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REVIEW 3 major objections 6 minor 101 references

Patchy Helium and Hydrogen Reionization from the Kinetic Sunyaev-Zel'dovich Effect and Galaxies

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

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Pith's one-line read Helium reionization becomes measurable via kSZ-galaxy cross-correlation.

desk verdict The K-eta cross-correlation is a genuine new statistic, but the headline He reionization constraints are conditional on idealized velocity reconstruction that could easily erase them. read the letter →

arxiv 2506.11188 v1 pith:QWSHJ5RT submitted 2025-06-12 astro-ph.CO astro-ph.GA

Neha Anil Kumar , Mesut Çal{i}şkan , Selim C. Hotinli , Marc Kamionkowski , Simone Ferraro , Kendrick Smith This is my paper
classification astro-ph.COastro-ph.GA
keywords kineticSunyaev-Zel'dovicheffectpatchyreionizationhydrogenheliumCMBtrispectrumvelocityreconstructiongalaxysurveysFisherforecast
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 argues that the kinetic Sunyaev-Zel'dovich (kSZ) effect, a small-scale CMB distortion from scattering off free electrons, can be turned into a joint probe of both hydrogen (H) and helium (He) reionization. The key move is to add a redshift-resolved cross-correlation: the kSZ temperature-squared maps used in earlier trispectrum work are correlated with the squared radial-velocity field reconstructed from galaxy surveys at redshifts below about 5. Using forecasts tied to CMB-S4-like and CMB-HD-like surveys crossed with LSST-like and MegaMapper-like galaxy data, the paper finds that the CMB-HD x MegaMapper combination can measure the midpoint and duration of He reionization at about 1-sigma while determining all H reionization parameters below 1-sigma. This matters because He reionization is tied to quasars and active galactic nuclei, so measuring both epochs together would let observations separate the roles of stars and quasars in ionizing the intergalactic medium.

What carries the argument

The central object is the four-point (trispectrum) kSZ statistic built from filtered temperature-squared maps. The CMB map is split into high-$\ell$ bands; each band is squared to make a field $K_i(\hat{n})$ measuring local small-scale kSZ power. Large-scale variations of $K_i$ are sourced by the squared radial peculiar velocity field $\eta(\hat{n},z) = v_r^2 / \langle v_r^2 \rangle$, whose coherence length sets the angular-scale dependence of the statistic. The paper's new ingredient is a cross-correlation between these $K_i$ fields and redshift-binned $\eta_\alpha$ fields reconstructed from galaxy surveys through the linear continuity equation, with a minimum-variance estimator whose noise is set by shot noise in the galaxy density. This cross-correlation adds tomographic information at $z \lesssim 5$, where He reionization is taking place, and it is what lifts the He signal out of the redshift-integrated background.

What would settle it

A concrete test would be to run the same Fisher pipeline with a velocity-reconstruction noise model taken from realistic light-cone galaxy mocks that include photo-z scatter, redshift-space distortions, fingers-of-God, and survey masks instead of the shot-noise formula in Eq. (39); if the reconstructed-$\eta$ SNR falls by the factor of about 2 reported for LSST-like photo-z samples, the CMB-HD x MegaMapper He-reionization constraints in Fig. 10 would degrade below 1-$\sigma$ detectability. A separate check would be to replace the analytical bubble model with a simulation-based reionization map and recompute the kSZ trispectrum and cross-correlation amplitudes, which would test whether the assumed bubble radii and ionized-electron power spectrum are the main drivers of the forecasted sensitivity.

