as model-dependent rather than universal. The work is therefore a solid, falsifiable prediction for Magneticum-like baryonic physics and a useful benchmark for forward-modelling of X-ray survey selection.

major comments (2)
  1. The central claim is carefully limited to Magneticum, but the Introduction and Discussion note that Hyenas and Flamingo find the opposite LX–formation-time correlation. Because the measured Δblin is therefore simulation-model-dependent, the paper should state more explicitly (Abstract and Conclusions) that the sign and magnitude are not yet a universal prediction, and should outline the minimal observational or multi-simulation test that would discriminate the models.
  2. Section 2.1 mentions a consistency check with the larger Box2b/hr for the gas-fraction split, but those measurements are not shown. Given that jackknife errors on the largest scales are limited by the finite volume of Box2/hr, a quantitative comparison (or a short table of Δblin) for the gas-fraction signal in Box2b/hr would strengthen the claim that the result is not volume-driven.
minor comments (5)
  1. Figure 2 and Figure 5: the shaded jackknife bands are hard to distinguish from the solid/dotted lines at low k; a slightly thicker line or a different hatch would improve readability.
  2. Section 2.3: the mass-bin width (0.06 dex) is stated once; a brief note that the results are stable under modest changes of bin width would reassure readers that residual mass mismatch is negligible.
  3. Section 3.2 / Figure 3: the Tinker et al. (2010) curve is shown, but the Castro et al. (2021, 2024b) Magneticum-calibrated model is only mentioned in text; adding it to the figure would make the comparison more transparent.
  4. Typographical consistency: “V oit” appears with a space in several references; standardise to “Voit”.
  5. Appendix A: the percentage excess Δblin/blin|faint is useful; stating the absolute Δblin values for each k_lin in a short table would make the robustness check fully quantitative.

Circularity Check

0 steps flagged

No significant circularity: direct Phm/Pmm measurement on mass-matched percentile splits; self-citations supply interpretation only.

full rationale

The central result is an empirical measurement inside Magneticum: mass-matched LX (and fgas) percentile tails are constructed by ranking within narrow M200 bins, then blin is extracted as the large-scale average of Phm(k)/Pmm(k). The reported Δblin values, mass dependence, redshift evolution, and reduction after z50 matching are therefore outputs of that procedure, not quantities forced by a fitted parameter or by a prior equation that already encodes the answer. Self-citations (Marini et al. 2025a on LX–assembly trends; Castro et al. on bias calibrations) provide physical context and a consistency check against a mass-only baseline, but they are not load-bearing for the existence or magnitude of the measured bias difference itself. The paper explicitly scopes the claim to Magneticum and notes opposite LX–formation-time trends in other suites, so no uniqueness or ansatz is smuggled in as external fact. Minor self-citation for interpretation raises the score from 0 to 1; nothing reduces by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The central claim is a simulation measurement. It rests on standard cosmological and numerical assumptions plus the specific Magneticum subgrid model; no new free parameters are fitted to produce the bias difference, and no new physical entities are postulated.

free parameters (3)
  • percentile cuts (84/16 and 67/33) = 84th–16th (fiducial), 67th–33rd (robustness)
    Chosen by hand to define bright/faint tails; results are shown to be consistent across both choices, so not load-bearing for the existence of the signal.
  • k_lin cutoff for linear bias average = 0.2 h cMpc^{-1} (fiducial)
    Maximum wavenumber used to average b(k); varied 0.1–0.2 h/cMpc in Appendix A with stable Δb.
  • mass-bin width for ranking = 0.06 dex
    0.06 dex bins used to rank LX or gas fraction at fixed mass; ensures mass matching but is a procedural choice.
axioms (5)
  • domain assumption WMAP7 cosmology and Magneticum Box2/hr resolution and volume adequately sample the group-scale halo population for large-scale bias.
    Section 2.1; finite-volume jackknife is used, with a qualitative check on larger Box2b/hr for gas fraction only.
  • domain assumption Magneticum subgrid physics (AGN feedback, cooling, star formation, chemical enrichment) produce a realistic correlation between baryon retention, X-ray luminosity, and halo assembly history.
    Core modelling assumption; Introduction explicitly notes opposite LX–formation trends in Hyenas and Flamingo.
  • standard math Linear bias can be estimated as the large-scale average of P_hm(k)/P_mm(k) and is approximately scale-independent for k ≤ k_lin.
    Section 2.4; standard halo-bias definition on linear scales.
  • domain assumption Halo formation time z50 (redshift when main progenitor reaches half final mass) is a sufficient proxy for the assembly history that drives the secondary bias.
    Section 2.3 and 3.5; matching on z50 reduces the signal below 2σ, supporting but not proving completeness.
  • domain assumption X-ray luminosity computed with PHOX (vapec + wabs, 0.5–2 keV, ICM gas only within R200) is a valid ranking observable for the intrinsic simulation population.
    Section 2.2; authors carefully distinguish this from observed catalogue luminosities.

