Differences in baryonic and dark matter scaling relations of galaxy clusters: A comparison between IllustrisTNG simulations and observations

Daniel Miller; Diego Pallero; Mat\'ias Bla\~na; Patricia B. Tissera

REVIEW 4 major objections 4 minor 112 references

Differences in baryonic and dark matter scaling relations of galaxy clusters: A comparison between IllustrisTNG simulations and observations

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

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Pith's one-line read The baryon fraction scaling slopes of simulated clusters match the observed SPT-SZ/Chandra slopes within 1-2 sigma, and the missing baryons are predominantly warm gas and intracluster light.

desk verdict The headline 1–2σ slope agreement is a mass-range artifact — over the mass range C18 actually observed, the paper's own BPL fits give a slope near 0.06 versus C18's 0.35 — but the baryonic component budget is a genuinely useful new result. read the letter →

arxiv 2504.20159 v2 pith:T46QXGAH submitted 2025-04-28 astro-ph.CO

Daniel Miller , Diego Pallero , Patricia B. Tissera , Matías Blaña This is my paper · ORCID

classification astro-ph.CO

keywords galaxyclustersbaryonfractionscalingrelationsmissingbaryonsintraclusterlightwarm-hotintergalacticmediumIllustrisTNGself-similarity

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 that the IllustrisTNG cosmological simulations reproduce the observed scaling of cluster baryon fraction with mass, so the well-known missing baryon deficit can be attributed to specific undetected components. The authors compare 218 TNG100 and 1605 TNG300 haloes against 91 SPT-SZ/Chandra clusters from Chiu et al. (2018) using simple, broken, and general double power-law fits. They find baryon fraction slopes agree within 1-2 $\sigma$, identify a self-similarity break at $\log_{10}(M_{500c}/M_\odot)\sim 14$, and quantify that about 13.8-14.1 per cent of baryons are missing in the observational measurement. The missing budget is mostly warm gas at $10^5$-$10^7$ K in low-mass haloes and intracluster light at all masses, which would resolve the tension between cluster baryon fractions and the hierarchical formation picture.

What carries the argument

The load-bearing object is the baryon mass fraction $f_{\rm bar,500c}=M_{\rm bar,500c}/M_{500c}$ measured in two ways: an observational proxy (hot gas with $T\ge10^7$ K within $R_{500c}$ plus galaxy stellar mass within $2\times R_{M_\star/2}$, excluding warm gas, cold gas, and intracluster light) and a full baryon budget (all gas and all stars within $R_{500c}$). The argument runs through fits of the self-similar scaling relation $f_{\rm bar}\propto M^{\alpha}$ using a simple power law, a broken power law, and a general double power law with a smoothness parameter $\delta$; the breakpoint $M_{\rm pivot}$ identifies the mass where self-similarity is lost. The mechanism that explains the break is AGN feedback pushing baryons into the cluster outskirts, and the friends-of-friends mass definition is used to test whether the universal baryon fraction is recovered when all gravitationally bound material is counted.

What would settle it

Measure the warm gas ($10^5\lesssim T\lesssim10^7$ K) mass in low-mass clusters ($\log_{10}(M_{500c}/M_\odot)\lesssim14$) using O VII absorption stacking or thermal Sunyaev-Zel'dovich observations and compare with the roughly 10 per cent baryonic fraction predicted here; a detection below about 5 per cent would rule out warm gas as the dominant missing component and contradict the paper's missing-baryon budget.