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Extended reading notes

Core claim

The paper's central claim is that the redshift-integrated kSZ trispectrum, already sensitive to patchy H reionization, can be extended to He reionization by cross-correlating the kSZ-weighted temperature-squared field $K(\hat{n})$ with a galaxy-reconstructed squared radial-velocity field $\eta(\hat{n}, z)$ binned in redshift. The authors model both ionization epochs with a halo-model and bubble prescription, derive the ionized-electron power spectrum including H, He, and mixed terms, and then perform an information-matrix forecast. Their headline quantitative result is that adding the $z$-binned $\eta$-field data allows measurement of the He reionization parameters $y_{\rm re}^{\rm He}$ and $\Delta_y^{\rm He}$ near 1-$\sigma$ for a CMB-HD x MegaMapper baseline, while the same baseline yields sub-1-$\sigma$ errors on all H reionization parameters. Without the galaxy cross-correlation, the auto-correlation trispectrum leaves He parameters essentially unconstrained. The paper therefore proposes that the kSZ effect, previously regarded as a hydrogen-reionization timing statistic, can become a quantitative probe of both epochs if the assumed galaxy velocity reconstruction is achieved.

Load-bearing premise

The forecast assumes that galaxy surveys can reconstruct the squared radial-velocity field $\eta$ with essentially ideal errors: linear continuity between galaxy density and velocity, velocity-reconstruction bias $b_v = 1$, shot-noise-only errors, and no degradation from photo-z errors, redshift-space distortions, or masks; if real reconstruction is noticeably worse, the helium reionization constraints, already near 1-$\sigma$, would weaken.

Editorial extensions

If this is right

  • If He reionization parameters can be measured, the epoch of the second ionization of helium becomes a direct observable tied to quasar and AGN activity rather than only an inference from Lyman-$\alpha$ forest or intergalactic-medium temperature measurements.
  • Jointly fitting H and He parameters prevents neglected-He biases; the paper finds that using $\ell$-binned $K$ fields keeps H-He covariance minimal, so omitting He would not strongly bias H constraints when that binning is used.
  • The forecast detection SNR for CMB-HD x MegaMapper reaches roughly 100 at $L_{\rm max} \sim 50$ when combining the auto- and cross-correlation signals, so the fields do not need to be reconstructed to very small angular scales for a detection.
  • If only the redshift-evolution parameters $y_{\rm re}$ and $\Delta_y$ are targeted, without marginalizing over bubble-size parameters, the CMB-HD x MegaMapper baseline can place roughly $3\sigma$ constraints on all four midpoint and duration parameters for both epochs at $L_{\rm max} \sim 200$.
  • The constraints depend on the assumed small-scale electron profile; switching to a $W_e(k) \times$ NFW profile changes H parameter errors by up to about a factor of 2 and He parameter errors by up to about a factor of 1.5.

Reading between the lines

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

  • Beyond the paper's forecasts, the same $K \times \eta$ framework could be extended to a bispectrum-level statistic correlating the $K$ fields with galaxy density itself, which would be more sensitive to small-scale patchiness and quasar clustering during He reionization.
  • If velocity reconstruction degrades by the factor of about 2 that the cited photometric-redshift studies find for LSST-like samples, the He parameter errors would roughly double, making the headline He detection marginal rather than secure.
  • A successful joint measurement would allow kSZ-based constraints on quasar-driven helium reionization to be combined with fast-radio-burst dispersion measures and He II Lyman-$\alpha$ forest observations, providing independent cross-checks on the timing and morphology of the epoch.
  • The reliance on linear continuity and an assumed velocity-reconstruction bias $b_v = 1$ suggests that realistic survey masks, fingers-of-God, and residual redshift-space distortions will need to be folded into the Fisher forecasts; the relative advantage of a spectroscopic follow-up like MegaMapper over a photometric sample may therefore be understated in the paper.
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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. This paper extends the kSZ trispectrum estimator of Smith & Ferraro (2017) to model the joint contribution of hydrogen and helium reionization to the small-scale CMB temperature field, and introduces a new cross-correlation between the kSZ-squared field K(ˆn) and a galaxy-reconstructed, redshift-binned radial-velocity-squared field eta_alpha(ˆn) (Eqs. 30, 42, 43). The ionized-electron power spectrum is derived from an HOD-based bubble model following Refs. [13, 43, 47], with explicit dependence on the assumed small-scale electron profile. Fisher-matrix forecasts (Eq. 49) are presented for two baselines, CMB-S4 x LSST and CMB-HD x MegaMapper, jointly marginalizing over ten reionization parameters plus a velocity-to-galaxy bias ratio b_vg. The authors find that the KK auto-correlation alone constrains only H reionization (y_re^H within 1 sigma), while adding the K eta cross-correlation yields sub-1 sigma errors on all H reionization parameters and roughly 1 sigma errors on the He redshift-evolution parameters y_re^He and Delta_y^He for CMB-HD x MegaMapper (Figs. 9-10). The He signal is shown to be strongly suppressed relative to H in the redshift-integrated KK statistic, which motivates the tomographic cross-correlation. The paper's closing claims are explicitly conditional on an idealized velocity-reconstruction model and on the neglect of several non-Gaussian foreground terms, as discussed in the major comments.

