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The Power Spectrum of the Thermal Sunyaev-Zeldovich Effect

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The thermal Sunyaev-Zeldovich power spectrum reconstructed from Planck, ACT and SPT temperature data is much lower and shallower at ℓ ≳ 2000 than the baseline FLAMINGO ΛCDM prediction, and the authors argue that the cause is…

desk verdict A genuine new measurement of the tSZ power spectrum from CMB temperature spectra, with a robust exclusion of the FLAMINGO baseline at high ell; the main caveat is the fixed CMB model subtraction, but the discrepancy is large. read the letter →

arxiv 2502.10232 v2 pith:Y6TG33HK submitted 2025-02-14 astro-ph.CO

George Efstathiou , Fiona McCarthy This is my paper · ORCID
classification astro-ph.CO
keywords thermalSunyaev-ZeldovicheffecttSZpowerspectrumcosmicmicrowavebackgroundbaryonicfeedbackFLAMINGOsimulationsS8tensiongalaxyclustersforegroundsubtraction
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 establish that the thermal Sunyaev-Zeldovich (tSZ) effect — the distortion of CMB photons by hot gas in galaxy clusters — is much weaker at small angular scales than the baseline FLAMINGO hydrodynamical simulations predict. The authors extract the tSZ signal from 100 GHz temperature power spectra of Planck, ACT and SPT rather than from Compton-$y$ maps, an approach that is insensitive to the poorly known cosmic infrared background. The inferred tSZ amplitude relative to the FLAMINGO template falls from about 0.8 at Planck multipoles to 0.46 for ACT and 0.30 for SPT, excluding the simulation prediction at $\ell \gtrsim 2000$ at very high significance. They argue that recent CMB lensing and DESI measurements make a low matter-fluctuation amplitude extremely unlikely as the explanation, so the discrepancy points to underestimated baryonic feedback in the simulations.

What carries the argument

The load-bearing object is the spectral signature of the thermal Sunyaev-Zeldovich effect, $\Delta T/T_{\rm CMB}=f(x)y$ with $f(x)=x(e^x+1)/(e^x-1)-4$, where $y$ is the Compton integral $\int n_e k_B T_e/(m_e c^2)\sigma_T\,dl$ through the cluster gas and $x=h_p\nu/k_B T_{\rm CMB}$. That unique frequency dependence is what lets the authors work in temperature power spectra instead of $y$-maps: after subtracting the primary CMB with a dust-cleaned $143\times217$ GHz cross-spectrum, the $100\times100$ minus $143\times217$ difference contains essentially only tSZ and a Poisson radio-source term whose $\ell^2$ shape is known. On the theory side, the one-halo model of Komatsu & Seljak (2002) — integrating the halo mass function against projected pressure profiles — supplies the FLAMINGO template and the scaling $C^{yy}\propto S_8^{8.1}$, which is why the amplitude of the tSZ spectrum is such a sensitive probe of matter clustering. The template-free reconstruction with 13 free node amplitudes is the mechanism that exposes the shallower slope, since it does not assume the simulation's spectral shape.

What would settle it

A future high-resolution CMB measurement in the 30–100 GHz range that recovers $10^{12}D^{yy}\approx1.7$ at $\ell\approx2870$, rather than the $\sim0.6$ that the paper's reconstruction gives, would directly contradict the central claim.

Watch

Extended reading notes

Core claim

The central claim is that the unresolved tSZ power spectrum, extracted from $\sim100$ GHz temperature bandpowers rather than from $y$-maps, is far lower and shallower than the baseline FLAMINGO $\Lambda$CDM prediction. Fitting the FLAMINGO template with a free amplitude gives $A^{\rm SPT}_{\rm tSZ}=0.297\pm0.023$ from SPT 95 GHz and $A^{\rm ACT}_{\rm tSZ}=0.463\pm0.096$ from ACT 98 GHz, where unity would mean agreement with the simulation; the two experiments exclude the prediction at very high significance. A template-free reconstruction across $\ell\approx200$–$7000$ yields $10^{12}D^{yy}_{2870}=0.567\pm0.062$ against the FLAMINGO prediction of $1.69$, with similar low values out to $\ell\sim4000$, and a spectrum that is shallower than the simulation's. The authors argue that this cannot be cured by a low $S_8$: matching the measured amplitude would require $S_8\approx0.73$, while Planck lensing, ACT lensing, lensing-galaxy cross-correlations, and DESI full-shape measurements favour $S_8\approx0.8$. They conclude that baryonic feedback in the baseline FLAMINGO simulations is likely underestimated, while noting that even a simulation variant with gas fractions $8\sigma$ below baseline does not fully match the data.

