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Measurements of the Temperature and E-mode Polarization of the Cosmic Microwave Background from the Full 500-square-degree SPTpol Dataset

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Using the full four-year SPTpol 500-square-degree dataset, this paper presents TE and EE CMB power spectra over $50<\ell<8000$ and argues they are the most sensitive lensed-damping-tail measurements for $\ell>1700$ in TE and $\ell>2000$…

desk verdict A careful, honest data-release paper whose headline damping-tail claims hold up; the TE transfer-function construction is the soft spot to push on in review. read the letter →

arxiv 2501.06890 v2 pith:KXO3DA3N submitted 2025-01-12 astro-ph.CO

T.-L. Chou , P. A. R. Ade , A. J. Anderson , J. E. Austermann , L. Balkenhol , J. A. Beall , A. N. Bender , B. A. Benson
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F. Bianchini L. E. Bleem J. E. Carlstrom C. L. Chang P. Chaubal H. C. Chiang R. Citron C. Corbett Moran T. M. Crawford A. T. Crites T. de Haan M. A. Dobbs D. Dutcher W. Everett J. Gallicchio E. M. George N. Gupta N. W. Halverson G. P. Holder W. L. Holzapfel J. D. Hrubes N. Huang J. Hubmayr K. D. Irwin L. Knox A. T. Lee D. Li A. Lowitz J. J. McMahon J. Montgomery T. Natoli J. P. Nibarger G. I. Noble V. Novosad Y. Omori S. Padin S. Patil C. Pryke W. Quan C. L. Reichardt J. E. Ruhl B. R. Saliwanchik K. K. Schaffer C. Sievers G. Smecher A. A. Stark C. Tucker T. Veach J. D. Vieira G. Wang N. Whitehorn W. L. K. Wu V. Yefremenko J. A. Zebrowski
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classification astro-ph.CO
keywords cosmicmicrowavebackgroundE-modepolarizationangularpowerspectrumdampingtailSPTpolLambda-CDMmodelCMBlensingHubbleconstant
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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 uses the complete four-year SPTpol observation of a 500-square-degree patch of sky, in both the 95\,GHz and 150\,GHz bands, to measure the temperature$-$E-mode polarization cross-spectrum (TE) and the E-mode auto-spectrum (EE) over angular multipoles $50<\ell<8000$. Its central claim is that these are the deepest measurements of the lensed CMB damping tail to date, for roughly $\ell>1700$ in TE and $\ell>2000$ in EE. The authors show the dataset passes internal consistency checks across maps, frequency bands, and spectrum types, and that the full dataset is well fitted by the $\Lambda$CDM model, giving $H_0=70.48\pm2.16$\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ and $\Omega_m=0.271\pm0.026$ when a Planck-based prior on the reionization optical depth is adopted. They also report a persistent $\sim2\$\sigma$$ preference for a low lensing amplitude, $A_L=0.70\pm0.13$, and marginalizing over $A_L$ brings the parameters into agreement with Planck. If correct, the released spectra become the reference ground-based measurements of the small-scale CMB damping tail and a new cosmological constraint.

What carries the argument

The pipeline is a pseudo-spectrum analysis: cross-spectra of 50 map bundles are computed at $\Delta\ell=5$ and unbiassed by inverting the kernel $K=MFB^2$, where $M$ is the flat-sky analytic mode-coupling matrix from the apodization mask, $F$ is the filter transfer function, and $B$ is the beam. The transfer functions are solved iteratively from 226 simulated datasets generated from a single fiducial cosmology, with the TE transfer function constructed as the geometric mean of the TT and EE transfer functions because of TE zero-crossings; a 'TE bias' correction absorbs residual misrecovery of simulated TE spectra. The bandpower covariance combines a simulated signal-only part with an analytic noise form, and is 'further conditioned' by erasing 57 near-null eigenvectors before inversion. Cosmological fits use a CosmoPower-trained emulator for $\Lambda$CDM with nuisance parameters for calibration, beam eigenmodes, foregrounds, and super-sample lensing.

