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Reionization optical depth determination from Planck HFI data with ten percent accuracy

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Re-analyzing Planck HFI data with an upgraded mapmaker, this paper measures the reionization optical depth as $\tau = 0.059 \pm 0.006$ (68% C.L.), a 10% measurement it argues is the strongest constraint to date.

desk verdict A careful, credible reanalysis that likely gives the tightest CMB tau so far, but the quoted error bar is set by the same systematics model the mapmaker fits, so treat 0.006 as an optimistic floor. read the letter →

arxiv 1908.09856 v2 pith:TY3G7YQN submitted 2019-08-26 astro-ph.CO

L. Pagano , J.-M. Delouis , S. Mottet , J.-L. Puget , L. Vibert This is my paper · ORCID
classification astro-ph.CO
keywords reionizationopticaldepthcosmicmicrowavebackgroundpolarizationPlanckHFISRoll2map-makingADCnon-linearitylarge-scalecosmologicalparametersredshift
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 residual large-scale systematic contamination in the Planck High Frequency Instrument (HFI) polarization maps, left incompletely removed in the 2018 legacy release, can be pushed below the noise level with an upgraded map-making algorithm called SRoll2. The authors measure the reionization optical depth from the cleaned 100$\times$143 GHz EE cross-spectrum as $\tau = 0.0566^{+0.0053}_{-0.0062}$ (68% C.L.), and, within the $\Lambda$CDM model combined with the Planck temperature and high-$\ell$ polarization likelihoods, as $\tau = 0.059 \pm 0.006$, corresponding to a mid-point reionization redshift $z_{\rm re} = 8.14 \pm 0.61$. Since the CMB sees the primordial fluctuation amplitude only through $A_s e^{-2\tau}$, a 10% measurement of $\tau$ gives about 1% accuracy on $A_s$ and breaks the main degeneracy that has made $\tau$ the least constrained $\Lambda$CDM parameter. The result matters because reionization is the last major phase transition of the universe and its timing is a direct probe of early galaxy formation.

What carries the argument

The load-bearing element is SRoll2, an upgraded version of the SRoll map-making code described in the companion paper. It corrects the second-order ADC non-linearity by fitting a two-dimensional spline per bolometer as a function of signal value and time, so that a single gain fits the entire mission and the temperature-to-polarization dipole leakage is removed. The analysis proceeds with the 100$\times$143 GHz EE cross-spectrum estimated with a quadratic maximum-likelihood estimator (QML) on a 50% sky mask, and a simulation-based likelihood, lowE-S2, constructed from 500 noise-plus-systematics-plus-foreground-residual Monte Carlo realizations, interpolated over a grid in $\tau$ with $10^9 A_s e^{-2\tau} = 1.875$ fixed.

What would settle it

Re-run the SRoll2 pipeline on simulated timelines with a known input $\tau = 0.051$ while injecting ADCNL residuals at twice the amplitude used in the published simulation set; if the recovered $\tau$ moves upward by the roughly 0.008 shift seen between Planck 2018 and SRoll2, the systematic estimate is under-correcting. Equivalently, an independent map-making code that does not use the SRoll2 spline model, applied to the same raw data, should reproduce the same EE quadrupole and octupole within the reported noise.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the second-order analogue-to-digital converter non-linearity in the Planck HFI readout chains, when modelled with a per-bolometer spline fit, removes the dipole-to-polarization leakage that dominated the lowest multipoles of the 2018 legacy maps; the cleaned 100$\times$143 GHz EE spectrum then gives $\tau = 0.0566^{+0.0053}_{-0.0062}$ from polarization alone. Combining the new lowE-S2 likelihood with Planck's low-$\ell$ Commander temperature likelihood and high-$\ell$ temperature and polarization likelihood gives $\tau = 0.059 \pm 0.006$ (68% C.L.), $z_{\rm re} = 8.14 \pm 0.61$, and $\sigma_8 = 0.8128 \pm 0.0053$. The paper states this is the strongest reionization optical depth constraint to date, with the uncertainty reduced by roughly 40% relative to the Planck 2018 legacy value $\tau = 0.051 \pm 0.009$; the central value shifts upward by about one $\sigma$ while the 95% upper limit stays near $\tau \lesssim 0.07$.

Load-bearing premise

The result assumes that the N+S+F-MC simulations, built with the same SRoll2 code and a simulated sky model, reproduce the real instrument's residual systematics faithfully; if the ADCNL model or the input sky is incomplete, the quoted error bars and the upward shift in $\tau$ would be underestimated.

