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The Thermal Sunyaev-Zel'dovich Effect from the Epoch of Reionization

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The epoch of reionization produces a thermal SZ signal of mean Compton y ~ 3-4 x 10^-8, about one percent of cluster power at survey scales and potentially dominant near multipole 10^5.

desk verdict First RHD-based maps and power spectra of EoR tSZ; the small-scale dominance claim is not convergence-tested. read the letter →

arxiv 2412.04385 v1 pith:CUL44465 submitted 2024-12-05 astro-ph.CO

Ilian T. Iliev , Azizah R. Hosein , Jens Chluba , Luke Conaboy , David Attard , Rajesh Mondal , Kyungjin Ahn , Stefan Gottlöber
show 6 more authors
Joseph Lewis Pierre Ocvirk Hyunbae Park Paul R. Shapiro Jenny G. Sorce Gustavo Yepes
This is my paper · ORCID
classification astro-ph.CO
keywords thermalSunyaev-Zel'dovicheffectepochofreionizationComptony-parameterradiation-hydrodynamicssimulationscosmicmicrowavebackgroundsecondaryanisotropiesintergalacticmediumquadraticDopplerdistortions
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 compute the thermal Sunyaev-Zel'dovich (tSZ) signal produced during the epoch of reionization, a contribution that cluster-based templates have largely ignored. Using a suite of fully coupled radiation-hydrodynamics simulations, the authors build lightcones of electron pressure over $z \sim 6$ to 12 and integrate them along the line of sight to obtain maps and angular power spectra of the Compton $y$-parameter. They find a mean $y$ of a few times $10^{-8}$, roughly one percent of the cluster-dominated tSZ power at arcminute-resolution survey scales, with quadratic Doppler distortions adding about ten percent to that value. At much smaller scales, near multipole $\ell \sim 10^5$, the reionization signal peaks and can rival or exceed the post-reionization template. If the claim holds, future high-resolution CMB experiments would need to include reionization-era gas when modelling the tSZ foreground.

What carries the argument

The carrying object is the Compton $y$-parameter, $y = (\sigma_T/m_e c^2) \int p_e\, dl$, the line-of-sight integral of electron pressure, evaluated on lightcones built by interpolating gas pressure and ionization fraction between simulation snapshots. For a hydrogen-only gas the electron pressure is $p_e = x_{\mathrm{HII}}/(1+x_{\mathrm{HII}})\, p_{\mathrm{gas}}$, with a post-processing correction for singly ionized helium. A second-order Doppler term, $y = (\sigma_T/3cH_0) \int n_e\langle v^2\rangle\,(1+z)^{-1}E(z)^{-1}\, dz$, is added and corrected for velocity power missing from finite simulation boxes. These lightcone integrals convert the patchy structure of reionization directly into $y$-maps and angular power spectra.

What would settle it

Run the same reionization physics at progressively higher spatial resolution and check whether the rare cells above $10^6$ K and the $y$ power at $\ell \sim 10^5$ converge; if the high-temperature tail shrinks or disappears with resolution, the claimed small-scale dominance is numerical. Observationally, a future arcsecond-resolution CMB survey could search for the predicted compact peaks with $y \sim 10^{-6}$, and their absence would rule out the smallest-scale part of the claim.

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Extended reading notes

Core claim

The central claim is that the epoch of reionization produces a measurable tSZ signal with mean Compton parameter $y \sim 3$--$4 \times 10^{-8}$, whose angular power spectrum is flatter than the cluster template and crosses it near $\ell \sim 10^5$. The signal grows with the redshift at which reionization completes: simulations that end reionization near $z \sim 6.6$ reach mean $y$ values up to two or three times those of runs that finish near $z \sim 5.6$. The high-pressure regions that drive the small-scale power are rare cells heated to millions of kelvin by supernova explosions and structure-formation shocks; lower-resolution runs smear these cells out and lose the high-$y$ tail. Isolating the density, temperature, and ionization contributions shows that the patchiness of reionization broadens the $y$ distribution, while the supernova-heated temperature fluctuations are responsible for its high-$y$ tail.

Load-bearing premise

The predicted small-scale dominance rests on the simulation resolving rare cells heated above a million kelvin by supernova feedback and shocks; if those hot cells are numerical artefacts of resolution or if feedback is weaker, the small-scale peak would not surpass the cluster template.