What would settle it

Recompute the TE bandpowers using a directly simulated TE transfer function (rather than the geometric mean of TT and EE) and compare with the published spectra; a shift of the $\ell>1700$ TE bandpowers by more than their quoted uncertainties would refute the headline sensitivity claim. Separately, an independent high-resolution CMB experiment covering the same patch and multipole range would settle whether $A_L=0.70\pm0.13$ is a real preference or a statistical fluctuation.

Watch

Extended reading notes

Core claim

The paper's discovery claim is that the SPTpol 500\,\text{deg}^2 field, observed for four years in two frequency bands, produces TE and EE power spectra that are the most sensitive probes of the lensed CMB damping tail for $\ell>1700$ (TE) and $\ell>2000$ (EE). On the paper's own terms, the full dataset is self-consistent, fits $\Lambda$CDM well (goodness-of-fit PTE of 0.10), and yields $H_0=70.48\pm2.16$\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$, $\Omega_m=0.271\pm0.026$, and $\sigma_8=0.758\pm0.022$ under a Planck-based $\tau$ prior. The data favor a lensing amplitude $A_L=0.70\pm0.13$, about $2\$\sigma$$ below unity; this low-$A_L$ preference drives most of the mild inconsistency between $\ell<1000$ and $\ell>1000$ parameter constraints, and when $A_L$ is floated the SPTpol constraints become consistent with Planck. The authors interpret the low $A_L$ as more likely a statistical fluctuation than evidence for reduced lensing, because lensing-reconstruction analyses of the same field are consistent with $A_L=1$.

Load-bearing premise

The analysis assumes that the 226 simulated time streams, generated from a single fiducial cosmology, reproduce the real telescope's filtering and noise response well enough that the derived transfer functions and TE bias corrections are unbiased; if the real data respond differently in a way the tests do not catch, the headline TE and EE damping-tail bandpowers would be biased.

Editorial extensions

If this is right

  • The released TE/EE bandpowers over $50<\ell<8000$ become the deepest ground-based reference for the lensed damping tail, sharpening constraints on parameters sensitive to small-scale damping (e.g., $n_s$, $H_0$, $\Omega_m$) in the multipole range 1700$-$8000.
  • The reported $H_0=70.48\pm2.16$\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ provides an independent ground-based CMB estimate (with a Planck $\tau$ prior) that sits between Planck and late-universe values.
  • If the $A_L\approx0.7$ preference is real, it would indicate that the acoustic peaks in this patch are less smoothed by lensing than $\Lambda$CDM predicts; the paper's own lensing-reconstruction cross-check indicates this is likely a statistical fluctuation.
  • The consistency between 95\,GHz and 150\,GHz, and between TE and EE, supports the foreground and calibration models used in the analysis, making the systematic budget credible for future combined analyses.

Reading between the lines

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

  • Because the TE transfer function is a geometric mean of TT and EE rather than a directly measured TE response, any scale-dependent difference between TE and TT/EE filtering would imprint a bias in the TE damping tail; a direct TE transfer-function calibration in simulations would test this and could alter the $\ell>2000$ TE claim.
  • The flat-sky mode-coupling matrix is cross-checked against a curved-sky version only over $500<\ell<3000$ in the 150\,GHz EE band; recomputing the full bandpower set with a curved-sky $M$ would test whether the low-$A_L$ preference could be a mode-coupling artifact.
  • The public release of maps, bandpowers, and covariance invites external reanalyses, e.g., with different $\tau$ priors or free neutrino mass, which would test the robustness of the reported $H_0$ and $A_L$ constraints.
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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 measurements of the CMB temperature-E-mode cross-power spectrum (TE) and E-mode auto-power spectrum (EE) from the full four-year SPTpol 500 deg^2 survey, using both the 95 GHz and 150 GHz bands and covering 50 < ell < 8000. The analysis uses pseudo-spectra from map bundles, an analytic flat-sky mode-coupling kernel, simulation-based filter transfer functions, and absolute calibration anchored to the Planck 143 GHz map. Under LCDM with a Planck-based prior on the reionization optical depth, the authors find H0 = 70.48 +/- 2.16 km/s/Mpc and Omega_m = 0.271 +/- 0.026, and they report a preference for AL = 0.70 +/- 0.13. The central claim is that the released TE and EE spectra are the most sensitive measurements of the lensed CMB damping tail for roughly ell > 1700 in TE and ell > 2000 in EE. The paper includes an extensive set of internal consistency checks: seven jackknife null tests, frequency-split consistency, minimum-variance bandpower tests, data-split parameter comparisons, and an alternate-cosmology pipeline recovery.