Editorial extensions

If this is right

  • The $\tau$ uncertainty drops to about 10%, which propagates to roughly 1% accuracy on the primordial fluctuation amplitude $A_s$ via the $A_s e^{-2\tau}$ degeneracy.
  • The mid-point reionization redshift $z_{\rm re} = 8.14 \pm 0.61$ gives a direct CMB-side target for astrophysical models of early galaxy formation and for high-redshift galaxy surveys.
  • Replacing the Planck 2018 lowE likelihood with lowE-S2 leaves the other $\Lambda$CDM parameters essentially unchanged, while tightening $\sigma_8$ to $0.8128 \pm 0.0053$ and slightly lowering the lensing amplitude parameter $A_L$ to $1.163 \pm 0.064$.
  • Systematics no longer dominate the low-$\ell$ EE error budget: cosmic variance does, so further tightening from the same sky requires either more sky coverage or a different observable.
  • The $\tau$ upper limit remains close to $0.07$ at 95% C.L., so the minimal one-parameter extensions of $\Lambda$CDM explored in the paper are not significantly affected.

Reading between the lines

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

  • If the systematics estimates are right, an independent re-analysis of the same raw timelines with a map-making code that does not assume the SRoll2 spline model should reproduce the recovered quadrupole and octupole in EE within the reported errors; agreement would effectively close the map-making chapter of Planck HFI large-scale polarization.
  • The same second-order ADC non-linearity correction strategy could be applied to other bolometric CMB instruments with similar readout chains, potentially cleaning their large-scale polarization before launch or in re-processing.
  • The paper notes a semi-analytical likelihood is now feasible; because cosmic variance dominates the error budget, that likelihood should give nearly identical $\tau$ posteriors, and disagreement would flag a problem in the simulation-based estimate.
  • If the true $\tau$ is near 0.059 rather than the earlier 0.051, reionization models need somewhat more ionizing photons around $z \sim 8$; future high-redshift observations should see a correspondingly earlier or more efficient reionization history.
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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

2 major / 4 minor

Summary. This paper presents a new low-multipole polarization analysis of Planck HFI data using the SRoll2 map-making algorithm, which is designed to remove the second-order ADC nonlinearity (ADCNL) systematic that produces temperature-to-polarization dipole leakage. The authors build a 100x143 GHz EE cross-spectrum likelihood from an empirical distribution of signal plus N+S+F Monte Carlo simulations, and measure tau = 0.0566 (+0.0053, -0.0062) at 68% CL from the EE spectrum alone, with the external normalization 10^9 A_s e^{-2 tau} = 1.875. Combined with the Planck 2018 temperature and high-multipole polarization likelihoods, they report tau = 0.059 +/- 0.006, corresponding to z_re = 8.14 +/- 0.61 and sigma_8 = 0.8128 +/- 0.0053, and claim this is the strongest tau constraint to date with ten percent accuracy. The analysis includes extensive stability tests over sky fractions, multipole ranges, foreground templates, and null spectra.

Significance. If the systematics model is realistic, this is an important result: it reduces the Planck 2018 legacy-release uncertainty on tau by about 40% and breaks the A_s-e^{-2 tau} degeneracy more effectively, yielding a tight sigma_8 constraint. The paper is careful in its internal consistency checks: multiple masks, multipole cuts, alternative foreground tracers, and a large Monte Carlo suite are used, and the maps, simulations, and likelihood are made public. The main limitation is that the error budget and the claim that the ADCNL systematic is below noise are validated with simulations generated from the same ADCNL model that SRoll2 fits, so the quoted 10% uncertainty is conditional on the completeness of that model.