Significance. The proposed K-eta cross-correlation is a genuinely new observable, and the joint H+He treatment with explicit H x He mixed terms is more complete than earlier forecasts. If the He constraints hold up, the kSZ trispectrum becomes a quantitative joint probe of both reionization epochs, and the LSST-versus-MegaMapper comparison gives a concrete, actionable argument for a Stage-5 spectroscopic survey. Strengths worth naming explicitly: all signal and noise expressions are given in closed form (Eqs. 31-32, 39-43, 48), making the forecasts reproducible from the text alone; the P^ion_ee derivation reduces to the established expressions of Refs. [13, 43, 47] in the appropriate limits; the manuscript is transparent about its omitted effects (photo-z errors, scale-dependent velocity-reconstruction bias, tSZ/lensing/CIB non-Gaussian terms) and cites Refs. [91, 92] for the magnitude of the photo-z degradation; and the electron-profile dependence of the forecasts is explored rather than ignored. The tension between these explicit limitation statements and the strength of the abstract's and Sec. IV C's claims is the main reason the revision is major rather than minor.

major comments (3)
  1. [III B, Eqs. (35)-(43); Sec. V] The headline He reionization claim (Fig. 10: y_re^He and Delta_y^He measurable at roughly 1 sigma) rests on the idealized model of the galaxy-reconstructed eta field in Eqs. (35)-(43). The signal template in Eq. (43) uses the true power spectrum P_etaeta, which is only recovered if the estimator weights satisfy P_{eta-hat,eta} = P_etaeta exactly (Eq. 36), and the only velocity noise is the shot-noise term of Eq. (39) with b_v = 1 at all redshifts. The manuscript itself lists the violations (photo-z errors, redshift-space distortions and fingers-of-God, survey masks, satellite velocity bias, smoothing) and states in Sec. V that 'we do not include the effects of photo-z errors,' citing Refs. [91, 92] for a factor of about 2 SNR reduction at low redshift for LSST-like samples. Because the projected He fractional errors in Fig. 10 sit close to unity at the plateau beyond L_max ~ 100-200, a factor-of-2 suppression of C^{K eta} or inflation of N^{eta eta} pushes y_re^He and Delta_y^He above unit fractional error, erasing the central claim for He; a single marginalization over b_vg cannot absorb the scale-dependent transfer functions found in Refs. [91, 92]. I regard this as the decisive sensitivity of the paper's main claim, and I request a quantitative stress test that propagates a fiducial scale-dependent reconstruction transfer function and noise model (or, minimally, a factor-of-2 degradation applied to C^{K eta} and N^{eta eta}) and that reports whether the He parameters remain below unit fractional error.
  2. [IV A; Sec. V] The KK noise model N^{KK}_L (Eq. 32) and the covariance (Eq. 48) assume a Gaussian small-scale temperature field. The tSZ Poisson contribution ('roughly modeled as a constant offset for large L'), the lensing-induced trispectrum ('comparable to the reconstruction noise N^{KK}_L'), and non-Gaussian CIB/tSZ cross terms are explicitly left out, and the authors state in Sec. IV A that they 'do not account for nuisance parameters to marginalize over this shot-noise effect.' These terms enter the covariance of both the KK and K eta spectra and hence influence the He and H parameter errors directly. This omission matters at the claimed precision: the paper's own electron-profile variation study in Sec. IV C shows changes in forecasted fractional errors up to factors of about 2 between the NFW/AGN and W_e x NFW electron profiles, and the late-time electron distribution is not itself marginalized. I request that at least one representative nuisance marginalization be added (for example, a free amplitude for the late-time kSZ/tSZ offset and a free late-time electron-profile amplitude), or that the authors demonstrate quantitatively that these terms do not shift the Fig. 10 error bars in the relevant direction.