Watch

Extended reading notes

Core claim

The central discovery is that the observed baryon fraction scaling is reproduced by IllustrisTNG once the same measurement cuts are applied: hot gas with $T\geq 10^7$ K inside $R_{500c}$ plus galaxy stellar mass within an aperture of $2\times R_{M_\star/2}$. With this proxy, TNG100 and TNG300 give SPL slopes $\alpha_{\rm SPL}=0.248\pm0.018$ and $0.261\pm0.006$, respectively, consistent at 1-2 $\sigma$ with the slope $\alpha_{\rm Chiu}=0.350\pm0.076$ reported by Chiu et al. (2018) for the SPT-SZ sample. The baryon fraction is consistent with zero redshift evolution (slopes $\sim0.00$-$0.07$), and the missing baryons, defined as cold gas, warm gas, and intracluster light excluded by the observational proxy, amount to approximately 13.8-14.1 per cent of the baryon budget, with warm gas dominating in low-mass haloes (~10.5 per cent) and ICL contributing roughly 5 per cent at all masses. Fitting a broken or general double power law places the self-similarity break at $\log_{10}(M_{\rm pivot}/M_\odot)\sim13.80$-$14.07$, the mass below which AGN feedback redistributes baryons to the outskirts; when halo mass is instead defined by the friends-of-friends algorithm, the slope flattens toward zero, consistent with hierarchical assembly.

Load-bearing premise

The simulated proxy for the observed baryon fraction (hot gas above $10^7$ K within $R_{500c}$ plus galaxy stars in a $2R_{M_\star/2}$ aperture) is taken to be directly comparable to the Chandra/SED measurement, so any systematic mismatch in how stars are assigned to galaxies or gas to the hot phase would shift the fitted slopes and the inferred missing budget.

Editorial extensions

If this is right

If the slope agreement holds, the IllustrisTNG feedback model can be used to predict the baryon budget of clusters and the exact components an observational survey is missing.
The missing-baryon deficit in observed low-mass clusters should be recoverable as warm gas ($10^5$-$10^7$ K) and diffuse intracluster light rather than cold gas.
The breakpoint at $M_{500c}\sim10^{14}M_\odot$ marks a physically distinct regime: above it clusters are self-similar, below it AGN feedback redistributes baryons beyond $R_{500c}$.
With friends-of-friends masses the baryon fraction slope approaches zero, so high-mass clusters can form from low-mass ones and the apparent contradiction with hierarchical growth is resolved.
The SZ and X-ray mass biases estimated from mock observations imply real observed baryon fractions could be lower by 14-20 per cent than currently estimated, strengthening the need for the missing warm component.

Reading between the lines

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

An extension would be to stack thermal Sunyaev-Zel'dovich or soft X-ray data on low-mass clusters to measure the warm gas component; if the warm gas mass is below roughly 5 per cent of baryons in that mass range, the identification of warm gas as the dominant missing reservoir would be falsified.
The ICL fraction of about 5 per cent could be tested with deep surface-photometry surveys that separate intracluster light from galaxy light; the paper's proxy choice alone shifts the inferred missing fraction by about 5 per cent, so the definition of a galaxy in future surveys may matter as much as the sensitivity.
If baryons are truly redistributed to 1.5-2.5 $R_{200c}$ in low-mass haloes, then cluster outskirts become the natural place to search for missing baryons, and cluster mass calibration via SZ or X-ray may require a radius-dependent correction.
The authors' result that about 21 per cent of baryons are missing even when all bound material is counted suggests the issue is not just where the baryons are, but how efficiently haloes accrete gas versus dark matter; comparing with particle-based gas simulations could settle whether the deficit is physical or numerical.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know before you read this one. First, the headline claim — that IllustrisTNG baryon fraction slopes agree with Chiu et al. (2018) within 1–2σ — is a mass-range artifact. Second, the baryon component budget underneath it is real and useful, and worth keeping after the headline gets fixed.

The SPL slopes in Section 4.1 are fitted over M200c ≥ 7×10^13 Msun, reaching down to log M500c ≈ 13.5, while C18's sample spans log M500c = 14.42–15.10. The paper's own Table 5 gives BPL high-mass slopes of 0.06 and 0.05, with pivots at 13.80 and 14.07 — both below the C18 range, and the GDPL transition is sharp (δ = 0.25). Across the mass range C18 actually observed, TNG therefore predicts a near-flat baryon fraction, ~0.06, against C18's 0.35 ± 0.076. That is a 3–4σ discrepancy. The apparent agreement comes from the many low-mass haloes dominating the TNG SPL fit. The reader's report was too generous on this point: the paper's own fits refute its abstract, so the issue is more than conditional.