major comments (2)
  1. [§2, Figs. 1–3; §4 (N+S+F-MC)] The central claim that SRoll2 brings the second-order ADCNL dipole-leakage systematic below the noise level is established with simulated timelines that contain exactly the ADCNL model fitted by SRoll2 and are then processed with SRoll2 itself. This is a self-consistency test, not an independent validation of the completeness of the ADCNL model or the realism of the simulated instrument noise. The empirical likelihood and the quoted 68% errors in Eq. (3) are built from N+S+F-MC simulations generated with the same model, so the error budget inherits the same assumption; the data-based PTE tests in Table 2 are also computed against the same simulations. The persistent poor PTEs of the null TE spectra reported in Section 4 are a data-side indication that the systematics model may not be complete. I therefore ask for a quantitative robustness test, for example rerunning the tau likelihood with residual maps from a deliberately different ADCNL model (varied spline flexibility or amplitude, or SRoll1 maps) and reporting the induced shift in tau, or adding an explicit model-error contribution to the error budget. Without such a test, the headline 10% error bar rests on a single assumed systematics model.
  2. [§4, TE-only result] The TE-only measurement tau = 0.057 (+0.012, -0.013) is presented as confirmation of the EE result, but the same paragraph states that the poor PTEs of the null TE spectra persist in this data version. Because the TE analysis uses the Commander temperature map based on SRoll1, the TE anomaly may not directly affect the EE pipeline, but the claim of an independent confirmation is weakened. Please quantify the sensitivity of the headline tau to the multipoles or angular scales most affected by the TE anomaly, for example by truncating the EE likelihood at l_min = 4 or 6, or by masking the regions where the TE null PTE is lowest, and state explicitly whether the anomaly is attributed to the temperature map or to residual polarization systematics, with a supporting test.
minor comments (4)
  1. [Table 1] The beta column header appears inconsistent with the entries: with the label beta x 10^2, the 100 GHz entry 1.86 gives beta = 0.0186, while the 143 GHz entry 0.0394 would give beta = 3.94 x 10^-4, contradicting the text's statement that the dust tracer is scaled by beta = 0.039. Please clarify the units or correct the typo.
  2. [§4 and Eq. (2)] The empirical likelihood is built from 500 simulations per tau value with piecewise-polynomial interpolation; the paper does not report how sensitive the final tau interval is to the number of simulations or to the interpolation order. A brief convergence statement would strengthen the result.
  3. [Figure 9] The correlation-matrix values in Figure 9 are very hard to read in the printed version; a color map with labeled axes would be much clearer and would make the claimed near-diagonality more immediately apparent.
  4. [Abstract and §4] The standalone EE value tau = 0.0566 is conditional on the fixed external normalization 10^9 A_s e^{-2 tau} = 1.875; this is disclosed in Section 4 but should be stated explicitly in the abstract or in the sentence quoting the standalone value, to avoid the impression that it comes from polarization data alone.

Circularity Check

1 steps flagged · score 2.0 of 10

Tau measurement is data-driven, but the systematics validation and error budget are self-referential: the ADCNL model fitted by SRoll2 is also the model used in the simulations that claim residuals are below noise.

  1. other [Section 2, Figs. 1-3; Section 3-4, N+S+F-MC likelihood construction]
    "New ADCNL correction is obtained by fitting the residuals with a bi-dimensional spline model per bolometer... Figure 1 shows polarization intensity maps ... obtained simulating realistic sky signal affected by ADCNL and projected with SRoll1 and SRoll2 codes. ... The simulated timelines contain dipole, sky signal, systematic effects and electronic noise only. ... The same cleaning procedure is applied to a set of 500 Monte Carlo simulations containing realistic sky signal, noise and systematic effects."

    The spline model used to correct ADCNL is fitted by the same SRoll2 algorithm; the simulations in Figs. 1-3 are generated with that exact fitted model and then processed with the same code, so the 'below the noise level' residuals demonstrate only that SRoll2 removes its own assumed systematic, not that the ADCNL model is complete. The N+S+F-MC simulations that define the empirical likelihood and the quoted ±0.006 uncertainty inherit this same fitted model, so the 10% accuracy claim is not validated against unmodeled systematics. The tau central value is measured from real maps rather than constructed from the model, so the circularity is partial and limited to the error budget and systematics claim.

full rationale

The central tau estimate is obtained by applying a QML cross-spectrum estimator to real 100x143 GHz SRoll2 maps and comparing with an empirical likelihood, so tau is not equal to any fitted input by construction. The fixed normalization 10^9 A_s e^{-2tau}=1.875 is an external input that does not determine tau. The main circularity burden is the self-referential ADCNL validation: the mapmaker's fitted ADCNL model is also the systematic injected into the simulations used to claim systematics are below noise and to build the N+S+F-MC error distribution. This makes the uncertainty estimate and the 'below noise' claim consistency checks of the assumed model rather than independent verifications, warranting a mild score of 2; the persistent TE null anomaly noted by the authors reinforces this as a correctness risk, not a further circularity.