Editorial extensions

If this is right

  • At angular scales probed by arcminute-resolution experiments ($\ell \sim 10^3$--$10^4$), the reionization tSZ contributes roughly one percent of the cluster-template power and should be included in foreground models for precision cosmology.
  • The quadratic Doppler effect adds about ten percent to the reionization tSZ $y$-parameter, with the exact fraction set by the reionization history and by large-scale velocity power missing from the simulation boxes.
  • Earlier reionization produces a stronger tSZ signal: mean $y$ increases roughly with the redshift at which reionization completes, with additional scatter from star formation efficiency and supernova heating.
  • At multipoles near $\ell \sim 10^5$, the reionization tSZ can dominate the post-reionization template, so future arcsecond-resolution CMB experiments would see reionization-era gas as a foreground that must be modelled.
  • The tSZ signal from reionization offers a redshift-independent probe of the thermal state, clumpiness, and timing of reionization, complementary to 21-cm and kinetic SZ probes.

Reading between the lines

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

  • If the small-scale dominance survives higher-resolution tests, the height and shape of the EoR tSZ peak near $\ell \sim 10^5$ could be used to constrain supernova feedback and the clumpiness of the ionized intergalactic medium, since the peak is controlled by rare hot cells rather than by the mean IGM temperature.
  • The same lightcone machinery could be cross-correlated with 21-cm emission or the kinetic SZ effect; the patchy ionization and hot-cell structure should produce a distinctive cross-spectrum that separates the reionization contribution from low-redshift clusters.
  • Because the analytic uniform-IGM estimate ($y \approx 4 \times 10^{-8}$) lies close to the simulated means, a moderately improved analytic model that treats temperature fluctuations and patchiness could predict the EoR tSZ without expensive radiative-transfer simulations.
  • A direct extension would replace the single-ionization helium correction with a full helium reionization history; helium reionization ends later than hydrogen and could change the electron pressure at the lower-redshift end of the lightcones by an amount the current correction does not capture.
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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 / 5 minor

Summary. The paper presents the first systematic simulation-based calculation of the thermal Sunyaev-Zel'dovich (tSZ) signal from the Epoch of Reionization. Using sixteen RAMSES-CUDATON radiation-hydrodynamics simulations (including CoDa II and a suite of auxiliary boxes), the authors construct electron-pressure lightcones over z ≈ 6–12, integrate them to obtain Compton y maps, and compute angular power spectra. The main results are mean y values of a few × 10^-8, a tSZ contribution of roughly one percent of the cluster-level signal at SPT scales (ℓ ∼ 10^3–10^4), a quadratic Doppler contribution of order 10% of the EoR tSZ signal, and a predicted rise in the EoR tSZ power spectrum at ℓ ∼ 10^5 where it may dominate over the post-reionization signal. The paper also separates the contributions of density, temperature, and ionization fluctuations and discusses phase diagrams of the simulated gas.

Significance. If the results hold, this is a useful first quantification of a previously neglected EoR contribution to a standard CMB foreground, with direct relevance for current SPT-scale analyses and for future high-resolution CMB experiments. The paper's strengths include the unusually large suite of calibrated simulations, the use of independent reionization observables (neutral fraction, optical depth, photoionization rate, star formation rate) rather than the tSZ signal itself for calibration, the explicit treatment of missing large-scale velocity power in the quadratic Doppler estimate, and the honest reporting of resolution-related limitations in Section 5.3. The central sub-dominance claim at ℓ < 10^4 appears robust across the simulation suite and is consistent in order of magnitude with the analytic estimate of Hill et al. (2015).