pith-pipeline@v1.1.0-grok45 · 22764 in / 3081 out tokens · 26356 ms · 2026-07-12T00:13:54.129142+00:00 · methodology

0 comments
read the original abstract

Galaxy groups and clusters trace the large-scale matter distribution, with their clustering usually interpreted mainly as a function of halo mass. Yet, at fixed mass, their baryonic properties retain information about halo growth, gas accretion, and feedback. The intrinsic scatter in X-ray luminosity and gas fraction suggests that X-ray-selected systems may not be a random subset of the halo population. If these observables correlate with halo assembly, they may trace secondary variations in halo bias. We test this using the Magneticum hydrodynamical simulation, measuring the clustering of systems selected by X-ray luminosity and gas fraction at fixed halo mass. We construct mass-matched subsamples by ranking halos in percentiles of X-ray luminosity and derive the linear halo-matter bias from the halo-matter cross-power spectrum. X-ray-bright halos are more strongly clustered than X-ray-faint halos at fixed mass. For the 84th-16th percentile split, we find $\Delta b_{\rm lin}=0.17\pm0.03$, corresponding to a $\sim17\%$ enhancement relative to the X-ray-faint sample. A 67th-33rd split gives a consistent signal, with $\Delta b_{\rm lin}=0.12\pm0.02$ and a $\sim12\%$ enhancement. The effect is strongest at group scales and negligible for cluster-size halos. Gas fraction shows an even stronger clustering dependence, with relative enhancements of $\sim39\%$ and $\sim26\%$ for the two percentile splits. This signal is present from $z\simeq2$, whereas X-ray luminosity becomes significant only at $z\simeq0.3$, once the gas thermodynamic state is more closely coupled to baryon retention. Matching halos by both mass and formation time reduces the large-scale bias difference to below $2\sigma$, indicating that formation time captures much of the signal. These results show that, in Magneticum, X-ray luminosity traces a baryonic manifestation of halo assembly bias beyond mass.

Figures

Figures reproduced from arXiv: 2607.03746 by Daudi Mazengo, Ilaria Marini, Klaus Dolag, Natan de Is\'idio, Paola Popesso, Tiago Castro, Veronica Biffi, Victoria Toptun.

Figure 1
Figure 1. Figure 1: Scaling relation between the X-ray luminosity within [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Scale-dependent bias for the full halo sample (black), and [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mean halo bias as a function of halo mass. Panel (a) shows the selection at fixed halo mass, with orange points indicating [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Significance of the large-scale clustering as a function [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Scale-dependent bias for the full halo sample (black), faint (blue) and bright (orange) when mass and formation time matched. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

86 extracted references · 1 linked inside Pith

  1. [1]

    E., Farahi, A., et al

    Aljamal, E., Evrard, A. E., Farahi, A., et al. 2025, MNRAS, 544, 67

  2. [2]

    W., Evrard, A

    Allen, S. W., Evrard, A. E., & Mantz, A. B. 2011, Annual Review of A&A, 49, 409

  3. [3]

    W., Schmidt, R

    Allen, S. W., Schmidt, R. W., Fabian, A. C., & Ebeling, H. 2003, MNRAS, 342, 287

  4. [4]

    & Grevesse, N

    Anders, E. & Grevesse, N. 1989, Geochimica et Cosmochimica Acta, 53, 197

  5. [5]

    Andreon, S., Moretti, A., Trinchieri, G., & Ishwara-Chandra, C. H. 2019, A&A, 630, A78

  6. [6]

    L., Moretti, A., & Trinchieri, G

    Andreon, S., Serra, A. L., Moretti, A., & Trinchieri, G. 2016, A&A, 585, A147

  7. [7]

