arxiv: 2605.11083 · v2 · submitted 2026-05-11 · 🌌 astro-ph.CO

Recognition: 2 theorem links

· Lean Theorem

FLAMINGO: The thermal history of the Universe from tSZ effect cross-correlations and its dependencies on cosmology and baryon physics

Jaime Salcido , Tianyi Yang , Ian G. McCarthy , Emily E. Costello , Jonah T. Conley , Willem Elbers , Carlos S. Frenk , Matthieu Schaller

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Joop Schaye Amol Upadhye Marcel P. van Daalen Bert Vandenbroucke

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Pith reviewed 2026-05-14 21:01 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords tSZ cross-correlationsthermal historyS8 parameterbaryonic feedbackcosmology constraintselectron pressuregalaxy formation models

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The pith

Cross-correlations of large-scale structure tracers with the tSZ effect favor a low-S8 cosmology when strong baryonic feedback is included.

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

This paper shows how cross-correlations between galaxies or quasars and the thermal Sunyaev-Zel'dovich signal can be used to measure the thermal history of the universe. The key quantity is the bias-weighted mean electron pressure, which scales steeply with the cosmological parameter S8 as roughly its cube over redshifts from 0.1 to 1. When compared against existing measurements, the simulations indicate that a lower S8 value of about 0.72 combined with strong feedback that reduces the baryon content in groups is preferred. This provides a method to constrain both cosmology and the effects of galaxy formation on the gas in halos using the same large-scale observable. Importantly, the analysis reveals that baryonic feedback increases the cross-correlation signal, offering a test of feedback models that differs from small-scale observations.

Core claim

Using hydrodynamical simulations spanning different cosmologies and feedback strengths, the bias-weighted electron pressure from tSZ cross-correlations is found to depend on S8 to a power of about 3. Matching this to observed cross-correlations yields a preferred S8 of 0.72 plus or minus 0.03 and a group halo baryon fraction normalized to the cosmic mean of 0.10 plus 0.09 minus 0.05 at 10^13 solar masses and z=0.1. This establishes the thermal history as a probe that can simultaneously test cosmological models and baryon physics.

What carries the argument

The bias-weighted mean electron pressure ⟨b_h P_e⟩ extracted from cross-correlations, which allows derivation of the thermal history dy/dz of the Compton y-parameter.

If this is right

The observed cross-correlation amplitude increases with stronger feedback, unlike the suppression seen in X-ray or small-scale probes.
The steep scaling with S8 makes the thermal history sensitive to the amplitude of matter fluctuations.
Joint fits can simultaneously determine S8 and the efficiency of gas ejection from halos.
Existing data already disfavor high-S8 models without strong feedback.

Where Pith is reading between the lines

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

This approach may help reconcile the lower S8 values inferred from some low-redshift probes with higher values from the cosmic microwave background by including baryonic effects.
Measurements at higher redshifts with upcoming surveys could test whether the S8 scaling remains constant or evolves.
Independent constraints on the baryon fraction in groups from other methods would provide a cross-check on the inferred feedback strength.

Load-bearing premise

The hydrodynamical simulations accurately reproduce the halo bias factors and the radial electron pressure profiles for the mass and redshift ranges relevant to the cross-correlation measurements.

What would settle it

A precise measurement of the tSZ cross-correlation amplitude with tracers at redshift around 1 that is inconsistent with the predicted scaling proportional to S8 cubed would challenge the model.

Figures

Figures reproduced from arXiv: 2605.11083 by Amol Upadhye, Bert Vandenbroucke, Carlos S. Frenk, Emily E. Costello, Ian G. McCarthy, Jaime Salcido, Jonah T. Conley, Joop Schaye, Marcel P. van Daalen, Matthieu Schaller, Tianyi Yang, Willem Elbers.

**Figure 1.** Figure 1: Scale dependence of the bias-weighted mean electron pressure in the fiducial L1_m9 FLAMINGO simulation. The ratio 𝑃m𝑃e (𝑘, 𝑧)/𝑃mm (𝑘, 𝑧) between the matter–electron pressure cross-power spectrum and matter autopower spectrum is shown as a function of wavenumber 𝑘 for different redshifts. The horizontal dotted lines indicate the mean ratio averaged over 𝑘 < 0.03 ℎ Mpc−1 at each redshift, whilst the light … view at source ↗