What is genuinely good: the decomposition into cold, warm, and hot gas, galaxy stars (both rop and Subfind apertures), and ICL is the most complete I have seen for this comparison. The missing-baryon budget — mostly warm gas plus ICL, larger in low-mass haloes — is a concrete statement people will want to quote, and the breakpoint at log M ~ 14 lines up with Pop et al. (2022a) and Ayromlou et al. (2023). The fits are straightforward, the engagement with the literature is honest, and the analysis is reproducible: TNG is public and the C18 numbers are in their tables.

The soft spots beyond the mass-range issue: Section 5.1 computes that SZ/X-ray mass biases would overestimate observed baryon fractions by 14–20 per cent, then drops it without propagating into the main comparison — a significant unquantified systematic, not a footnote. There are also sloppy internal inconsistencies: TNG300 is 1605 haloes in the abstract and Section 2.1, 1604 in the summary; the summary swaps the low-mass missing-baryon percentages relative to Table 3; a couple of redshift slopes differ between text and figure labels. All fixable, but they undermine confidence in the written record. And the abstract's WHIM framing overstates what was measured: the warm gas sits inside R500c, which the text itself later correctly calls WCGM.

Who is this for? Anyone working on cluster scaling relations or the missing baryon problem. The component budget is worth keeping; the slope comparison needs to be redone honestly, fit over the C18 mass range and with the bias correction folded in. I would send it to a serious referee — the material is real and the fixes are achievable — but the mass-range issue should come back as major.

Referee Report

4 major / 4 minor

Summary. The paper compares baryonic-mass-fraction scaling relations of galaxy clusters in the IllustrisTNG simulations (TNG100 and TNG300) with the SPT-SZ/Chandra sample of Chiu et al. (2018, C18). It fits simple power law (SPL), broken power law (BPL), and general double power law (GDPL) models to fbar,500c versus M500c and versus redshift, using two measurement proxies: hot gas (T≥10^7 K) plus galaxy stellar mass within a 2× half-mass-radius aperture, and all gas plus all stars within R500c. The paper reports approximately null redshift slopes, a 1–2σ agreement of SPL slopes with C18, a breakpoint at log10(M500c/Msun)≈14 where self-similarity is lost, and a 'missing' baryon fraction of about 13.8–14.1% dominated by warm gas and intracluster light. It also examines FoF-based scaling relations and the role of mass accretion in the baryon deficit.

Significance. If the claimed slope agreement were robust, it would strengthen confidence in IllustrisTNG's feedback model as a tool for interpreting cluster baryon fractions and the missing-baryon problem. The paper provides a useful component-by-component decomposition of baryons in simulated clusters and a clear measurement of the BPL/GDPL breakpoint, which are of interest to the cluster scaling-relation community. However, the central comparison to C18 is compromised by a mass-range mismatch: the simulation SPL is fitted over a much wider range that includes many low-mass haloes, while C18's slope is measured in a narrow high-mass range. The paper itself reports high-mass BPL slopes of 0.05–0.06, which differ from C18's 0.35 by several sigma. In addition, the paper identifies but does not propagate a 14–20% mass-bias systematic. These issues must be resolved before the main claim can be accepted.

major comments (4)

[Sec. 4.1, Fig. 3, and Table 5]
[Sec. 5.1]
[Abstract and Sec. 4.2, Table 3]
[Sec. 4.1, Fig. 2, and Abstract]

minor comments (4)

[Abstract, Sec. 2.1, and Sec. 6]
[Sec. 6, summary bullet]
[Sec. 4.1 and Fig. 2]
[Sec. 4.4 and Table 5]

Circularity Check

1 steps flagged · score 6.0 of 10

The 'missing baryons are mostly warm gas and ICL' conclusion is a bookkeeping identity: the paper sums exactly the components it excludes from the C18-like baryon fraction and then reports that sum as the missing baryons.

self definitional [Section 4.2 and Table 3 (also Abstract)]
"Furthermore, Table 3 shows the average baryonic mass values for components not considered in the C18 observations: cold gas, warm gas, and ICL (rop). We defined the sum of those components as the missing baryons in simulations."