    M., Murante, G., Arth, A., et al

    Beck, A. M., Murante, G., Arth, A., et al. 2016, MNRAS, 455, 2110

  8. [8]

    2013, MNRAS, 428, 1395

    Biffi, V ., Dolag, K., & Böhringer, H. 2013, MNRAS, 428, 1395

  9. [9]

    2012, MNRAS, 420, 3545

    Biffi, V ., Dolag, K., Böhringer, H., & Lemson, G. 2012, MNRAS, 420, 3545

  10. [10]

    2018, MNRAS, 481, 2213

    Biffi, V ., Dolag, K., & Merloni, A. 2018, MNRAS, 481, 2213

  11. [11]

    H., et al

    Biffi, V ., Dolag, K., Reiprich, T. H., et al. 2022, A&A, 661, A17

  12. [12]

    2025, A&A, 698, A238

    Biffi, V ., Rasia, E., Borgani, S., et al. 2025, A&A, 698, A238

  13. [13]

    2023, 55, 110.17

    Bogdan, A., Khabibullin, I., Kovacs, O., et al. 2023, 55, 110.17

  14. [14]

    2008, Space Science Re- views, 134, 269

    Borgani, S., Diaferio, A., Dolag, K., & Schindler, S. 2008, Space Science Re- views, 134, 269

  15. [15]

    2002, MNRAS, 336, 409

    Borgani, S., Governato, F., Wadsley, J., et al. 2002, MNRAS, 336, 409

  16. [16]

    2025, The origin of scat- ter in the X-ray luminosity - halo mass relation of galaxy clusters

    Braspenning, J., Schaye, J., Pillepich, A., & Nelson, D. 2025, The origin of scat- ter in the X-ray luminosity - halo mass relation of galaxy clusters

  17. [17]

    2022, A&A, 661, A1

    Brunner, H., Liu, T., Lamer, G., et al. 2022, A&A, 661, A1

  18. [18]

    Bryan, G. L. & Norman, M. L. 1998, ApJ, 495, 80

  19. [19]

    2022, A&A, 661, A10

    Bulbul, E., Liu, A., Pasini, T., et al. 2022, A&A, 661, A10

  20. [20]

    2021, MNRAS, 500, 2316

    Castro, T., Borgani, S., Dolag, K., et al. 2021, MNRAS, 500, 2316

  21. [21]

    2023, MNRAS, 522, 1601

    Chiu, I.-N., Klein, M., Mohr, J., & Bocquet, S. 2023, MNRAS, 522, 1601

  22. [22]

    I., Dolag, K., Lyskova, N., & Sunyaev, R

    Churazov, E., Khabibullin, I. I., Dolag, K., Lyskova, N., & Sunyaev, R. A. 2023, MNRAS, 523, 1209

  23. [23]

    2024, A&A, 687, A238

    Clerc, N., Comparat, J., Seppi, R., et al. 2024, A&A, 687, A238

  24. [24]

    2020, The Open Journal of As- trophysics, 3

    Comparat, J., Eckert, D., Finoguenov, A., et al. 2020, The Open Journal of As- trophysics, 3

  25. [25]

    2021, Physical Review D, 103, 043522

    Costanzi, M., Saro, A., Bocquet, S., et al. 2021, Physical Review D, 103, 043522

  26. [26]

    E., McCarthy, I

    Costello, E. E., McCarthy, I. G., Salcido, J., et al. 2025, FLAMINGO: Tracing the co-evolution of hot gas and black holes in galaxy groups and clusters

  27. [27]

    2024, MNRAS, 534, 1247–1256 Di Matteo, T., Springel, V ., & Hernquist, L

    Cui, W., Jennings, F., Dave, R., Babul, A., & Gozaliasl, G. 2024, MNRAS, 534, 1247–1256 Di Matteo, T., Springel, V ., & Hernquist, L. 2005, Nature, 433, 604

  28. [28]

    2009, MNRAS, 399, 497

    Dolag, K., Borgani, S., Murante, G., & Springel, V . 2009, MNRAS, 399, 497

  29. [29]

    M., et al

    Dolag, K., Remus, R.-S., Valenzuela, L. M., et al. 2025, Encyclopedia Mag- neticum: Scaling Relations from Cosmic Dawn to Present Day

  30. [30]