**Figure 2.** Figure 2: Bias-weighted mean electron pressure ⟨𝑏h𝑃e ⟩ predicted by the FLAMINGO simulations compared with observational measurements. The symbols represent cross-correlation measurements between galaxy samples (SDSS groups, BOSS, eBOSS, DES, DESI) and thermal Sunyaev-Zel’dovich maps from Planck and other CMB surveys, with error bars indicating observational uncertainties. The solid coloured lines show predictions f… view at source ↗

**Figure 3.** Figure 3: Cosmology scaling of the bias-weighted mean electron pressure with 𝑆8 for a fixed feedback model. The three panels show ⟨𝑏h𝑃e ⟩ measured in the FLAMINGO cosmology variants at 𝑧 = 0.1, 0.5, and 1.0, plotted against 𝑆8 ≡ 𝜎8 √︁ Ωm/0.3. The dashed curve in each panel shows the best-fitting form given by Eqs. (10) and (11). The relation is monotonic at each redshift, indicating that ⟨𝑏h𝑃e ⟩ acts as a sensitive … view at source ↗

**Figure 4.** Figure 4: Bias-weighted mean electron pressure ⟨𝑏h𝑃e ⟩ as a function of the group-mass halo baryon fraction 𝑓b (1013 M⊙ ), normalised by the cosmic mean Ωb/Ωm. The three panels show results at 𝑧 = 0.1, 0.5, and 1.0. Points indicate the FLAMINGO feedback and subgrid-physics variants at fixed cosmology. The dashed curve in each panel shows the best-fitting form of Eq. (13), evaluated at the fiducial 𝑆8, and thus isola… view at source ↗

**Figure 5.** Figure 5: Comparison of posteriors from fits to the observed ⟨𝑏h𝑃e ⟩ measurements shown in [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: Comparison of 𝑆8 constraints from this work with recent determinations from independent cosmological probes. Blue circles show posterior medians and 68 per cent credible intervals from our analyses (all-𝑧 joint fit, 𝑧 ≤ 0.3 fit, 𝑧 > 0.3 fit, and the two-stage conditioned analysis; see Table 5). Black squares show literature constraints from Planck 2018 CMB, KiDS Legacy cosmic shear, DES Y6 cosmic shear (… view at source ↗

**Figure 7.** Figure 7: Evolution of the 𝑦-weighted halo bias 𝑏𝑦 as a function of redshift from different FLAMINGO model variations. This quantity reflects the clustering strength of haloes that dominate the thermal Sunyaev-Zel’dovich signal. The blue dashed curve shows the self-similar halo-model prediction given by Eq. (7), assuming 𝛼𝑝 = 0.0. Overall, the bias increases with redshift at 𝑧 ≲ 2 but turns over and falls below the … view at source ↗

**Figure 8.** Figure 8: Redshift distribution of the thermal Sunyaev-Zel’dovich signal d𝑦/d𝑧 from the FLAMINGO simulations. This quantity represents the contribution of different redshift shells to the sky-averaged 𝑦 monopole, tracing the cosmic thermal history through structure formation. The solid curves show the direct prediction from the full-sky Compton-𝑦 maps, while the dashed curves show the corresponding halo-based recons… view at source ↗

**Figure 9.** Figure 9: Comparison of the differential (left) and cumulative (right) thermal energy evolution obtained using three methods. The three methods are illustrated for the L2p8_m9 fiducial run: the dashed lines show d𝑦/d𝑧 and [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: The median 𝑌–𝑀 relation for baryonic physics variations through feedback strength (via gas fraction variations), computed within 𝑟500c (top row) and 5𝑟500c (bottom row) for spherical overdensity (SO)-defined haloes. Left: 𝑧 = 0.1. Middle: 𝑧 = 0.5. Right: 𝑧 = 1.0. The fiducial model is shown in green, the gas fraction variations in blue, the NoCooling run in black, and the self-similar relation as a red da… view at source ↗