Load-bearing premise

The load-bearing assumption is that the primary CMB signal subtracted from the ACT and SPT bandpowers is exactly the best-fit standard-cosmology spectrum; a slightly different CMB spectrum, from unmodeled foregrounds or parameter shifts, would move every inferred tSZ amplitude.

Editorial extensions

If this is right

  • Above $\ell\approx2000$ the baseline FLAMINGO $\Lambda$CDM tSZ spectrum is excluded at very high significance, so simulation suites used for cosmological inference need to reproduce a lower, shallower unresolved tSZ spectrum.
  • Baryonic feedback is a leading-order ingredient in shaping the tSZ power spectrum; analyses that use tSZ to constrain cosmology while ignoring feedback will be biased.
  • A low $S_8$ cannot rescue the simulations: matching the ACT/SPT amplitudes would require $S_8\approx0.73$, in conflict with Planck and ACT lensing, lensing-galaxy cross-correlations, and DESI full-shape measurements that favour $S_8\approx0.8$.
  • Independent ACT DR6 fits ($a^{\rm tSZ}_{yy}=0.49\pm0.06$, $\alpha_{\rm tSZ}=-0.6\pm0.2$) agree with the low, shallow spectrum, indicating the result is not specific to one experiment or template.

Reading between the lines

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

  • The paper leaves open how much feedback is needed; a direct next step would be to fit a physical pressure-profile model to the reconstructed node amplitudes rather than to a fixed template, which would test whether any single feedback prescription can produce a spectrum this shallow.
  • Because the template-free reconstruction neglects the kinetic Sunyaev-Zeldovich effect, the recovered tSZ amplitudes are upper limits; including a positive kSZ contribution would make the gap with FLAMINGO larger, not smaller.
  • The same 100 GHz temperature-spectrum subtraction could be applied to ACT DR6 and to future 30–100 GHz ground-based surveys, sharpening the $\ell\gtrsim3000$ reconstruction and breaking degeneracies the paper leaves in place.
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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

3 major / 6 minor

Summary. The paper challenges the FLAMINGO hydrodynamic-simulation prediction for the thermal Sunyaev-Zeldovich (tSZ) power spectrum. Instead of using Planck y-maps, which the authors argue are heavily contaminated by CIB, radio sources, and map-making-dependent residuals, they analyze temperature power spectra of the CMB. For Planck, they use the difference between a dust-cleaned 100 GHz spectrum and a dust-cleaned 143x217 GHz spectrum after subtracting the primary CMB, fitting a tSZ template plus a Poisson radio-source component, with a point-source number-count prior. For ACT 98 GHz and SPT 95 GHz, they fit bandpowers to the sum of the RGE22 ΛCDM CMB spectrum, a FLAMINGO-calibrated tSZ template, Poisson point sources, and calibration parameters, finding A_SPT_tSZ = 0.297 ± 0.023 and A_ACT_tSZ = 0.463 ± 0.096. A template-free combination of the Planck, ACT, and SPT likelihoods reconstructs the tSZ spectrum at 13 nodes and indicates that the spectrum is shallower and has much lower amplitude at ℓ ≳ 2000 than the FLAMINGO baseline prediction. The authors argue that a low-S8 cosmology is disfavored by independent lensing and DESI measurements and that underestimated baryonic feedback is the more likely explanation.

Significance. If correct, the result is significant: it provides an independent, high-significance tension between ΛCDM-based hydrodynamical simulations and CMB temperature data, with direct implications for baryonic feedback and for the S8 tension. The paper has clear strengths: it is transparent, uses public ACT/SPT/Planck data, tests y-map contamination with simulations, breaks the tSZ/point-source degeneracy using source counts at 100 GHz, and presents a template-free reconstruction that agrees with the ACT DR6 tSZ shape published after the first version. However, the central high-ℓ exclusion is only as strong as the assumption that the primary CMB is exactly the RGE22 ΛCDM model, because at 95/98 GHz the tSZ signal is extracted from a single frequency band against a much larger, fixed CMB contribution.