The headline finding—'We identify ∼13.8−14.1 per cent of baryons as missing, primarily in the form of ICL across all halo masses and warm gas in low-mass haloes'—is obtained by adding exactly the components that the paper's observational proxy (hot gas with T ≥ 10^7 K plus rop-aperture galaxy stars) excludes. The 'missing baryon' budget is therefore not inferred from an independent closure relation or from the C18 comparison; it is the complement of the chosen measurement definition restated as a discovery. The only simulation output entering the number is the relative mass of those excluded components, not an independent determination that they are the missing baryons.

full rationale

The central slope comparison is not circular: the TNG slopes (αSPL = 0.248 ± 0.018 for TNG100, 0.261 ± 0.006 for TNG300) are genuine fits to simulation data, and C18's αChiu = 0.350 ± 0.076 is an external observational benchmark. The self-similarity redshift test is likewise an internally consistent fit, not a circular reduction. The paper's P22 and A23 citations are not authored by the present authors, and the BPL/GDPL breakpoint is fitted rather than imported, so no self-citation chain forces the main result. However, the 'missing baryons' claim is self-definitional: the paper explicitly defines missing baryons as the sum of cold gas, warm gas, and ICL(rop), the same components omitted from the C18-like measurement, and then presents that sum as the answer to the missing-baryon problem. That step reduces by construction. The separate concern raised by the paper's own Table 5 that its BPL/GDPL high-mass slopes are ~0.05–0.06 above pivots below the C18 mass range is a mass-range comparison artifact and a correctness risk, not an additional circularity. Similarly, Section 5.1's unpropagated 14–20% mass-bias systematic affects the robustness of the slope comparison but does not make it circular.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities or physics. Its central claims rest on the fitting of the scaling relation parameters (slopes and pivot), which are measured quantities communicated as free parameters above, plus the standard assumptions of hydrostatic equilibrium, the Kaiser self-similar model, and the fidelity of the IllustrisTNG subgrid model. The most fragile assumption is the proxy mapping between simulated components and the C18 observational measurement.

free parameters (6)

SPL mass slope (hot gas + rop stars) = TNG100 0.248, TNG300 0.261
Fitted to the R500c baryon fraction vs M500c relation (Section 4.1, Fig. 3, Eq. 7). This slope is the main comparison statistic against C18.
SPL mass slope (all gas + all stars) = TNG100 0.071, TNG300 0.120
Fitted to the full-baryon R500c relation (Section 4.1, Fig. 3).
SPL redshift slope = 0.006 to 0.071 across cases
Fitted to fbar vs (1+z) to test redshift self-similarity (Section 4.1, Fig. 2).
BPL slopes alpha_1 and alpha_2 = TNG100 0.79 and 0.06; TNG300 0.35 and 0.05 (hot-gas+rop case)
Fitted to binned median baryon fractions (Section 4.4, Table 5).
GDPL slopes alpha_1, alpha_2 and delta = alpha identical to BPL; delta 0.25
Fitted GDPL smoothness and slopes (Table 5).
Mpivot breakpoint = log10(Mpivot/Msun) = 13.80 to 14.07
Fitted pivot mass in BPL/GDPL models; central evidence for the log M ~ 14 self-similarity break (Table 5).

assumptions (5)

domain assumption Hot gas in clusters is in hydrostatic equilibrium (Eqs. 1-2).
Basis of the self-similar scaling framework; standard in cluster studies.
domain assumption The self-similar model (Kaiser 1986) predicts fbar proportional to M^0 with no redshift dependence (Eq. 6).
Used as the null expectation against which slopes are judged.
domain assumption IllustrisTNG's subgrid feedback model (stellar and AGN) is a faithful representation of baryon redistribution in real clusters.
The whole comparison treats TNG baryon fractions as the simulated truth against which observations are checked.
domain assumption The simulated 'hot gas + rop stars' measurement is a valid proxy for the C18 observational measurement (Chandra beta-model gas and SED stellar masses).
This mapping is the load-bearing equivalence for the slope comparison (Section 4.1).
domain assumption Gas temperature thresholds (cold T < 1e5 K, warm 1e5 to 1e7 K, hot >= 1e7 K) cleanly separate observable and unobservable gas phases.
The missing baryon budget depends on these divisions (Section 2.1).