Significance. If the results hold, the public SPTpol spectra provide the deepest high-ell view of the CMB damping tail in TE and EE from a ground-based experiment, and the cosmological constraints are competitive with other contemporary CMB data sets. The paper's strengths are the breadth and care of its internal consistency program, the external anchoring of the calibration chain to Planck 143 GHz rather than to the paper's own target parameters, the candid discussion of the AL < 1 preference and the unexplained TE-only goodness-of-fit, and the public release of maps, bandpowers, covariance, and likelihood. The main correctness risks are concentrated in the simulation-based TE transfer-function and TE-bias corrections, which rest on a single fiducial cosmology, and in the conditioning of the bandpower covariance matrix, which requires erasing 57 eigenmodes before the internal consistency test is passed. These issues are concrete and testable, and they bear directly on the headline damping-tail claim, so they should be addressed before the paper is accepted.

major comments (3)
  1. [Section 4.3 and Section 4.6] The TE transfer function is not measured directly; it is defined as the geometric mean of the TT and EE transfer functions (Section 4.3), and the residual 'TE bias' is estimated from 226 simulated datasets generated from a single fiducial cosmology, Planck base_plikHM_TT_lowTEB_lensing (Section 4.6). The alternate-cosmology test in Section 6.3 uses 90 realizations of a very different cosmology, applies the same unbiasing kernel, and checks parameter recovery, but it does not compare the TE bias at the bandpower level. If the true sky's TE spectrum shape, or the foreground polarization levels, differ from the fiducial assumptions in a way that changes the TE bias, the high-ell TE bandpowers that support the headline damping-tail claim would be biased. Please either compute the TE bias for the alternate cosmology and compare it bandpower-by-bandpower with the fiducial TE bias, or measure the TE transfer function directly using a zero-crossing-safe procedure, or provide an analytic argument for why the geometric-mean and bias corrections are insensitive to the TE spectrum shape.
  2. [Section 5.3] The bandpower covariance matrix as constructed fails the minimum-variance internal consistency test (chi^2 too high for 280 degrees of freedom), and the paper conditions the matrix by setting 57 eigenvalues below 2.619e-5 of the largest eigenvalue to very large values. The justification is that a Kolmogorov-Smirnov test on 226 simulated chi^2 values passes and that parameter constraints are degraded by less than 6% in width. However, the erased eigenmodes are precisely the directions in which the estimated covariance is smallest; if those small eigenvalues are not purely spurious but reflect genuine near-degeneracies in the data vector, erasing information along them could hide real inconsistencies or underestimate uncertainties in those directions. The current tests check widths, not bias. Please report the eigenvalue spectrum, the projections of the actual data residual onto the 57 erased modes, and the sensitivity of the reported parameters and PTEs to the conditioning threshold.
  3. [Section 7.1, Table 4] The TE-only data split has a best-fit LCDM chi^2 = 238.11 for 180 degrees of freedom, corresponding to a PTE of 0.24%, and the paper states that the origin of this low PTE is not completely understood. The PTE improves to 1.5% when the highest-ell 95x95 TE bin (7000 < ell < 8000) is removed, so the discrepancy is concentrated in the high-ell TE bandpowers that anchor the damping-tail claim. Because the paper's central claim is the sensitivity of the TE damping-tail measurement, an unresolved systematic in TE directly affects that claim. Please investigate whether the low PTE is connected to the TE bias or transfer-function approximations, the beam and calibration nuisance parameters, or a specific high-ell bin, or alternatively soften the damping-tail claim in the abstract and conclusions until the origin is understood.
minor comments (5)
  1. [Title] The title contains stray spaces in 'T emperature' and 'F ull' in the manuscript text; these should be fixed.
  2. [Abstract and Section 4.4] The abstract's phrase 'using only the SPTpol data and a Planck-based prior on the optical depth' should be clarified, because the SPTpol temperature calibration and low-ell beam amplitude are fitted against the Planck 143 GHz map in Section 4.4. The text should state explicitly that the calibration is anchored to Planck, not just that a Planck tau prior is used.
  3. [Section 5.2] The definition of the effective number of degrees of freedom nu_b in Eq. (6) and its inversion 'backwards' from simulated auto-spectra is described tersely; a brief explanation of how nu_b is determined for the final coarse bins would improve reproducibility.
  4. [Section 6.2] The nuisance parameter E95to150_cal is defined as T95cal * P95cal / (T150cal * P150cal), but the notation is dense; a table listing all nuisance parameters, their definitions, and their priors would improve readability.
  5. [Figures 4 and 5] The captions of Figures 4 and 5 note that small offsets in ell have been added for plotting, but the corresponding subpanels in Figures 6 and 7 do not state this; please add the same note there.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the SPTpol spectra are measured data products with independently anchored calibration; the TE transfer-function treatment is a robustness concern, not a by-construction reduction.