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

The central tau measurement rests on a standard simulation-based likelihood, but the cleaned maps depend on fitted foreground scalings, a fixed external amplitude normalization, and the assumption that the authors' SRoll2 simulations capture the instrument systematics. No new physical entities are introduced.

free parameters (6)
  • alpha_100 (synchrotron template scaling for 100 GHz) = 0.0095 ± 0.0007
    Fitted to data in foreground template cleaning; Table 1. It sets the amplitude of the synchrotron template subtracted from the 100 GHz maps.
  • beta_100 (dust template scaling for 100 GHz) = 0.0186 ± 0.00015
    Fitted to data in foreground template cleaning; Table 1. It sets the amplitude of the dust template subtracted from the 100 GHz maps.
  • alpha_143 (synchrotron template scaling for 143 GHz) = 0.0163 ± 0.0021
    Fitted to data in foreground template cleaning; Table 1. It sets the amplitude of the synchrotron template subtracted from the 143 GHz maps.
  • beta_143 (dust template scaling for 143 GHz) = 0.000394 ± 0.00014
    Fitted to data in foreground template cleaning; Table 1. It sets the amplitude of the dust template subtracted from the 143 GHz maps.
  • Diagonal regularization noise added to covariance = 20 nK
    Added to keep the covariance matrices invertible after downgrading to Nside=16 and windowing; Section 3. Chosen by hand.
  • Baseline sky fraction for tau measurement = f_sky = 0.50
    Chosen as the baseline among the masks in Figure 6; Section 4. All masks give consistent tau within 1.3 sigma, but the final reported value is tied to this mask.
assumptions (6)
  • domain assumption 10^9 A_s e^{-2 tau} = 1.875 is fixed when building the EE-only likelihood.
    Section 4: this external normalization, taken from Planck Collaboration Int. XLVI (2016), breaks the A_s-tau degeneracy in the standalone low-l EE estimate.
  • domain assumption The other LambdaCDM parameters are fixed to the Planck 2018 best fit when sampling tau from the EE spectrum.
    Section 4: theoretical spectra C_l(tau, theta) are generated with theta fixed to Planck Collaboration VI (2019) values.
  • domain assumption FFP8 covariance matrices adequately describe the noise of the QML estimator.
    Section 3: the paper states these matrices are suboptimal but unavoidable and capture only white and 1/f noise, not systematic variance.
  • domain assumption Multipoles l = 2 to 29 are negligibly correlated in the tau likelihood.
    Section 4, Eq. 2: the likelihood sums per-multipole log-probabilities; Figure 9 supports weak correlation in the relevant range but not exact zero.
  • domain assumption Residual foregrounds after template cleaning are negligible at low multipoles.
    Sections 2-3: cleaned maps are used as CMB signal; tests with alternative tracers are shown, but the template amplitudes are not marginalized over.
  • domain assumption The N+S+F-MC simulations faithfully represent the noise, systematics, and foreground residuals in SRoll2 maps.
    Sections 2-3 and Table 2: all error bars and consistency tests use these simulations, which are produced with the same authors' SRoll2 pipeline.

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Cite this review

Pith. "Pith review of Reionization optical depth determination from Planck HFI data with ten percent accuracy." pith.science (2026). https://pith.science/paper/TY3G7YQN

@misc{pith2026190809856,
  author       = {Pith},
  title        = {Pith review of: Reionization optical depth determination from Planck HFI data with ten percent accuracy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TY3G7YQN}},
  note         = {Machine review of arXiv:1908.09856}
}
abstract

We present an estimation of the reionization optical depth $\tau$ from an improved analysis of the High Frequency Instrument (HFI) data of Planck satellite. By using an improved version of the HFI map-making code, we greatly reduce the residual large scale contamination affecting the data, characterized, but not fully removed, in the Planck 2018 legacy release. This brings the dipole distortion systematic effect, contaminating the very low multipoles, below the noise level. On large scale polarization only data, we measure $\tau=0.0566_{-0.0062}^{+0.0053}$ at $68\%$ C.L., reducing the Planck 2018 legacy release uncertainty by $\sim40\%$. Within the $\Lambda$CDM model, in combination with the Planck large scale temperature likelihood, and the high-$\ell$ temperature and polarization likelihood, we measure $\tau=0.059\pm0.006$ at $68\%$ C.L. which corresponds to a mid-point reionization redshift of $z_{\rm re}=8.14\pm0.61$ at $68\%$ C.L.. This estimation of the reionization optical depth with $10\%$ accuracy is the strongest constraint to date.

Figures

Figures reproduced from arXiv: 1908.09856 by the authors.