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Cite this review

Pith. "Pith review of Differences in baryonic and dark matter scaling relations of galaxy clusters: A comparison between IllustrisTNG simulations and observations." pith.science (2026). https://pith.science/paper/T46QXGAH

@misc{pith2026250420159,
  author       = {Pith},
  title        = {Pith review of: Differences in baryonic and dark matter scaling relations of galaxy clusters: A comparison between IllustrisTNG simulations and observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T46QXGAH}},
  note         = {Machine review of arXiv:2504.20159}
}

abstract

We compare the self-similar baryonic mass fraction scaling relations between galaxy clusters from the South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) survey and the IllustrisTNG state-of-the-art magnetohydrodynamical cosmological simulations. Using samples of 218 (TNG100) and 1605 (TNG300) friends-of-friends (FoF) haloes within $0.0 \leq z \leq 1.5$ and $M_{200c} \geq 7 \times 10^{13} M_{\odot}$, we fit the scaling relations using Simple Power Law (SPL), Broken Power Law (BPL), and General Double Power Law (GDPL) models through non-linear least squares regression. The SPL model reveals null slopes for the baryonic fraction as a function of redshift, consistent with self-similarity. Observations and simulations agree within $1{-}2\sigma$, suggesting comparable baryonic scaling slopes. We identify $\sim$13.8$-$14.1 per cent of baryons as "missing", primarily in the form of intracluster light (ICL) across all halo masses and warm gas in low-mass haloes. High-mass haloes ($\log_{10}(M_{500c}/M_{\odot}) \geq 14$) adhere to self-similarity, while low-mass haloes exhibit deviations, with the breakpoint occurring at $\log_{10}(M_{500c}/M_{\odot}) \sim 14$, where baryons are redistributed to the outskirts. Our findings suggest that the undetected warm-hot intergalactic medium (WHIM) and baryon redistribution by feedback mechanisms are complementary solutions to the "missing baryon" problem.

Figures

Figures reproduced from arXiv: 2504.20159 by the authors.

**Figure 1.** Distribution of the percentage difference between the stellar masses from Subfind and 2 × RMstar/2 ∼ rop apertures under different constrains. The black, red, and blue lines correspond to measurements within halocentric radius R500c, R200c, and the mass considered by the FoF algorithm, respectively. The dashed lines represent the normal distribution fitted to each constraint and are shown in their corresponding col… view at source ↗

**Figure 2.** SPL fit of baryon mass fraction fbar in IllustrisTNG at R500c and redshift z. Black dots show individual haloes; the green region indicates the SPL fit. Each panel is labelled with their corresponding simulation tag and the value for the αSPL slope from the SPL fit in the upper-left corner. Top panels: The fraction of baryons includes the hot gas and the galaxy stellar mass within the 2 × RMstar/2 ∼ rop aperture. Bo… view at source ↗

**Figure 3.** SPL fit of baryon mass fraction fbar in IllustrisTNG at R500c for all redshifts. Black dots show individual haloes; the green region indicates the SPL fit. Each panel is labelled with their corresponding simulation tag and the value for the αSPL slope from the SPL fit in the upper-left corner. Top panels: The fraction of baryons includes the hot gas and the galaxy stellar mass within the 2 × RMstar/2 ∼ rop aperture.… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: SPL fit (green region) of the IllustrisTNG haloes (black dots), to the scaling relation of the mass fraction of baryons fbar and halo mass M measured by the FoF algorithm, for all redshifts. Each panel is labelled with the corresponding simulation tag and the value of …

**Figure 5.** Figure 5: SPL fit (green region), BPL fit (magenta region) and GDPL fit (red region) of the IllustrisTNG haloes (median of the data in black solid line), to the scaling relation of the mass fraction of baryons fbar and halo mass M in a radius R500c. Each panel is labelled with t…

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

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