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KSZ Velocity Reconstruction with ACT and DESI-LS using a Tomographic QML Power Spectrum Estimator

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper reports an 11.7σ detection of the kSZ velocity-galaxy cross-correlation and measures its amplitude at 0.39 ± 0.04 of the halo-model prediction, evidence for strong feedback in massive halos.

desk verdict A real kSZ velocity reconstruction detection at ~9.4σ, but the 11.7σ headline is a second-iteration rescaling and should not be the headline number. read the letter →

arxiv 2506.21684 v1 pith:QKSM7DVJ submitted 2025-06-26 astro-ph.CO

Anderson C. M. Lai , Yurii Kvasiuk , Moritz Münchmeyer This is my paper
classification astro-ph.CO
keywords kineticSunyaev-Zel'dovicheffectkSZvelocityreconstructionquadraticmaximumlikelihoodestimatorCMBsecondaryanisotropiesgalaxy-CMBcross-correlationDESIlegacysurveyLRGshalomodelelectronprofilebaryonicfeedback
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

The paper's target is the kinetic Sunyaev-Zel'dovich (kSZ) effect, the Doppler imprint left on cosmic microwave background photons when they scatter off free electrons that share the large-scale velocity of the gas. Using ACT DR6 temperature maps and DESI-LS DR9 luminous red galaxies, the authors reconstruct the line-of-sight velocity field in 20 redshift bins and cross-correlate it with the galaxy density field. They report an $11.7\sigma$ detection of this velocity-galaxy cross-correlation, the highest signal-to-noise claimed for kSZ velocity reconstruction to date, and an amplitude $A = 0.39 \pm 0.04$ relative to a halo-model prediction. Because $A<1$, the measured kSZ signal is weaker than the fiducial model, which they interpret as evidence for strong feedback in massive halos. The analysis also introduces a quadratic maximum likelihood (QML) power spectrum estimator for redshift-binned maps that roughly doubles the signal-to-noise of the standard pseudo-$C_\ell$ approach.

What carries the argument

The velocity reconstruction is carried by the quadratic estimator $\hat{v}_\alpha(\hat n) = -N^{vv,\alpha} a'_\alpha(\hat n)\, \delta'_{g,\alpha}(\hat n)$, where $a'$ and $\delta'_g$ are the CMB temperature and galaxy overdensity maps filtered by $C^{\tau g}_\ell/C^{gg}_\ell$; this converts the small-scale kSZ temperature signal into an estimate of the line-of-sight velocity. For the cross-power measurement, the QML estimator acts on a pixel-space covariance matrix $C = S + N$ built from $2\times20$ redshift-binned fields, is mode-purified so that only galaxy-velocity pairs contribute, and computes the Fisher matrix analytically. The halo-model electron-galaxy cross-power $C^{\tau g}_\ell$, built from the AGN electron profile and the DESI LRG halo occupation distribution, fixes the velocity scale and therefore the amplitude calibration of the final measurement.

What would settle it

Repeat the measurement with the electron-galaxy cross-spectrum $C^{\tau g}_\ell$ replaced by a different electron profile, for example one calibrated to thermal SZ measurements of the same halos, while keeping all other analysis choices fixed; if the fitted amplitude $A$ moves by much more than the quoted $0.04$ or the significance drops substantially, the central claims are template-dependent rather than a model-independent detection.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that kSZ velocity reconstruction works at high significance on a photometric galaxy sample alone. Reconstructing velocities with the quadratic estimator applied to ACT DR6 90 and 150 GHz maps and DESI-LS DR9 galaxies, then estimating the velocity-galaxy cross-spectrum with the QML estimator, the authors measure the cross-correlation with significance $11.7\sigma$ and an overall amplitude $A=0.39\pm0.04$ relative to their halo-model template. They further show that the QML pipeline recovers about twice the signal-to-noise of pseudo-$C_\ell$ ($6.06\sigma$) with identical choices, and that the low value of $A$ is consistent with earlier evidence for strong AGN feedback and with a simultaneous independent analysis. The paper treats these results as establishing both a physics claim about gas in halos and a methodological claim that optimal QML power-spectrum estimation is feasible at this resolution.