full rationale

The central products are bandpowers measured from map cross-spectra through a pseudo-spectrum pipeline, with the transfer function, beam, and calibration estimated from simulations and external calibrators. The ΛCDM fit uses a disclosed Planck-based prior on τ because SPTpol alone cannot constrain reionization, and the resulting H0 = 70.48 ± 2.16 is not equal to the Planck input value, so the parameter inference is not forced by construction. The TE transfer function is defined as the geometric mean of the TT and EE transfer functions (Sec. 4.3), and a "TE bias" is computed from 226 simulations generated from the Planck base_plikHM_TT_lowTEB_lensing cosmology and subtracted from the data (Sec. 4.6). This is a modeling assumption that could bias high-ℓ TE/EE bandpowers if the correction is cosmology-dependent; however, the paper tests this with 90 alternate-cosmology realizations (Sec. 6.3) and finds sub-σ parameter shifts. That is an external robustness check rather than a circular reduction: the corrected bandpowers are not fitted parameters renamed as predictions, and the final cosmological constraints remain consistent with but distinct from the simulation input. Self-citations to H18 and Dutcher et al. are methodological precedents for the same instrument and analysis, while Wu et al. (2019) and Bianchini et al. (2020) are used as a lensing-reconstruction cross-check on the same field but with a different estimator; none of these carry the derivation by themselves. The paper itself flags limitations: the TE-only subset has a low PTE of 0.24% (Sec. 7.1), and the 150 GHz polarized point-source upper limit is described as artificially tight (Sec. 7). These are acknowledged weaknesses and robustness concerns, not instances of a conclusion reducing to its own input. Overall, the derivation chain is self-contained: the spectra are measured, the calibration is anchored to Planck 143 GHz temperature and 150 GHz cross-calibration, and the model-dependence of the transfer-function treatment is explicitly stress-tested rather than assumed away.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central claims rest on the standard ΛCDM framework, a Planck-derived τ prior, and a calibration chain anchored to the Planck 143 GHz map; the genuinely in-paper fitted quantities are calibration, beam, and foreground nuisance parameters whose priors propagate into the cosmology fit. No new physical entities are introduced.