major comments (3)
  1. [Abstract; Sec. 5.1.2; Sec. 5.2; Sec. 5.3] The headline claim that the EoR tSZ signal 'peaks and can potentially dominate the total signal' at ℓ ∼ 10^5 is not supported by a resolution-converged result. The high-ℓ power is produced by the high-y tail (log10 y ∼ -6 to -5.5), which Sec. 5.2 attributes to gas heated by supernovae and shocks to T > 10^6–10^7 K. However, Sec. 5.3 and Fig. 8 explicitly describe the density-temperature bifurcation as an '(unphysical) resolution effect' that disappears as resolution increases, and note that such hot cells appear only in the higher-resolution runs. Since the two high-resolution runs (CoDa II and the 10 Mpc boxes) differ in volume, resolution, and feedback model, they do not constitute a controlled convergence test. The small-scale dominance prediction should either be backed by a fixed-physics resolution study or explicitly qualified as a simulation-dependent upper bound.
  2. [Sec. 4.2, Eqs. (11)–(12); Sec. 4.3.1, Eqs. (18)–(19)] There appears to be a factor-of-two error in the conversion from gas density to electron number density. For the stated definition of x_HII as an ionized fraction in [0,1], full ionization gives x_HII = 1, but Eq. (11) then yields ρe = ρgas/2, implying n_e = ρgas/(2 m_p) for pure hydrogen. The correct electron number density for fully ionized hydrogen is n_e = ρgas/m_p; the factor 1/(1+x_HII) is appropriate for converting gas pressure to electron pressure, not for converting gas density to electron density. This same factor enters the analytic uniform-IGM estimate in Eqs. (18)–(19), so the quoted reference value y ≈ 4.22 × 10^-8 (and the helium-corrected 3.46 × 10^-8) is likely too low by a factor of about two for T = 30,000 K. The authors should clarify the definition of x_HII and correct the density-lightcone and analytic estimates, or explicitly justify why the factor 1/(1+x_HII) is present in the density conversion.
  3. [Sec. 4.5, Eqs. (30)–(31); Fig. 10] The implementation of the missing large-scale velocity power correction is ambiguous and load-bearing for the reported ~10% quadratic Doppler contribution. Eq. (25) requires the average ⟨n_e v²⟩ over each snapshot, and Eq. (31) defines the missing ⟨v²⟩, but the text does not state whether ⟨v²⟩_missing is added to each cell's v² before multiplying by the local n_e, or whether it is added as a global term ⟨n_e⟩ ⟨v²⟩_missing. These two prescriptions can differ at the tens-of-percent level because n_e is strongly clustered where the velocity field is nonlinear. Please specify the exact operation used to produce the filled markers in Fig. 10 and justify it against the alternative.
minor comments (5)
  1. [Fig. 6 caption] The caption contains a typo: 'oour simulations' should read 'our simulations'.
  2. [Sec. 4.1 vs Sec. 5.1.2] The template used for comparison is introduced as Shaw et al. (2010) in Sec. 4.1 but the results and figures use the Bolliet et al. (2018) template; please make the template references consistent throughout.
  3. [Sec. 3.1] The CoDa II lightcones are constructed from the coarsened 2048^3 stored pressure field, not the native 4096^3 grid; this effective resolution should be stated where the 'full-resolution' maps and high-ℓ power spectra are presented, since it sets a hard limit on the small-scale signal.
  4. [Sec. 4.1, Eq. (9)] The sigmoid interpolation between snapshots is introduced without any sensitivity test; a brief statement on the robustness of the integrated y to the choice of β and to the snapshot spacing would strengthen the methodology.
  5. [Abstract; Sec. 5.4] The phrase 'contributing an additional ∼10% to the tSZ signal' in the abstract is potentially confusing; the authors mean 10% of the EoR tSZ signal, not 10% of the total (cluster-dominated) tSZ signal. Please rephrase for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the EoR tSZ signal is an emergent prediction from simulations calibrated to independent reionization observables, not to the tSZ signal itself.

full rationale

The derivation chain is self-contained. The tSZ y-parameter is computed from Eq. (6) as the line-of-sight integral of the electron pressure field produced by the RAMSES-CUDATON radiation-hydrodynamics simulations; the pressure and ionization fields are inputs, and y is an emergent output. The simulations are calibrated in Sec. 3.3 against external reionization observables (neutral fraction, photoionization rate, Thomson optical depth, and star formation rate) that do not include the tSZ signal, so the mean y and power spectra are not fitted targets. The quadratic Doppler contribution (Sec. 4.5) uses standard linear-theory velocity power to correct for missing large-scale modes; this is an independent, parameter-free correction, not a fit to the tSZ signal. Comparisons to the Bolliet et al. (2018) and Shaw et al. (2010) templates are external benchmarks, and agreement with the analytic estimate of Hill et al. (2015) is a consistency check, not a circular input. The paper's own caveats—that the small-scale peak is driven by rare supernova-heated cells and that lower-resolution runs show an unphysical density-temperature bifurcation (Sec. 5.3)—are resolution and robustness concerns, not circularity: the prediction is not equivalent to its inputs by construction. Self-citations, such as Ocvirk et al. (2018) for CoDa II and Iliev et al. (2006b) for inside-out reionization, are not load-bearing in a circular sense because the cited results do not contain the tSZ prediction and the simulation is independently calibrated. Verdict: no significant circularity.