    2005, MNRAS, 364, 753

    Dolag, K., Vazza, F., Brunetti, G., & Tormen, G. 2005, MNRAS, 364, 753

  31. [31]

    2020, The Open Journal of As- trophysics, 3, 12

    Eckert, D., Finoguenov, A., Ghirardini, V ., et al. 2020, The Open Journal of As- trophysics, 3, 12

  32. [32]

    2009, A&A, 501, 61–73

    Ettori, S., Morandi, A., Tozzi, P., et al. 2009, A&A, 501, 61–73

  33. [33]

    2010, MNRAS, 401, 1670 Galárraga-Espinosa, D., Aghanim, N., Langer, M., & Tanimura, H

    Fabjan, D., Borgani, S., Tornatore, L., et al. 2010, MNRAS, 401, 1670 Galárraga-Espinosa, D., Aghanim, N., Langer, M., & Tanimura, H. 2021, A&A, 649, A117

  34. [34]

    Gao, L., Springel, V ., & White, S. D. M. 2005, MNRAS, 363, L66

  35. [35]

    2024, A&A, 689, A298

    Ghirardini, V ., Bulbul, E., Artis, E., et al. 2024, A&A, 689, A298

  36. [36]

    2022, A&A, 664, A198

    Gouin, C., Gallo, S., & Aghanim, N. 2022, A&A, 664, A198

  37. [37]

    2024, A&A, 687, A178

    Grandis, S., Ghirardini, V ., Bocquet, S., et al. 2024, A&A, 687, A178

  38. [38]

    A., et al

    Groth, F., Valentini, M., Seidel, B. A., et al. 2026, The Astrophysical Journal, 1000, 75

  39. [39]

    & Madau, P

    Haardt, F. & Madau, P. 2001, Modelling the UV/X-ray cosmic background with CUBA (eprint: arXiv:astro-ph/0106018)

  40. [40]

    2014, MNRAS, 442, 2304

    Hirschmann, M., Dolag, K., Saro, A., et al. 2014, MNRAS, 442, 2304

  41. [41]

    P., Suto, Y ., & Mo, H

    Jing, Y . P., Suto, Y ., & Mo, H. J. 2007, ApJ, 657, 664

  42. [42]

    1986, MNRAS, 222, 323

    Kaiser, N. 1986, MNRAS, 222, 323

  43. [43]

    2010, Classical and Quantum Gravity, 27, 124010

    Komatsu, E. 2010, Classical and Quantum Gravity, 27, 124010

  44. [44]

    V ., Vikhlinin, A., & Nagai, D

    Kravtsov, A. V ., Vikhlinin, A., & Nagai, D. 2006, ApJ, 650, 128

  45. [45]

    2025, Journal of Cosmology and Astroparticle Physics, 2025, 007

    Kruglov, A., Khabibullin, I., Lyskova, N., Dolag, K., & Biffi, V . 2025, Journal of Cosmology and Astroparticle Physics, 2025, 007

  46. [46]

    T., Nagai, D., Bogdán, A., et al

    Lau, E. T., Nagai, D., Bogdán, A., et al. 2025, ApJ, 984, 190

  47. [47]

    2024, The ApJ Letters, 977, L40

    Li, D., Fang, T., Ge, C., et al. 2024, The ApJ Letters, 977, L40

  48. [48]

    G., Sahlén, M., & Nadathur, S

    Manolopoulou, M., Hoyle, B., Mann, R. G., Sahlén, M., & Nadathur, S. 2021, MNRAS, 500, 1953

  49. [49]

    B., Allen, S

    Mantz, A. B., Allen, S. W., Morris, R. G., & Schmidt, R. W. 2016, MNRAS, 456, 4020

  50. [50]

    B., von der Linden, A., Allen, S

    Mantz, A. B., von der Linden, A., Allen, S. W., et al. 2015, MNRAS, 446, 2205

  51. [51]

    2024, A&A, 689, A7

    Marini, I., Popesso, P., Lamer, G., et al. 2024, A&A, 689, A7

  52. [52]

    Mo, H. J. & White, S. D. M. 1996, MNRAS, 282, 347

  53. [53]

    & McCammon, D

    Morrison, R. & McCammon, D. 1983, ApJ, 270, 119

  54. [54]

    M., Hallman, E

    Motl, P. M., Hallman, E. J., Burns, J. O., & Norman, M. L. 2005, ApJ, 623, L63 Article number, page 9 of 11 A&A proofs:manuscript no. aa60015-26