free parameters (8)
  • Abeam (150 GHz low-ℓ beam amplitude) = best-fit value not stated numerically in text
    One-parameter model for low-ℓ beam uncertainty, fit against the Planck 143 GHz temperature map in Eq. 5 (Section 4.4).
  • Abeam (95 GHz low-ℓ beam amplitude) = best-fit value not stated numerically in text
    Same one-parameter beam model, fit against SPTpol 150 GHz (Section 4.4).
  • Tcal 150 GHz temperature calibration = prior 1σ = 0.00271; best-fit used for calibration
    Absolute temperature calibration fit against the Planck 143 GHz map in Eq. 5; floated as a nuisance parameter with a Gaussian prior centered on unity.
  • Tcal 95-to-150 calibration ratio = prior 1σ = 0.00115
    95 GHz calibrated against 150 GHz (Section 4.4); the ratio is floated as an independent nuisance parameter in cosmology fits.
  • Pcal 95 GHz polarization calibration = 1.043
    Measured in this work (Section 4.4); P150 = 1.06 is adopted from H18.
  • Foreground nuisance parameter set = A80 dust amplitudes 0-2 µK² (uniform prior); α = -2.42 ± 0.02; DPSE point-source amplitudes 0-2 µK² (uniform prior)
    Eight parameters for Galactic dust and polarized point sources (Section 6.2), marginalized in cosmology fits with priors motivated by Planck Collaboration et al. (2016a).
  • κ super-sample lensing convergence = prior 1σ = 0.001
    Nuisance parameter for the mean lensing convergence in the field, applied to theory spectra at every MCMC step (Section 6.2).
  • Seven beam eigenmode amplitudes = Gaussian priors with widths equal to eigenvalues
    Eigenmodes extracted from Venus beam variation, pointing jitter, and low-ℓ beam covariance (Section 5.2); floated as nuisance parameters in the cosmology fit.
assumptions (6)
  • standard math Pseudo-spectrum formalism with flat-sky analytic mode-coupling matrix Mλλ' (Hivon et al. 2002)
    Used throughout Sections 4.1 and 4.2 for spectrum estimation; the flat-sky approximation is the appropriate regime for this small patch.
  • domain assumption ΛCDM as the theory model with a fixed neutrino mass sum of 0.06 eV
    Section 6: the emulator is trained on CLASS outputs and CAMB is used for ΛCDM+AL; all parameter constraints assume this model.
  • domain assumption Foreground model functional forms (dust power law, ℓ² point sources, tSZ template from Shaw et al. 2010)
    Sections 4.3 and 6.2: used in simulations and as nuisance templates; TT is omitted to avoid modeling the cosmic infrared background and thermal Sunyaev-Zeldovich effect.
  • domain assumption Planck-based Gaussian prior on the reionization optical depth τ = 0.0540 ± 0.0074
    Section 6.1: SPTpol alone cannot constrain τ; the quoted H0 and Ωm depend on this external prior.
  • ad hoc to paper TE transfer function as the geometric mean of the TT and EE transfer functions
    Section 4.3: chosen because TE zero-crossings make direct transfer-function estimation numerically unstable; combined with a simulated 'TE bias' subtraction in Section 4.6.
  • ad hoc to paper The 57 erased covariance eigenmodes below 2.619e-5 of the largest eigenvalue are spurious
    Section 5.3: the covariance is nearly rank-deficient because only 226 simulated auto-spectra were used; conditioning erases these modes, justified by the small change in parameter widths (≤6%).

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Cite this review

Pith. "Pith review of Measurements of the Temperature and E-mode Polarization of the Cosmic Microwave Background from the Full 500-square-degree SPTpol Dataset." pith.science (2026). https://pith.science/paper/KXO3DA3N

@misc{pith2026250106890,
  author       = {Pith},
  title        = {Pith review of: Measurements of the Temperature and E-mode Polarization of the Cosmic Microwave Background from the Full 500-square-degree SPTpol Dataset},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KXO3DA3N}},
  note         = {Machine review of arXiv:2501.06890}
}
abstract

Using the full four-year SPTpol 500 deg$^2$ dataset in both the 95 GHz and 150 GHz frequency bands, we present measurements of the temperature and $E$-mode polarization of the cosmic microwave background (CMB), as well as the $E$-mode polarization auto-power spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) in the angular multipole range $50<\ell<8000$. We find the SPTpol dataset to be self-consistent, passing several internal consistency tests based on maps, frequency bands, bandpowers, and cosmological parameters. The full SPTpol dataset is well-fit by the $\Lambda CDM$ model, for which we find $H_0=70.48\pm2.16$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_m=0.271\pm0.026$, when using only the SPTpol data and a Planck-based prior on the optical depth to reionization. The $\Lambda CDM$ parameter constraints are consistent across the 95 GHz-only, 150 GHz-only, $TE$-only, and $EE$-only data splits. Between the $\ell<1000$ and $\ell>1000$ data splits, the $\Lambda CDM$ parameter constraints are borderline consistent at the $\sim2\sigma$ level. This consistency improves when including a parameter $A_L$, the degree of lensing of the CMB inferred from the smearing of acoustic peaks. When marginalized over $A_L$, the $\Lambda CDM$ parameter constraints from SPTpol are consistent with those from Planck. The power spectra presented here are the most sensitive measurements of the lensed CMB damping tail to date for roughly $\ell > 1700$ in $TE$ and $\ell > 2000$ in $EE$.