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

The central predictions depend on the sub-grid star formation parameters, which are calibrated to reionization observations, and on the simulation's ability to resolve small hot cells. These parameters are not fitted to the tSZ signal, so the circularity burden is low, but they set the amplitude of the small-scale signal.

free parameters (5)
  • Star formation efficiency (epsilon_star) = 0.01 to 0.08 across suite
    Sub-grid parameter calibrated so simulated reionization histories match observed neutral fraction, photoionization rate, and star formation rate (Sec. 3.3, Table 1). Directly controls the number of supernovae and hence the small-scale pressure peaks.
  • Ionizing photon escape fraction (f_esc) = 0.1 to 0.5 across suite
    Chosen to adjust the timing of reionization to match observations; a higher escape fraction allows reionization to complete earlier, increasing the y-parameter (Sec. 3.3, Table 1).
  • Star formation density threshold (delta_star) = 20 to 200 times mean density
    Tied to grid resolution; varied to match observed star formation rates and reionization timing (Table 1).
  • Supernova feedback mass fraction (eta_SN) = 0.1 or 0.15
    Small variation shown to have a weak effect on reionization timing but affects local gas heating (Table 1).
  • Sigmoid interpolation parameter beta = 2
    Hand-chosen in Sec. 4.1 (Eq. 9) for the lightcone interpolation between snapshots; no sensitivity test is presented.
assumptions (6)
  • domain assumption Lambda-CDM cosmology with Planck 2014/2018 parameters
    Adopted in Sec. 3.1 and 3.2; the tSZ power spectrum and lightcone construction assume this cosmology, with the matter density and Hubble parameter affecting pressure evolution.
  • domain assumption The RAMSES-CUDATON code solves coupled gravity, hydrodynamics, and radiative transfer correctly at the adopted grid resolutions
    All results inherit the accuracy of the simulation toolchain (Sec. 3); no convergence study across resolution is shown for the tSZ signal itself.
  • domain assumption Einstein-de Sitter approximation for time steps in lightcone construction
    Sec. 4.1, 'Assuming an Einstein-de Sitter universe, which is a good approximation at high redshift', used to convert cell crossing times to redshifts.
  • domain assumption Neglect of relativistic corrections to the tSZ spectral function
    Sec. 2.1 states delta_SZ is neglected; temperatures up to 10^7 K in supernova-heated cells make this approximation questionable for the small-scale tail.
  • standard math Linear theory for the missing large-scale velocity power
    Sec. 4.5 uses Eqs. 28-30 with the continuity equation and f equal to Omega_m^0.6 to add the power missing from finite simulation boxes.
  • domain assumption Pure hydrogen gas in the simulations with helium added in post-processing
    Sec. 4.4; the simulation tracks only hydrogen, and helium is assumed singly ionized wherever hydrogen is ionized, reducing y by 18 percent.

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Pith. "Pith review of The Thermal Sunyaev-Zel'dovich Effect from the Epoch of Reionization." pith.science (2026). https://pith.science/paper/CUL44465

@misc{pith2026241204385,
  author       = {Pith},
  title        = {Pith review of: The Thermal Sunyaev-Zel'dovich Effect from the Epoch of Reionization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CUL44465}},
  note         = {Machine review of arXiv:2412.04385}
}
abstract

The thermal Sunyaev-Zel'dovich (tSZ) effect arises from inverse Compton scattering of low energy photons onto thermal electrons, proportional to the integrated electron pressure, and is usually observed from galaxy clusters. However, we can expect that the Epoch of Reionization (EoR) also contributes to this signal, but that contribution has not been previously evaluated. In this work we analyse a suite of fully-coupled radiation-hydrodynamics simulations based on RAMSES-CUDATON to calculate and study the tSZ signal from the Reionization Epoch. We construct lightcones of the electron pressure in the intergalactic medium for $6<z$ to calculate the resulting Compton y-parameters. We vary the box sizes, resolutions and star formation parameters to investigate how these factors affect the tSZ effect. We produce plots of maps and distributions of y, as well as angular temperature power spectra of the tSZ signal obtained from integrating the lightcones constructed for each simulation. We find that the tSZ signal from reionization is generally sub-dominant to the post-reionization one at larger scales ($\ell< 10^4$), but can contribute non-trivially and potentially contaminate the measured signals. At scales probed by current experiments like SPT ($\ell\sim10^3-10^4$), we find that the tSZ signal power spectrum from reionization contributes at roughly a percent level compared to the current templates, with the quadratic Doppler effect contributing an additional $\sim10\%$ to the tSZ signal. At smaller scales the tSZ from reionization peaks and can potentially dominate the total signal and is thus a potentially much more important contribution to take into account in any future, more sensitive experiments.