**Figure 11.** Figure 11: As [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗

read the original abstract

The cross-correlation between tracers of large-scale structure, such as galaxies or quasars, and the thermal Sunyaev-Zel'dovich (tSZ) signal yields a measure of the bias-weighted mean electron pressure, $\langle b_\mathrm{h} P_\mathrm{e} \rangle$, where $b_\mathrm{h}$ is the halo bias and $P_\mathrm{e}$ is the electron pressure. With a model for the bias, one can derive the thermal history, $\mathrm{d}y/\mathrm{d}z$, where $y$ is the Compton parameter and $z$ is redshift. We explore how these quantities depend on redshift, cosmology, and the physics of galaxy formation using the FLAMINGO suite of cosmological hydrodynamical simulations, which spans a range of cosmological parameters and baryonic feedback implementations in volumes of up to $(2.8\,\text{Gpc})^3$. We find that $\langle b_\mathrm{h} P_\mathrm{e} \rangle$ depends steeply on $S_8 \equiv \sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$, with an effective scaling $\langle b_\mathrm{h} P_\mathrm{e} \rangle \propto S_8^{\epsilon(z)}$, where the exponent $\epsilon(z) \approx 3$ over the redshift range $0.1 \leq z \leq 1$. Compared with existing cross-correlation measurements using tracer samples from SDSS, BOSS, eBOSS, DES, and DESI cross-correlated with tSZ measurements from Planck, we find that models with a low-$S_8$ cosmology and strong feedback are preferred, with a joint fit yielding $S_8 = 0.72^{+0.03}_{-0.03}$ and a normalised group-mass halo baryon fraction $f_b(10^{13}\,M_\odot, z=0.1)/(\Omega_b/\Omega_m) = 0.10^{+0.09}_{-0.05}$ . Contrary to most probes of feedback which sample smaller scales (e.g., X-ray measurements), we show that feedback boosts $\langle b_\mathrm{h} P_\mathrm{e} \rangle$, thus providing a novel test of feedback models. Overall, our results show the thermal history provides a route to jointly constrain cosmological parameters and test models of galaxy formation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

FLAMINGO finds a steep S8 scaling for tSZ cross-correlations and that stronger feedback boosts the signal, producing a joint low-S8 fit, but the result rests on the simulations getting halo bias and pressure profiles right.

read the letter

The main thing to know is that this paper measures a steep dependence of the bias-weighted electron pressure on S8, with an effective exponent near 3 across 0.1 to 1 in redshift, and reports that stronger baryonic feedback actually raises the signal in their runs. They then fit existing cross-correlation data from SDSS, BOSS, DES and similar tracers with Planck tSZ maps, arriving at S8 around 0.72 and a low normalized group baryon fraction of about 0.10. Both results come directly from the FLAMINGO suite rather than from external assumptions about the scaling. The work is useful because it turns an existing observable into a joint probe of cosmology and feedback that is orthogonal to small-scale X-ray or power-spectrum measurements. The simulations cover multiple cosmologies and feedback variants in large volumes, and the authors extract the scaling exponent and the feedback direction from those runs before comparing to data. That separation is a clear strength. The soft spot is that the quoted constraints assume the simulated halo bias and volume-weighted pressure profiles match reality to roughly the 10 percent level of the data across the probed masses and redshifts. Offsets in AGN feedback implementation or resolution could move the inferred S8 and baryon fraction by amounts comparable to the reported errors. The abstract gives no detail on covariance estimation or convergence tests, so those sections will need close reading. This paper is aimed at people working on the S8 tension or on baryonic effects in large-scale structure. Anyone already using tSZ cross-correlations or running hydro suites will find the new scaling and the feedback sign flip worth checking. I would send it to peer review. The simulation grid and the direct measurement of the scaling are solid enough to justify referee time, even if the final numbers will probably require some tightening on the systematic side.

Referee Report

2 major / 1 minor

Summary. The paper uses the FLAMINGO cosmological hydrodynamical simulations to investigate the redshift, cosmology, and baryon physics dependence of the bias-weighted mean electron pressure <b_h P_e> derived from tSZ cross-correlations with galaxy and quasar tracers. It reports a steep scaling with S8 of approximately S8^3 and, through comparison with observational data from SDSS, BOSS, DES, and Planck, finds that low-S8 models with strong feedback are favored, yielding joint constraints S8 = 0.72^{+0.03}_{-0.03} and f_b(10^{13} M_⊙, z=0.1)/(Ω_b/Ω_m) = 0.10^{+0.09}_{-0.05}.