major comments (3)
  1. [Sec. 4.2, Eqs. (21)-(22)] The quoted exclusions of the FLAMINGO template (A_tSZ = 1) assume that the RGE22 best-fit ΛCDM spectrum is the exact primary CMB over the multipole range ℓ ≈ 2000–3500. The calibration parameters c_SPT and c_ACT absorb only an overall multiplicative gain, and the ACT/SPT covariance matrices propagate sample variance and noise but not systematic uncertainty in the fixed CMB template. Since the primary CMB power is of order 10^3 μK^2 while the tSZ signal is of order 10 μK^2, a scale-dependent CMB error of even ~1% is comparable to the entire tSZ signal. The statement in Sec. 4.2 point (ii) that 'no plausible changes' to the primary CMB or foreground model could reconcile the data is therefore not supported by the analysis as presented. I ask the authors to quantify this by perturbing the CMB model, for example by varying cosmological parameters within their Planck posteriors or by adding a smooth residual CMB component with a prior, and to report how A_SPT_tSZ and A_ACT_tSZ shift.
  2. [Sec. 4.3, Table 1] The template-free reconstruction and the conclusion that the tSZ spectrum is shallower than the FLAMINGO prediction inherit the same fixed-CMB assumption as Sec. 4.2, and the reported node errors do not include any contribution from primary-CMB model uncertainty. In addition, the reconstruction neglects the kSZ effect; as the authors note, kSZ neglect biases the inferred tSZ upward, so it cannot rescue the FLAMINGO prediction, but it does affect the quantitative shape comparison and the inferred slope. The dip at ℓ ≈ 2000 and the apparent jump between Planck and SPT nodes should be tested for stability when the CMB model is varied.
  3. [Sec. 4.1, Eq. (9)] The Planck tSZ amplitude estimate depends on subtracting a fixed power-law foreground from the dust-cleaned 143x217 spectrum, with amplitude and slope taken from the RGE22 foreground model. No uncertainty in this subtraction is propagated into A_Planck_tSZ. While the Planck measurement is not the basis for the high-ℓ exclusion, it is used in the template-free reconstruction at ℓ ≲ 1000 and therefore affects the inferred slope and the comparison with the ACT/SPT amplitudes.
minor comments (6)
  1. [Abstract] The abstract contains grammatical errors, including 'This paper present' and 'l > 2000 compared to'; a copyedit is needed.
  2. [Fig. 11 caption] The caption refers to 'RGE21', but the cosmological model is from RGE22 (Rosenberg et al. 2022).
  3. [Sec. 4.2, Eq. (20)] The normalization of the Poisson point-source amplitudes is not explained; please state explicitly the reference multipole (presumably ℓ = 3000) at which the coefficients 7.71 and 16.25 correspond to unit amplitude.
  4. [Sec. 2 and Fig. 1] The text calls the dashed line in Fig. 1 the 'FLAMINGO tSZ template', but that line is a one-halo model designed to match the FLAMINGO simulation result rather than the simulation spectrum itself; this distinction should be stated clearly in Sec. 4.2 where the fits are described.
  5. [Sec. 4.1] The description of how Eq. (9) is derived from the RGE22 foreground model is terse; a short explanation of how the power-law amplitude and slope are fixed would improve reproducibility.
  6. [Sec. 3] The simulation tests rely on rescaling the Websky CIB to frequencies below 143 GHz with an assumed dust temperature and spectral index; this is a reasonable approximation, but it should be listed among the limitations of the y-map contamination study.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the FLAMINGO comparison is an external template fit, and the template-free reconstruction breaks any self-reference.

full rationale

The paper's derivation chain is self-contained and compares against an external benchmark rather than reducing to its own inputs. In Sections 4.1 and 4.2, the authors fit a free amplitude A_tSZ to a fixed tSZ template shape (the one-halo model that matches FLAMINGO, and the FLAMINGO template itself), alongside a Poisson point-source component and the RGE22 LambdaCDM primary CMB spectrum. The fitted amplitudes are then compared to the FLAMINGO prediction A=1. This is a legitimate template fit and hypothesis test: the data could have produced A close to 1, and nothing in the construction forces the fitted amplitude to equal the simulation prediction. The Planck point-source degeneracy is broken independently using external source counts (Eq. 18), not by the tSZ model. More importantly, Section 4.3 performs a template-free reconstruction in which the tSZ spectrum is represented by 13 free node amplitudes with no FLAMINGO shape imposed; the resulting spectrum is then compared with FLAMINGO, which is not circular. The cited prior work by the authors (EG21, RGE22, MH24) provides the Planck power-spectrum pipeline and the primary CMB template, but these are independent products not derived from the tSZ measurement being tested, and the FLAMINGO simulations are external to this analysis and are not adjusted to the data. The fixed RGE22 CMB spectrum is a model-dependence or robustness concern, not a circularity: the paper's exclusion claim could weaken if the CMB shape were wrong, but that is a question of external validity, not of the argument reducing to its inputs by construction. No fitted parameter is renamed as a prediction, and no load-bearing claim relies on a self-citation chain.