Figures

Figures reproduced from arXiv: 2501.06890 by the authors.

Figure 1
Figure 1. SPTpol 500 deg2 low-ℓ focused signal and noise maps, for temperature and E-mode polarization, for 150 GHz and 95 GHz. The 95 GHz signal maps are omitted because they look similar to the 150 GHz signal maps. The noise maps are made with the coadd of left-going scans minus the coadd of right-going scans, then divided by 2. 4.3. Transfer Function The filter transfer function F accounts for the ef￾fects of time stream p… view at source ↗
Figure 2
Figure 2. SPTpol 500 deg2 noise spectra. For ℓ < 500, we use the low-ℓ focused dataset; for ℓ > 500, we use the high-ℓ focused dataset, and the dashed line at ℓ = 500 shows this stitch. These are unbiased spectra but multiplied by the beam function again (B 2 ℓ ) to show the white noise level. Units on both axes are provided as a handy reference for conversion between µK2 and µK-arcmin. theory C T T ℓ and C EE ℓ are known, so… view at source ↗
Figure 3
Figure 3. The fiducial SPTpol 150 GHz beam (blue), and on top of it, the range of ∆B S150 ℓ that corresponds to 1-σ uncertainties in the A S150 beam parameter (red region). Gray data points with error bars represent the right hand side of Eq. 5 with uncertainties. 0.007(−0.022) for 150(95) GHz, with an uncertainty of ±0.002. We also test for T-to-P leakage beyond a monopole, which we refer to as the “leakage beam.” The leakag… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: SPTpol 500 deg2 T E angular power spectrum, with an inset plot zooming in at high ℓ. The gray line is the Planck best-fit ΛCDM model, and the colored error bars are the square root of the diagonal elements of the bandpower covariance matrix without “further conditionin…
Figure 5
Figure 5. Figure 5: SPTpol 500 deg2 EE angular power spectrum. The gray line is the Planck best-fit ΛCDM model, and the colored error bars are the square root of the diagonal elements of the bandpower covariance matrix without “further conditioning” (see Section 5.3). We plot residuals ∆D…
Figure 6
Figure 6. Figure 6: SPTpol and other contemporary measurements of the T E angular power spectrum, with an inset plot zooming in at high ℓ. Black points and error bars are the SPTpol minimum-variance bandpowers in this work. SPT-3G 2018 T T/T E/EE bandpowers are in green (Balkenhol et al. …
Figure 7
Figure 7. Figure 7: SPTpol and other contemporary measurements of the EE angular power spectrum. Black points and error bars are the SPTpol minimum-variance bandpowers in this work. SPT-3G 2018 T T/T E/EE bandpowers are in green (Balkenhol et al. 2023), BICEP2/Keck in blue (BICEP2 and Kec…
Figure 8
Figure 8. Figure 8: ΛCDM parameter constraints from the full SPTpol 500 deg2 dataset (baseline), several data splits, and H18. For comparison, the horizontal lines and gray bands are the best-fit values and 1σ uncertainty ranges of Planck. The 150 GHz T E and EE parameter constraints are …
Figure 9
Figure 9. Figure 9: Marginalized ΛCDM parameter constraints (posteriors) for SPTpol (this work, blue), SPT-3G 2018 T T/T E/EE (Balkenhol et al. 2023, orange), ACT DR4 (Aiola et al. 2020, gray), and Planck (black line contours). We note that the SPTpol and SPT-3G 2018 constraints are not i…
Figure 10
Figure 10. Figure 10: Marginalized constraints on ΛCDM parameters for the baseline, the full dataset but with AL floated, the 150 GHz ℓ < 1000 and ℓ > 1000 data splits with AL fixed to 0.7 or unity, and H18. The horizontal lines and gray bands are the best-fit values and 1σ uncertainty ran…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.