Load-bearing premise

The load-bearing premise is that we know how free electrons are arranged around galaxies well enough to build the filter used in the velocity reconstruction; if the electron profile is wrong in its redshift or scale dependence, the recovered velocity field is biased and both the amplitude $A=0.39$ and the $11.7\sigma$ significance change.

Editorial extensions

If this is right

  • Photometric galaxy surveys can supply both the small-scale filter and the large-scale tracer for kSZ velocity reconstruction, so future wide-field surveys can pursue the method without a spectroscopic velocity template.
  • The QML estimator saturates most of the available signal by $\ell \simeq 60$ and computes the covariance analytically, making it a practical tool for high-resolution kSZ analyses with many tomographic bins.
  • If $A\simeq0.4$ is correct, halo models with the fiducial AGN electron profile overpredict the gas content of massive halos, so cosmological uses of the kSZ effect will need to marginalize over the electron profile rather than treat it as known.
  • The same pipeline, with the cross-power step replaced by a parameter model, is set up for large-scale cosmological inference from velocity-galaxy correlations, the extension to $f_{\mathrm{NL}}$ that the paper defers to future work.

Reading between the lines

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

  • A test the authors do not report is to rerun the pipeline with the halo-model electron profile replaced by a non-AGN or tSZ-calibrated profile; the size of the shift in $A$ would show how much of the quoted $0.04$ uncertainty is model-driven.
  • Because the QML covariance already contains all cross-redshift couplings, the same estimator should transfer directly to other low-$\ell$ cross-correlations such as CMB lensing $\times$ galaxies or tSZ $\times$ galaxies, where most of the signal also sits at $\ell<100$.
  • The linear velocity-from-galaxy maps could be combined with the kSZ maps in a single joint map-space fit, which would give a cleaner spatial diagnostic of where the two reconstructions agree than the reported correlation coefficients alone.
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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 a kSZ velocity reconstruction using ACT DR6 temperature maps and DESI-LS DR9 LRG galaxies, analyzed with a novel implementation of a quadratic maximum likelihood (QML) power spectrum estimator operating on 20 tomographic redshift bins. The authors measure the cross-power between the reconstructed velocity field and the galaxy overdensity field and report an 11.7σ detection, together with an amplitude A = 0.39 ± 0.04 relative to a Battaglia AGN halo-model prediction. They also compare their QML results with a pseudo-Cℓ analysis, finding roughly a factor of two improvement in signal-to-noise, and validate a linear galaxy-based velocity reconstruction on simulations. The central claims are the high detection significance and the low amplitude relative to the halo model, which is interpreted as evidence for strong feedback in massive halos.

Significance. If the result holds, it is a significant advance: it demonstrates that a dense-matrix QML estimator with analytic covariance is tractable for a 40-field, NSIDE=32 analysis and provides one of the strongest kSZ velocity-reconstruction detections to date, with implications for baryon feedback. The paper includes several concrete strengths: an analytic covariance calculation, validation of the linear velocity estimator on Gaussian simulations, and an explicit comparison with pseudo-Cℓ. However, the quoted headline significance is weakened by the two-step rescaling issue described below, and the model dependence of the amplitude is not fully propagated. The first-iteration significance of 9.35σ remains a strong model-independent detection, but the paper's headline claim as currently stated is not fully supported.