Assumptions & free parameters 11 free parameters · 6 assumptions · 0 invented entities

The central measurement is a template amplitude fit, so the main free parameters are the foreground amplitudes, calibration parameters, and the 13 node points in the template-free reconstruction. The main axioms are the pressure profile, halo mass function, CMB model, and foreground shapes. No new physical entities are introduced.

free parameters (11)
  • APlanck_tSZ = 0.815 +/- 0.128 with point source prior; 0.706 +/- 0.243 without
    Amplitude of the FLAMINGO-shaped tSZ template fitted to the Planck 100x100 minus 143x217 power spectrum (Eqs. 12 and 19).
  • APlanck_PS = 0.931 +/- 0.052
    Poisson radio source amplitude in the Planck spectrum, fitted with the number count prior from Eq. 18.
  • ASPT_tSZ = 0.297 +/- 0.023
    tSZ template amplitude from the SPT 95 GHz fit (Eq. 21).
  • ASPT_PS = 1.000 +/- 0.051
    Poisson radio source amplitude from the SPT 95 GHz fit (Eq. 21).
  • AACT_tSZ = 0.463 +/- 0.096
    tSZ template amplitude from the ACT 98 GHz fit (Eq. 22).
  • AACT_PS = 1.003 +/- 0.139
    Poisson radio source amplitude from the ACT 98 GHz fit (Eq. 22).
  • cSPT and cACT calibration = cSPT = 1.0057 +/- 0.0054, cACT = 0.9918 +/- 0.0082
    Relative calibration parameters between Planck and SPT/ACT spectra, with Gaussian priors described in Section 4.2.
  • Point source count parameters = Ac = 8.55 +/- 0.35 Jy^1.5 sr^-1, xc = 1565 +/- 420, alpha_c = 0.419 +/- 0.025, beta_c = 3.63 +/- 1.65, gamma_c = 0.307…
    Fit to 100 GHz source counts from Eq. 14, used to set the prior on APlanck_PS.
  • D143x217 correction coefficient = 12.295 muK^2 at l = 1500 with index 1.701
    Power-law subtracted from the dust-cleaned 143x217 spectrum to reproduce the RGE22 base LambdaCDM spectrum (Eq. 9).
  • 13 tSZ node amplitudes = 1e12 Dyy from 0.310 at l = 200 to 0.846 at l = 5853; see Table 1
    Template-free tSZ power spectrum reconstruction node amplitudes, fitted jointly with point source amplitudes and calibration parameters.
  • epsilon evolution parameter = 0 for template, 1 for comparison model
    Hand-set parameter in the halo model Eq. 5 used to generate comparison curves, not fitted to data.
assumptions (6)
  • domain assumption The Arnaud et al. (2010) universal pressure profile describes electron pressure in clusters and groups in the FLAMINGO simulations and in real clusters.
    Used to construct the tSZ template and halo model predictions in Section 2.
  • domain assumption The Jenkins et al. (2001) halo mass function provides an accurate mass function for the relevant mass and redshift range.
    Used in Eq. 8a for halo model tSZ spectra.
  • domain assumption The primary CMB anisotropy is described by the RGE22 best-fit base LambdaCDM power spectrum.
    Subtracted from SPT and ACT bandpowers in Section 4.2 to isolate tSZ plus point sources.
  • domain assumption The CIB contribution is negligible at 100 GHz and does not bias the tSZ amplitude.
    Based on the normalized Béthermin et al. (2012) CIB model giving D ~ 0.25 muK^2 at l = 500 versus observed tSZ D ~ 6.9 muK^2; the paper notes the model is uncertain below 217 GHz.
  • domain assumption The kinetic SZ (kSZ) contribution is small enough to ignore; neglecting it can only overestimate the tSZ amplitude.
    Stated in Section 4.2 point (i); kSZ is frequency independent and very uncertain, but ignoring it is conservative for the tension claim.
  • domain assumption Poisson radio source power spectrum scales as l(l+1) and is fully characterized by source counts below 400 mJy.
    Used to break the tSZ/point source degeneracy in Section 4.1.