  3. [II C 2; Fig. 10] The amplitude of the He-dependent signal that drives the Fig. 10 constraints is set by the fiducial patchy-He parameters Rbar_He = 15 Mpc, sigma_lnR^He = ln 2, and b_He = 6.0, which the authors adopt 'due to weaker current constraints and a shortage in simulations of He reionization' (Sec. II C 2). In a Fisher forecast the parameter errors scale approximately inversely with the modeled signal amplitude, so the headline He result is conditional on the He bubble model in a way that the H result, anchored by more abundant observational and simulation input, is not. Because the He errors are marginal even at the fiducial point, I recommend a short robustness scan over the He bubble parameters (for example Rbar_He = 5 and 30 Mpc, and b_He = 4 and 10) to confirm that the measurability claim is not an artifact of the fiducial choice, or an explicit statement that the He constraints are model-conditional.
minor comments (6)
  1. [Figs. 9-10] The line-style mapping stated in Sec. IV C (solid = y_re, dashed = Delta_y, dot-dashed = Rbar, dotted = sigma_lnR) does not match the order in which the legend entries appear in the figure files (y_re, Delta_y, sigma_lnR, Rbar); please make the style-to-parameter mapping unambiguous and consistent between the text, the captions, and the legends.
  2. [IV C] The statement that in the absence of He terms and bubble parameters the forecasts 'appropriately condense to the forecasts presented in Ref. [26]' is asserted without a numerical check, despite Sec. III A reporting substantial model differences from Ref. [25] (for example, a stronger late-time contribution to C^{KK}_L); a short table comparing marginalized errors with Ref. [26] would substantiate this claim.
  3. [References] The bibliography contains duplicates: Refs. [15] and [17] are the same La Plante et al. paper, Refs. [16] and [18] are the same paper, Refs. [49] and [106] are the same Shaw, Rudd, and Nagai paper, and Refs. [45] and [80] are the same Planck result; please consolidate the duplicate entries.
  4. [Throughout] There are several typos, including 'due to is low relative abundance' in Sec. I, 'Ref, [25]' in Sec. III A, 'th CMB S4 x LSST' in the Fig. 10 caption, and 'the estimation SNR' in Sec. IV C; a careful proofread is needed.
  5. [II C 2] The sentence 'we assume sigma^H_lnR = sigma^He_lnR = ln 2' mixes the already-fixed H value with the new He assumption; it should read 'we assume sigma^He_lnR = ln 2 (the same value as sigma^H_lnR)' for clarity.
  6. [III A, after Eq. (31)] The statement that P^perp_etaeta 'results in a z-independent quantity' is asserted without a derivation; since this property underlies the use of Eq. (42) in the forecasts, a one-line confirmation of the cancellation (for example in Appendix B) would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a Fisher-matrix sensitivity forecast whose adopted reionization model is explicitly attributed to prior work and anchored to external data, so no prediction reduces to a fitted input or self-citation chain.