major comments (3)
  1. [Sec. 3.2, Table 1, App. D] The abstract and Sec. 5 quote 11.7σ as the detection significance, but Table 1 shows this is the SNR of the second QML iteration, obtained after rescaling the fiducial Cτg by the first-iteration amplitude A = 0.393 and recomputing the Fisher matrix. Appendix D, Eqs. (73)–(76), shows that the QML SNR is not invariant under such a rescaling: for b < 1 and signal-dominated velocity autopower, the correction factor b⁻¹M(b) exceeds unity. The final significance is therefore the result of a data-adaptive choice of filter, and the null distribution of this two-step procedure is not computed. The first-iteration 9.35σ is the appropriate model-independent detection significance unless simulations demonstrate that the second-iteration SNR is unbiased under the null. I recommend either quoting the first-iteration value as the headline or adding such a null test.
  2. [Secs. 2.5–2.6, Sec. 3.2] The amplitude A = 0.39 ± 0.04 and the final SNR both depend on the halo-model electron-galaxy cross-power Cτg, computed from the Battaglia AGN electron profile and the DESI LRG HOD (Eqs. 27–28). This quantity enters both the kSZ filter (Eqs. 8–11) and the template in the amplitude fit (Eqs. 33–40). The optical depth degeneracy is mentioned in Sec. 2.2, but its impact on A and on the quoted significance is not propagated. A redshift- or scale-dependent error in the electron profile would bias the reconstructed velocity field and change both A and the second-iteration SNR, so the stated precision and the feedback interpretation require a quantification of this model uncertainty.
  3. [Sec. 2.4] The paper states that the unbiasedness of the QML estimator and the correctness of its covariance matrix have been tested extensively on Gaussian simulations, but the results are deferred to an upcoming companion paper. Since the main amplitude and SNR are derived from these QML estimates, the current manuscript should include at least a summary of those validation tests, such as a null test or a recovery of input power spectra, to support the quoted error bars. Without this information, the reader cannot independently assess whether the analytic covariance accurately describes the estimator's scatter.
minor comments (5)
  1. [Sec. 2.1.2] There are several typos, including "normailzed" and "the the last few redshift bins" in Sec. 3.2; a careful proofread is needed.
  2. [Fig. 18 caption] The velocity cutoff range for the kSZ reconstruction is labeled "for the galaxy reconstruction" twice; the second occurrence should refer to the kSZ reconstruction.
  3. [Sec. 3.2] The sentence "we use the range ℓ = 7 to ℓ = 60 to avoid the largest modes" should be rephrased, since the largest angular scales correspond to the lowest multipoles; the text presumably means the modes most affected by systematics.
  4. [Eq. (5)] The chi-square expression is written as a plain squared norm without an inverse noise covariance; please clarify the weighting used in the regression.
  5. [App. G] The pseudo-Cℓ covariance is noted to be not fully converged for less-correlated redshift bins (Fig. 26); the 6.06σ comparison should be flagged as approximate in the main text.

Circularity Check

2 steps flagged · score 6.0 of 10

The 11.7σ headline detection is the second-iteration QML SNR after rescaling the fiducial Cgτ template by the same-data fitted amplitude A=0.39; the paper's own App. D shows this rescaling boosts the SNR, so the pre-specified detection significance is the first-iteration 9.35σ.

  1. fitted input called prediction [Sec. 3.2, 'Total Signal-To-Noise'; App. D, Eqs. (67)-(76); Table 1]
    "To increase the total SNR of the cross-correlation, we run two iterations of the QML, as described at the bottom of Sec. 2.4. In the first iteration, we measure A = 0.39 ± 0.04 for the kSZ amplitude. Then we adjust Cgτ by this value in the second iteration of the QML (i.e. we learned in the first iteration that the halo model has over-estimated the expected kSZ signal). The QML, unlike the pseudo-Cℓ, is not invariant under this rescaling, as we explain in more detail in App. D. This procedure gains about two σ in the cross-correlation significance."