Figure 1
Figure 1. Polarization intensity maps at 100 and 143 GHz obtained applying SRoll1 and SRoll2 to a set of simulated timelines. The input sky has been subtracted after the map projection. The simulated timelines contain dipole, sky signal, systematic effects and electronic noise only. The first row shows maps obtained running SRoll1 with only one gain for the entire mission, the middle row shows SRoll1 with 128 gain steps, as u… view at source ↗
Figure 2
Figure 2. EE pseudo auto-spectra evaluated for 100 GHz (solid) and 143 GHz (dashed) on the simulations shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Data Q and U maps at 100 GHz cleaned from synchrotron and dust emissions. Top row shows the Planck 2018 legacy re￾lease computation obtained with SRoll1, while the bottom one the SRoll2 computation. Sroll1 Q 2 ¹K 2 CMB Sroll1 U 2 ¹K 2 CMB Sroll2 Q 2 ¹K 2 CMB Sroll2 U 2 ¹K 2 CMB [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (11 more)
Figure 5
Figure 5. Figure 5: Data Q and U maps at 143 GHz cleaned from synchrotron and dust emissions. Top panel shows the Planck 2018 legacy re￾lease computation obtained with SRoll1, while the bottom one the SRoll2 computation. synchrotron at 100 and 143 GHz respectively. The scalings found are …
Figure 8
Figure 8. Figure 8: Comparison between Planck 2018 legacy release and SRoll2 error bars for 100 × 143 spectrum both on 50% of the sky. For SRoll1 Planck 2018 FFP10 Planck Collaboration III (2019) simulations have been used, for SRoll2 N+S+F-MC sim￾ulations presented in Delouis et al. (201…
Figure 6
Figure 6. Figure 6: Masks used for the present analysis. The 70% mask is used for the foreground cleaning, the others in the cosmological analysis. All the masks used in this analysis are binary maps, without any apodization applied. 5 10 15 20 25 Multipole - 0.00 0.05 0.10 0.15 E E [ K 2…
Figure 7
Figure 7. Figure 7: Low-` EE cross spectrum 100x143 for the Planck 2018 legacy release (blue points) and for the SRoll2 maps (orange). The mask used retains 50% of the sky. The error bars are Monte Carlo based and do include cosmic variance. The black line cor￾responds to a EE power spect…
Figure 10
Figure 10. Figure 10: Error comparison for the 100 × 143 spectrum on 60% of the sky. We show the total error (blue bar), the amount solely due to cosmic variance (orange), and only due to noise and sys￾tematic effects (green). The cosmic variance shown corresponds to τ = 0.055. 5 10 15 20 …
Figure 11
Figure 11. Figure 11: EE power spectra of 100 × 143 for different sky frac￾tions. Error bars are obtained from the distribution of 500 signal (with τ = 0.055) + N+S+F-MC simulations. The black solid line corresponds to a EE power spectrum with τ = 0.055. 5 10 15 20 25 Multipole - 0.15 0.10…
Figure 12
Figure 12. Figure 12: Low-` BB cross spectrum 100×143 for the Planck 2018 legacy release (blue points) and for the SRoll2 maps (orange). The mask used retains 50% of the sky. The error bars are Monte Carlo based and do include cosmic variance. – we generate 101 theoretical power spectra, C…
Figure 15
Figure 15. Figure 15: Posteriors of τ obtained removing one multipole at a time. 0.04 0.05 0.06 0.07 ¿ K - 30 K - Ka K - K 30 - Ka [PITH_FULL_IMAGE:figures/full_fig_p007_15.png]
Figure 16
Figure 16. Figure 16: Posteriors of τ obtained using different synchrotron trac￾ers for 100 and 143 GHz. The channels reported on the left side of the figure refer to the synchrotron tracers used for 100 and 143 GHz respectively. error bars, likely due to the smaller leverage of 217 GHz no…
Figure 14
Figure 14. Figure 14: shows the effect of changing the minimum multi￾pole used in Eq. 2. The τ posteriors are stable up to `min = 5, further explorations being less meaningful due to the drop of the reionization feature above those multipoles. 0.04 0.05 0.06 0.07 ¿ `min = 2 `min = 3 `min =…
Figure 18
Figure 18. Figure 18: History of τ determination from WMAP to Planck. With Planck T tag we refer to Planck low-` and high-` temperature likelihood, with Planck T-E, we refer to low-` and high-` tem￾perature likelihood combined with high-` T E and EE likelihood. WMAP 9yr + Planck 353 refers…

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