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Cite this review

Pith. "Pith review of The Power Spectrum of the Thermal Sunyaev-Zeldovich Effect." pith.science (2026). https://pith.science/paper/Y6TG33HK

@misc{pith2026250210232,
  author       = {Pith},
  title        = {Pith review of: The Power Spectrum of the Thermal Sunyaev-Zeldovich Effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y6TG33HK}},
  note         = {Machine review of arXiv:2502.10232}
}
abstract

The power spectrum of unresolved thermal Sunyaev-Zeldovich (tSZ) clusters is extremely sensitive to the amplitude of the matter fluctuations. This paper present an analysis of the tSZ power spectrum using temperature power spectra of the cosmic microwave background (CMB) rather than maps of the Compton y-parameter. Our analysis is robust and insensitive to the cosmic infrared background. Using data from Planck, and higher resolution CMB data from the Atacama Cosmology Telescope and the South Pole Telescope, we find strong evidence that the tSZ spectrum has a shallower slope and a much lower amplitude at multipoles l > 2000$compared to the predictions of the FLAMINGO hydrodynamic simulations of the LCDM cosmology. Recent results on CMB lensing, cross-correlations of CMB lensing with galaxy surveys and full shape analysis of galaxies and quasars from the Dark Energy Spectroscopic Instrument suggests that this discrepancy cannot be resolved by lowering the amplitude of the matter fluctuations. An alternative possibility is that the impact of baryonic feedback in the FLAMINGO simulations is underestimated.

Figures

Figures reproduced from arXiv: 2502.10232 by the authors.

Figure 1
Figure 1. The red points show estimates of the tSZ power spec￾trum from B18, together with 1σ errors. The blue and green points show the amplitudes of template tSZ power spectra at ℓ = 3000 inferred from high resolution ground based CMB power spectra measured by the ACT and SPT collaborations (Choi et al. 2020; Reichardt et al. 2021) The grey band is included to high￾light the fact that the ACT and SPT measurements are model … view at source ↗
Figure 2
Figure 2. The contribution to the tSZ power spectrum, computed from the one-halo model described in the text, plotted as a function of virial cluster mass MV (measured in M⊙), redshift and multipole. The evolution parameter ϵ in Eq. 5 has been set to ϵ = 1 in this example, leading to the sharp decline in power at z >∼ 1 (see Sect 5). The shaded regions show the approximate range of multipoles probed by Planck, ACT and SPT. . … view at source ↗
Figure 3
Figure 3. The green points show the power spectrum of the NILC×MILC y-map cross spectrum analysed by B18. The figure shows the contributions from the clustered CIB, infrared point sources, radio sources, resolved SZ clusters and unresolved tSZ determined by B18 by fitting template power spectra to the green points. The B18 tSZ power spectrum is a subdominant compo￾nent of the total power spectrum over most of the multipole ra… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: The curves labelled NILC and MILC show half-ring cross spectra of the Planck y-maps. The curves labelled MH show half-ring cross spectra of y-maps constructed by McCarthy & Hill (2024) with no deprojection (as in standard NILC) and with additional constraints applied t…
Figure 5
Figure 5. Figure 5: Contribution of each component to the measured power spectrum of a simulated NILC y-map Planck-like analysis. The blue points show the measured split power spectrum of our simulations, and the various coloured points show the contribution of the components, with the tr…
Figure 6
Figure 6. Figure 6: Mask applied to the Planck maps for the analysis described in Sect. 4.1 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: The 545 GHz dust-cleaned 100×100 cross spectrum (red points) and dust-cleaned 143 × 217 cross spectrum (blue points) with the best fit ΛCDM spectrum from RGE22 sub￾tracted. The spectra were computed using the 400 mJy 100GHz point source and extended object mask shown i…
Figure 8
Figure 8. Figure 8: The upper panel shows the difference of the two spectra plotted in [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: 68% and 95% contours on the parameters APlanck tSZ and APlanck PS derived by fitting the 100×100−143×217 power spectrum difference (red contours). Consistency with the predictions of the FLAMINGO ΛCDM prediction of [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Source counts at 100 GHz. The red points show source counts measured from Planck (Planck Collaboration et al. 2013). The blue points show counts from SPT (Everett et al. 2020) at 95 GHz rescaled to 100 GHz. The green line shows the best fit to the function of Eq.13 an…
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: Reconstruction of the tSZ power spectrum derived by combining the Planck, ACT and SPT likelihoods of the pre￾vious subsections (yellow points). We solve for the amplitude of Dyy at each of 13 node points and interpolate the tSZ spectrum between the nodes shown in the …

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Forward citations

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Pith tools

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