full rationale

This paper is a Fisher-matrix sensitivity forecast, not an observational measurement. The reionization model (tanh mean-ionization evolution, lognormal bubble-radius distribution) is explicitly adopted from Refs. [13,43] with fiducial values separately anchored to external data, including Planck optical-depth measurements and Ly-alpha forest observations; the paper does not fit those parameters to data and then relabel the fit as a prediction. The kSZ trispectrum signal and the proposed K-eta cross-spectrum are derived from the linear velocity power spectrum and the adopted ionized-electron power spectrum through Eqs. (29)-(43), with noise terms computed from Gaussian covariance and survey specifications. The claimed He-reionization constraints are inverse-Fisher errors around the fiducial model, so they are conditional on the model, but the derivation does not reduce a predicted quantity to an equivalent input by construction. The self-citations to Refs. [13,25,26,43] supply the estimator and signal model, but these are prior published results with external observational anchors; they are not invoked as an unverified uniqueness theorem or as the sole justification for a forced choice. Acknowledged limitations, such as neglected photo-z errors, velocity-reconstruction biases, and foreground trispectra, affect forecast robustness rather than circularity. No circular step was found.

Assumptions & free parameters 11 free parameters · 9 assumptions · 0 invented entities

The central forecast depends on ten fiducial reionization parameters plus a velocity bias parameter, all chosen by hand or carried from previous work, and on a set of physical approximations about reionization morphology and velocity reconstruction. No new physical entities are introduced; the reconstructed eta field is an estimator built from galaxy data, not a new substance.

free parameters (11)
  • y_re^H fiducial = 33.5
    Sets the midpoint of hydrogen reionization in the tanh model Eq. (15); chosen to match z~9 reionization and Planck tau, and used as fiducial for Fisher forecasts.
  • Delta_y^H fiducial = 8.0
    Duration of H reionization in Eq. (15); followed from Refs. [13,43].
  • y_re^He fiducial = 8.0
    Midpoint of helium reionization, z~3; chosen from quasar and IGM constraints, with no direct measurement of patchiness.
  • Delta_y^He fiducial = 3.5
    Duration of He reionization; chosen from quasar and IGM constraints.
  • Rbar_H fiducial = 5 Mpc
    Characteristic H bubble radius in the log-normal P(R), Eq. (16); from Dvorkin and Smith [43].
  • sigma_lnR^H fiducial = ln 2
    Width of the H bubble radius distribution; from [43].
  • Rbar_He fiducial = 15 Mpc
    Characteristic He bubble radius; chosen by hand, consistent with Refs. [8,13], with weak empirical constraints admitted in Sec. II C.
  • sigma_lnR^He fiducial = ln 2
    Assumed equal to the H width, justified only by a shortage of He reionization simulations (Sec. II C).
  • b_X bubble bias fiducial = 6.0
    Constant bubble bias for both H and He; not varied in the signal forecasts and marginalized in the Fisher forecasts.
  • b_vg = b_v/b_g fiducial = 1/b_g(z) with b_v=1
    Nuisance parameter combining velocity reconstruction bias and galaxy bias; b_v=1 is assumed with no photo-z degradation.
  • Electron profile piecewise choice = NFW for z>5, AGN for z<5
    Ad hoc switch between halo electron profiles; forecasted SNRs vary by factors up to roughly 4 in the H-dependent case depending on the assumed profile.
assumptions (9)
  • standard math Wick's theorem factorization of four-point functions in Eqs. (3) and (17)
    The ionized electron power spectrum is built by neglecting connected four-point terms and expanding products of two-point functions.
  • standard math Limber approximation in Eqs. (30), (42), and (43)
    Angular power spectra of C_KK, C_etaeta, and C_Keta are evaluated under the flat-sky Limber approximation.
  • domain assumption Linear-theory velocity power spectrum and z-independent P_perp_etaeta
    The eta-field power spectrum in Eq. (31) is computed in linear perturbation theory, ignoring nonlinear velocity contributions and redshift evolution of the integral.
  • domain assumption Bubble model: Poisson-distributed spherical ionized regions with log-normal radius distribution, bubbles trace linear matter density with constant bias, no redshift evolution of bubble distribution
    Equations (8)-(16) parameterize reionization through bubbles, adopted from Refs. [13,43,47].
  • domain assumption tanh redshift evolution of ionization fraction Eq. (15) and no overlap modeling beyond additive H and He fields
    The mean ionization fraction is a tanh function of (1+z)^(3/2), and He reionization is added linearly to H reionization.
  • domain assumption All electrons reside in halos with the cosmic baryon fraction, Eq. (6), neglecting gas collapse into stars
    The HOD model sets N_e(M,z) proportional to halo mass with no deficit from star formation, stated in Sec. II B.
  • domain assumption Galaxy density reconstructs the linear velocity field via Eq. (33) with no fingers-of-God, no photo-z errors, and shot-noise-dominated velocity noise
    The velocity reconstruction formalism in Sec. III B assumes the linear continuity equation and b_v=1.0, with all systematics deferred to future work.
  • domain assumption The Smith-Ferraro (2017) kSZ trispectrum statistic isolates kSZ from other non-Gaussian CMB signals; no lensing, tSZ, or CIB trispectrum marginalization
    The reconstruction noise in Eq. (32) assumes the small-scale temperature field is Gaussian apart from kSZ; foreground and lensing trispectra are neglected.
  • domain assumption Planck 2018 LambdaCDM cosmology
    All forecasts use Planck 2018 parameter values as the background cosmology, stated in the introduction.