    The headline 11.7σ is the second-iteration SNR, obtained after rescaling the fiducial electron-galaxy cross-power Cgτ by the same-data fitted amplitude A≈0.39 and recomputing the QML weights and Fisher matrix. Appendix D Eq. (73) gives SNR_QML = b^{-1}M(b) SNR, and Eq. (76) shows b^{-1}M(b)>1 for b<1 in the signal-dominated regime. Thus the quoted detection significance is not a fixed null-hypothesis statistic: it is the first-iteration SNR multiplied by a boost factor determined by the very amplitude fitted from the same data. The paper does not compute the null distribution of this two-step fit-then-renormalize procedure, so the model-independent detection significance is the first-iteration 9.35σ, not the headline 11.7σ.

  2. self definitional [Sec. 3.2, 'Dependence on ℓmin'; Table 1]
    "The left plot shows the cross power amplitude A, which falls around 0.39 at the first QML iteration and becomes close to 1 after the rescaling in the second QML iteration (by definition)."

    In the second QML iteration the fiducial Cgτ template is rescaled by the measured A≈0.39 before the amplitude is re-fit; re-fitting the same rescaled template returns A≈1 by construction. This step is self-referential by the paper's own wording: the second-iteration amplitude carries no independent information about the halo-model normalization, and the headline significance is computed using this data-adapted filter rather than a pre-specified one.

full rationale

The paper is largely self-contained: the first-iteration QML SNR of 9.35σ, the 20-bias SNR of 10.6, and the pseudo-Cℓ SNR of 6.06 are computed with a pre-specified fiducial model, and the QML implementation is validated on Gaussian simulations. The halo-model Cgτ (Battaglia AGN profile plus DESI LRG HOD) is used both as the kSZ filter and as the amplitude template, but that is model dependence acknowledged by the authors, not a logical circularity. Self-citations to [6, 44] introduce the quadratic-estimator formalism and optical-depth degeneracy but are not the load-bearing step here. The central issue is the two-iteration procedure: the amplitude A=0.39 measured from the data is fed back to rescale Cgτ, and the second-iteration SNR (11.5–11.7) is quoted as the detection. Appendix D explicitly derives a correction factor b^{-1}M(b) that boosts the SNR when b<1 in the signal-dominated regime, so the headline significance is partially manufactured from the fitted input. The first-iteration 9.35σ remains a strong pre-specified detection, and the A=0.39 measurement from iteration 1 is not itself circular; hence the score is 6 rather than higher.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The central result depends on fitted galaxy biases, a data-calibrated reconstruction noise, and a halo-model electron profile whose overall amplitude is later rescaled by the measured kSZ amplitude in the second QML iteration.

free parameters (3)
  • Galaxy bias b_g per redshift bin (20 values) = Approximately 1.7 to 2.1 across bins (Fig. 9)
    Fitted via chi-square to observed galaxy autopower at ell in [138,225] (Eq. 24). Used in fiducial C_gg, C_vg, and the 2-halo term of C_tau-g.
  • Empirical kSZ reconstruction noise amplitude N_vv,alpha = Ratio to theory between 1.1 and 1.7 depending on channel and redshift bin (Fig. 8)
    Fitted as the mean reconstructed velocity pseudo-Cell autopower over ell=100-300 (Sec. 2.2). Adopted as the fiducial noise in the QML covariance.
  • Rescaling of fiducial C_tau-g by first-iteration amplitude A = A=0.393
    The second QML iteration multiplies the halo-model C_tau-g by the measured first-iteration amplitude, changing the covariance and the final significance (Table 1, App. D).
assumptions (5)
  • domain assumption The electron-galaxy cross-power C_tau-g is described by the Battaglia AGN electron profile and the DESI LRG HOD.
    C_tau-g enters the kSZ quadratic estimator filter (Eqs. 8-11) and sets the normalization for the measured amplitude A. The paper notes the optical depth degeneracy: an incorrect amplitude linearly biases A (Sec. 2.5).
  • domain assumption Linear galaxy bias plus linear RSD term b_g^2 + f mu^2 describes galaxy clustering on the large scales used.
    Used for fiducial galaxy autopowers (Eq. 23) and hence for the QML covariance. Residual large-scale power after calibration suggests this model is imperfect (Sec. 2.1.2, Fig. 5).
  • domain assumption The kSZ reconstruction noise is Gaussian, isotropic, uncorrelated between pixels and redshift bins, and flat in ell on large scales.
    Stated in Sec. 2.2. Used to calibrate N_vv from data and to build the analytic QML covariance. The empirical noise differs from theory by 10 to 70 percent.
  • domain assumption CMB temperature and galaxy overdensity fields are Gaussian at the level required for the quadratic estimator and QML likelihood.
    Underlies Eqs. 7 and 17-20 and the Fisher-based significance. Corrections are referenced to [17] but not evaluated here.
  • domain assumption Photometric redshift errors are Gaussian with sigma_z=0.027 and are applied uniformly.
    Used to build window functions W(z) (Eq. 1). The paper notes the northern sky has different photo-z errors and adopts the smaller value, which may underestimate north photo-z scatter (Sec. 2.1.2).