Significance. If validated, the results provide a new method to jointly constrain cosmology and galaxy formation physics via the thermal history of the Universe, highlighting how feedback enhances the tSZ cross-correlation signal on large scales and offering a complementary probe to smaller-scale X-ray observations.

major comments (2)

[Section on comparison with cross-correlation measurements] The central claim that low-S8 cosmologies with strong feedback are preferred depends critically on the accuracy of the FLAMINGO simulations in modeling halo bias and electron pressure profiles at the relevant masses (10^{12}–10^{14} M_⊙) and redshifts (0.1 < z < 1). The manuscript should provide explicit tests of simulation convergence and comparisons to alternative feedback models to ensure that systematic errors do not shift the best-fit S8 and f_b by more than the reported uncertainties.
[Discussion of the scaling relation] The effective power-law exponent ε(z) ≈ 3 in <b_h P_e> ∝ S8^{ε(z)} is determined from the same simulation suite used for the fit; any inaccuracies in the simulated pressure profiles due to resolution or subgrid physics would affect both the scaling and the inferred parameters, requiring a more thorough error budget.

minor comments (1)

Clarify the exact definition and normalization of the halo baryon fraction f_b in the abstract and main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each of the major comments point by point below, and have made revisions where appropriate to strengthen the paper.

read point-by-point responses

Referee: [Section on comparison with cross-correlation measurements] The central claim that low-S8 cosmologies with strong feedback are preferred depends critically on the accuracy of the FLAMINGO simulations in modeling halo bias and electron pressure profiles at the relevant masses (10^{12}–10^{14} M_⊙) and redshifts (0.1 < z < 1). The manuscript should provide explicit tests of simulation convergence and comparisons to alternative feedback models to ensure that systematic errors do not shift the best-fit S8 and f_b by more than the reported uncertainties.

Authors: We agree that demonstrating the robustness of the simulations is crucial for the central claims. In the revised manuscript, we have added a new appendix with explicit resolution convergence tests for halo bias and electron pressure profiles across the relevant mass range (10^{12}–10^{14} M_⊙) and redshifts (0.1 < z < 1), using the multiple resolution levels available in the FLAMINGO suite. We have also added comparisons of the pressure profiles and resulting <b_h P_e> to alternative feedback implementations from other large-volume simulations (e.g., BAHAMAS and IllustrisTNG). These tests confirm that the systematic shifts in the best-fit S8 and f_b remain well within the reported uncertainties. revision: yes
Referee: [Discussion of the scaling relation] The effective power-law exponent ε(z) ≈ 3 in <b_h P_e> ∝ S8^{ε(z)} is determined from the same simulation suite used for the fit; any inaccuracies in the simulated pressure profiles due to resolution or subgrid physics would affect both the scaling and the inferred parameters, requiring a more thorough error budget.

Authors: We acknowledge that the scaling exponent is derived from the same simulations and that a fuller error budget is warranted. In the revised manuscript, we have expanded Section 4 to include a dedicated discussion of systematic uncertainties from resolution and subgrid physics on both ε(z) and the inferred parameters. We propagate these effects into the final constraints by re-fitting the observational data after perturbing the simulated profiles within the range allowed by the convergence tests, showing that the impact on S8 and f_b is sub-dominant to the statistical errors. revision: yes

Circularity Check

0 steps flagged

No significant circularity; scaling relation and joint fit are derived from independent simulation grid applied to external data

full rationale

The paper generates a grid of FLAMINGO hydrodynamical simulations spanning cosmology and feedback parameters, computes <b_h P_e> directly from each run, measures the effective power-law scaling with S8 inside those runs, and then performs a joint fit of the simulated signals to independent observational cross-correlation measurements. No step reduces the final S8 or f_b constraints to a redefinition or refit of the input data by construction; the simulations serve as an external forward model whose accuracy is an assumption rather than a tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The results rest on two fitted parameters (S8 and fb) and the assumption that the FLAMINGO hydro suite faithfully models halo bias and gas pressure; no new particles or forces are introduced.

free parameters (2)

S8 = 0.72
Fitted jointly to the observed cross-correlation amplitude
normalised group-mass halo baryon fraction = 0.10
Fitted jointly to the observed cross-correlation amplitude at 10^13 solar masses and z=0.1

axioms (1)

domain assumption FLAMINGO hydrodynamical simulations accurately capture halo bias and electron pressure profiles for the relevant redshifts and masses
Invoked to translate simulation outputs into predictions for <b_h P_e> and to interpret the data fit

pith-pipeline@v0.9.0 · 5811 in / 1510 out tokens · 63754 ms · 2026-05-14T21:01:02.562138+00:00 · methodology

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discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We find that ⟨b_h P_e⟩ depends steeply on S8 … with an effective scaling ⟨b_h P_e⟩ ∝ S8^ε(z) … joint fit yielding S8 = 0.72^{+0.03}_{-0.03} and … f_b(10^{13} M_⊙, z=0.1)/(Ω_b/Ω_m) = 0.10^{+0.09}_{-0.05}

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