  55. [55]

    2010, ApJ, 721, 875–885

    Okabe, N., Zhang, Y .-Y ., Finoguenov, A., et al. 2010, ApJ, 721, 875–885

  56. [56]

    D., Babul, A., Bahé, Y ., Butsky, I

    Oppenheimer, B. D., Babul, A., Bahé, Y ., Butsky, I. S., & McCarthy, I. G. 2021, Universe, 7, 209

  57. [57]

    Pillepich, A., Porciani, C., & Reiprich, T. H. 2012, MNRAS, 422, 44

  58. [58]

    2025, A&A, 704, A278

    Popesso, P., Marini, I., Dolag, K., et al. 2025, A&A, 704, A278

  59. [59]

    W., Croston, J

    Pratt, G. W., Croston, J. H., Arnaud, M., & Böhringer, H. 2009, A&A, 498, 361

  60. [60]

    J., Bazin, G., & Dolag, K

    Saro, A., Mohr, J. J., Bazin, G., & Dolag, K. 2013, ApJ, 772, 47

  61. [61]

    S., Biffi, V ., et al

    Scheck, D., Sanders, J. S., Biffi, V ., et al. 2023, A&A, 670, A33

  62. [62]

    2024, A&A, 686, A196

    Seppi, R., Comparat, J., Ghirardini, V ., et al. 2024, A&A, 686, A196

  63. [63]

    2023, A&A, 671, A57

    Seppi, R., Comparat, J., Nandra, K., et al. 2023, A&A, 671, A57

  64. [64]

    2025, A&A, 699, A206

    Seppi, R., Eckert, D., Finoguenov, A., et al. 2025, A&A, 699, A206

  65. [65]

    Sheth, R. K. & Tormen, G. 1999, MNRAS, 308, 119

  66. [66]

    2025, A&A, 697, A22

    Shreeram, S., Comparat, J., Merloni, A., et al. 2025, A&A, 697, A22

  67. [67]

    2026, A&A, 707, A287

    Shreeram, S., Galárraga-Espinosa, D., Comparat, J., et al. 2026, A&A, 707, A287

  68. [68]

    K., Brickhouse, N

    Smith, R. K., Brickhouse, N. S., Liedahl, D. A., & Raymond, J. C. 2001, ApJ, 556, L91

  69. [69]

    2005, MNRAS, 364, 1105

    Springel, V . 2005, MNRAS, 364, 1105

  70. [70]

    & Hernquist, L

    Springel, V . & Hernquist, L. 2003, MNRAS, 339, 289

  71. [71]

    Springel, V ., White, S. D. M., Tormen, G., & Kauffmann, G. 2001, MNRAS, 328, 726

  72. [72]

    M., Donahue, M., et al

    Sun, M., V oit, G. M., Donahue, M., et al. 2009, ApJ, 693, 1142

  73. [73]

    L., Robertson, B

    Tinker, J. L., Robertson, B. E., Kravtsov, A. V ., et al. 2010, ApJ, 724, 878

  74. [74]

    2025, A&A, 700, A167

    Toptun, V ., Popesso, P., Marini, I., et al. 2025, A&A, 700, A167

  75. [75]

    2026, The stellar-to-halo mass relation of central galaxies across three orders of halo mass

    Toptun, V ., Popesso, P., Marini, I., et al. 2026, The stellar-to-halo mass relation of central galaxies across three orders of halo mass

  76. [76]

    2007, MNRAS, 382, 1050

    Tornatore, L., Borgani, S., Dolag, K., & Matteucci, F. 2007, MNRAS, 382, 1050

  77. [77]

    H., Pacaud, F., et al

    Veronica, A., Reiprich, T. H., Pacaud, F., et al. 2024, A&A, 681, A108

  78. [78]

    2022, A&A, 661, A46

    Veronica, A., Su, Y ., Biffi, V ., et al. 2022, A&A, 661, A46

  79. [79]

    V ., Burenin, R

    Vikhlinin, A., Kravtsov, A. V ., Burenin, R. A., et al. 2009, ApJ, 692, 1060

  80. [80]

    2023, A&A, 669, A34

    Vladutescu-Zopp, S., Biffi, V ., & Dolag, K. 2023, A&A, 669, A34

Showing first 80 references.