Figures

Figures reproduced from arXiv: 2412.04385 by the authors.

Figure 1
Figure 1. Calibration of our simulations. For clarity not all simulations are shown as separate lines, but instead the 25 h−1Mpc box models are shown as bands, the rose-brown band indicates the range for early-reionization cases (25-δ30-f0.14-ϵ4 , 25-δ30-f0.2-ϵ4 , 25-δ30-f0.25- ϵ2.5 and 25-δ50-f0.3-ϵ3 ), while the blue band includes the late-reionization ones (25-δ30-f0.1-ϵ4 , 25-δ30-f0.2-ϵ2 , 25-δ30-f0.2-ϵ2-η15 , and 25-δ50-… view at source ↗
Figure 2
Figure 2. Evolution of the global star formation rate density. The dust-corrected and dust-uncorrected observations from Bouwens et al. (2015) are indicated by the grey shaded region. The yellow band includes the results from the four 100 Mpc boxes, the rose￾brown band indicates the range for early-reionization 25 h−1Mpc box models, and the blue band includes the late-reionization ones. at a reasonable time. For example, 25-δ… view at source ↗
Figure 3
Figure 3. PDF distributions of the comptonization y-parameter for our simulations, some of which are shown individually (as labelled) and for clarity the rest are grouped in two bands - turquoise one including 100-δ20-f0.3-ϵ5 , 100-δ20-f0.25-ϵ6 , 25-δ30-f0.1-ϵ4 , 25-δ30-f0.2-ϵ2 , 25-δ30-f0.2-ϵ2-η15 and 25-δ50- f0.5-ϵ1 , and coral one for 25-δ30-f0.14-ϵ4 , 25-δ30-f0.25-ϵ2.5 , and 25-δ50-f0.3-ϵ3 . - first includes 100-δ20-f0.3-… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: The mean y-parameter for each simulation (as indi￾cated in the legend) vs. z⟨xHI ⟩∼0.001, the redshift at which xHI ∼ 0.001. cant scatter. Curiously, the most significant outliers, namely CoDa II and 10-δ200-f0.25-ϵ3.5-η15 , are among the best￾resolved simulations in o…
Figure 5
Figure 5. Figure 5: Maps of the Comptonization y-parameter for CoDa II, 100 ϵ6, and 100 ϵ8 simulations. Left: full resolution maps sharing the same colour bar scale for y. Middle: maps smoothed with a Gaussian beam of FWHM 1.2 arcmin FWHM, corresponding to the resolution of the 150 GHz ch…
Figure 6
Figure 6. Figure 6: The angular temperature power spectra of the tSZ signals yielded by oour simulations. Power spectra calculated for the two SPT band-powers in which the tSZ effect is visible: 150 GHz (left) and 95 GHz (right). The black solid line is the 1-halo and 2-halo combined cont…
Figure 7
Figure 7. Figure 7: Distributions of the y-parameter for full CoDa II re￾sults (green), uniform global electron temperature (blue), both uniform global electron temperature and uniform ionized fraction (orange). Finally, the vertical black dashed line shows the analyti￾cal result for inst…
Figure 8
Figure 8. Figure 8: Phase diagrams showing the gas density vs. temperature at the end of the reionization (z ∼ 6), for selected subset of our simulations: (top left) CoDa II, (top right) 100-δ20-f0.25-ϵ6 , (bottom left) 50-δ30-f0.25-ϵ2.5 , and (bottom right) 10-δ200-f0.2-ϵ3.5 . photoioniz…
Figure 9
Figure 9. Figure 9: Phase diagrams showing the gas density vs. temperature at the end of the reionization (z ∼ 6), for selected subset of our simulations with same resolution, but varying parameters: (top left) 25-δ30-f0.14-ϵ4 , (top right) 25-δ30-f0.2-ϵ4 , (bottom left) 25-δ50- f0.3-ϵ3 ,…
Figure 10
Figure 10. Figure 10: As in [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.