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Cite this review

Pith. "Pith review of KSZ Velocity Reconstruction with ACT and DESI-LS using a Tomographic QML Power Spectrum Estimator." pith.science (2026). https://pith.science/paper/QKSM7DVJ

@misc{pith2026250621684,
  author       = {Pith},
  title        = {Pith review of: KSZ Velocity Reconstruction with ACT and DESI-LS using a Tomographic QML Power Spectrum Estimator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QKSM7DVJ}},
  note         = {Machine review of arXiv:2506.21684}
}
abstract

We perform kinetic Sunyaev-Zel'dovich (kSZ) velocity reconstruction on data from ACT DR6 and DESI-LS DR9. To estimate the cross-power between kSZ velocity reconstruction and galaxy density, we make use of a novel quadratic maximum likelihood QML power spectrum estimator implementation in red-shift binned spherical coordinates. We find a detection of the kSZ signal from the cross-correlation between the estimated velocity field and the large-scale galaxy field of $11.7 \sigma$. We estimate an amplitude $A=0.39 \pm 0.04$ of the kSZ signal with respect to a halo model prediction, possibly indicating a high feedback in massive halos, in agreement with previous studies. Our result demonstrates the feasibility of an optimal QML pipeline at the resolution required for this analysis, and will be a powerful tool for kSZ cosmology with upcoming high-resolution surveys.

Figures

Figures reproduced from arXiv: 2506.21684 by the authors.