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Cite this review

Pith. "Pith review of Patchy Helium and Hydrogen Reionization from the Kinetic Sunyaev-Zel'dovich Effect and Galaxies." pith.science (2026). https://pith.science/paper/QWSHJ5RT

@misc{pith2026250611188,
  author       = {Pith},
  title        = {Pith review of: Patchy Helium and Hydrogen Reionization from the Kinetic Sunyaev-Zel'dovich Effect and Galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QWSHJ5RT}},
  note         = {Machine review of arXiv:2506.11188}
}
read the original abstract

Upcoming cosmic microwave background (CMB) experiments will measure temperature fluctuations on small angular scales with unprecedented precision, enabling improved measurements of the kinetic Sunyaev-Zel'dovich (kSZ) effect. This secondary anisotropy has emerged as a valuable probe of the distribution of ionized electrons in the post-recombination Universe. Although the sensitivity of the kSZ effect has recently been utilized to study the high-redshift epoch of hydrogen (H) reionization, its redshift-integrated nature -- combined with anticipated improvements in measurement precision -- suggests that accounting for the later epoch of helium (He) reionization will become increasingly important in the near future. Joint characterization of the epochs will allow for a more coherent understanding of early-star and -quasar formation, as these sources drive the ionization of H and He in the intergalactic medium. In this paper, we extend the kSZ higher-order statistic introduced by Smith \& Ferraro (2017) to forecast the ability of upcoming CMB surveys to probe the morphology of both H and He reionization. Moreover, given that upcoming large-scale structure surveys will trace density fluctuations at redshifts overlapping with the epoch of He reionization, we propose a novel cross-correlation between the kSZ higher-order statistic and galaxy survey measurements. Using a joint information-matrix analysis of H and He reionization, we show that next-generation CMB and galaxy surveys will have sufficient statistical power to characterize the patchy morphology of H reionization and set constraints on the redshift evolution of its He counterpart.

Figures

Figures reproduced from arXiv: 2506.11188 by the authors.

Figure 1
Figure 1. FIG. 1. Summary of the patchy-reionization model assumed [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Lensed-primary CMB (pink-solid curve) and sepa [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The angular power-spectra [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Separate contributions to the binned [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Detection SNR as a function of the maximum ac [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Fractional errors on fiducial H and He reionization parameters as a function of maximum multipole [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Same fractional errors as Fig [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Fractional errors on reionization parameters [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Total electron power spectrum [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]

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