Figure 1
Figure 1. A figure illustrating the ACT DR5 90 GHz temperature map before and after the SZ cluster masking [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Left: A binary mask created from the apodized DR6 NILC analysis mask in [12]. The mask has been [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The redshift distribution of the 20 galaxy tomographic bins in an interval of 2 bins, objects between [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (29 more)
Figure 4
Figure 4. Figure 4: A selection of DESI LRG galaxy overdensity map used in this analysis. The overdensity maps are [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Galaxy autopower spectrum in 4 redshift intervals (consisting of 5 bins), showing the correction on [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: QML estimates on the large-scale Galaxy autopowers [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: The mask constructed from the overlapping region between the ACTDR6 CMB map and DESI-LS [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Figure comparing the theoretical kSZ reconstruction noise [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Left: A figure of the best-fit galaxy bias to the data across the redshift bins. The biases are defined [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: The electron-galaxy cross-powers C τ g,α ℓ for four redshift bins α = 1, 5, 9, 13. The linear power spectrum involved in the calculation are obtained from hmvec using the DESI one-percent survey LRG parame￾ters [48] for galaxy HOD and Battaglia ’AGN’ model [2] for the…
Figure 11
Figure 11. Figure 11: A summary of the kSZ reconstruction noises [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: QML estimates of the velocity auto-powers [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: Left: A figure the shows the covariance of the cross-powers between the redshift bin combination [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: Left: Part of the analytic covariance matrix between the first cross power in redshift bin ( [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]
Figure 15
Figure 15. Figure 15: QML estimates of the 16 galaxy-velocity cross-powers formed by averaging from the 20 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]
Figure 16
Figure 16. Figure 16: The best-fit velocity biases bv obtained from analytic solution Eq. 36 over the 20 redshift bins. The errorbars are retrieved from the diagonal terms of the covariance matrix for the velocity biases. The biases are defined with respect to a halo model calculation of C…
Figure 17
Figure 17. Figure 17: Summary of the QML galaxy-velocity cross-power analysis, blue and orange curve give the results in [PITH_FULL_IMAGE:figures/full_fig_p020_17.png]
Figure 18
Figure 18. Figure 18: A side-by-side comparison between the kSZ reconstructed velocity field and the galaxy reconstructed [PITH_FULL_IMAGE:figures/full_fig_p022_18.png]
Figure 19
Figure 19. Figure 19: The correlation coefficient Rℓ between the velocity maps from galaxy reconstruction and kSZ re￾construction for 4 redshift bins. The data point covers modes from ℓ = 7 to ℓ = 48 in bandpowers of 4. It can be seen that most data points lie above the black horizontal li…
Figure 20
Figure 20. Figure 20: The imaging properties used for constructing the linear regression model and their best-fit values, the [PITH_FULL_IMAGE:figures/full_fig_p026_20.png]
Figure 21
Figure 21. Figure 21: The imaging properties used for constructing the linear regression model and their best-fit values, [PITH_FULL_IMAGE:figures/full_fig_p027_21.png]
Figure 22
Figure 22. Figure 22: A figure that illustrates the fisher forecast for various configurations, the covariance matrix is [PITH_FULL_IMAGE:figures/full_fig_p028_22.png]
Figure 23
Figure 23. Figure 23: Illustrations of the QML SNR correction factor Eq. 76 with varying rescaling [PITH_FULL_IMAGE:figures/full_fig_p031_23.png]
Figure 28-31
Figure 28-31. Figure 28-31: Each plot contains a 10 × 10 = 100 cross-powers that corresponds to a block from the full 20 × 20 plot. It is noted that while there is no averaging over redshift bins, a bandpowering from ℓ = 7 to ℓ60 in intervals of 6 is still implemented to facilitate visualizat…
Figure 24
Figure 24. Figure 24: The velocity fields reconstructed from the masked galaxy overdensity maps (left column) to the true [PITH_FULL_IMAGE:figures/full_fig_p034_24.png]
Figure 25
Figure 25. Figure 25: Left: The correlation coefficient Rℓ between the reconstructed velocity fields and true velocity fields for redshift bins around the edge of the interval. Right: The velocity autopowers directly computed from the unmasked pixels, neither fsky approximation or pseudo-C…
Figure 26
Figure 26. Figure 26: The covariance of the velocity-galaxy cross-power between [PITH_FULL_IMAGE:figures/full_fig_p035_26.png]
Figure 27
Figure 27. Figure 27: A summary of the results from the pseduo- [PITH_FULL_IMAGE:figures/full_fig_p035_27.png]
Figure 28
Figure 28. Figure 28: Part for the full 20-bins galaxy maps by 20-bins velocity maps cross-power from QML estimates. [PITH_FULL_IMAGE:figures/full_fig_p036_28.png]
Figure 29
Figure 29. Figure 29: Same as Fig. 28 but with [PITH_FULL_IMAGE:figures/full_fig_p036_29.png]
Figure 30
Figure 30. Figure 30: Same as Fig. 28 but with [PITH_FULL_IMAGE:figures/full_fig_p037_30.png]
Figure 31
Figure 31. Figure 31: Same as Fig. 28 but with [PITH_FULL_IMAGE:figures/full_fig_p037_31.png]

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Forward citations

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