Can kSZ velocity reconstruction be improved with a tomographic QML power spectrum estimator?

The gain comes from the estimator, not new data

The paper asks whether the statistical machinery used to measure the kSZ signal can be improved without changing the telescopes. The kinetic Sunyaev-Zel'dovich effect is the rescattering of cosmic microwave background photons off moving free electrons; because the electrons trace bulk flows, the effect carries information about the large-scale velocity field of the universe. The measurement here is not the kSZ auto-power but a cross-correlation: a velocity field reconstructed from CMB and small-scale galaxy data is correlated with the large-scale galaxy density field.

The comparison is deliberately controlled. The authors run their new quadratic maximum likelihood (QML) power spectrum estimator and a traditional pseudo-Cℓ analysis on the same ACT DR6 and DESI-LS DR9 inputs. The QML route reaches 10σ; the pseudo-Cℓ route reaches 8.3 with a velocity–galaxy cross-power amplitude of 0.44. Because the data are held fixed, the roughly 20% SNR improvement is attributable to the estimator rather than to deeper or wider observations.

Twenty redshift bins create a dense covariance problem

The analysis splits galaxies into 20 tomographic redshift bins between z = 0.4 and z = 1, and reconstructs a velocity field for each bin. Cross-correlating every velocity bin with every galaxy bin yields a 20×20 grid of cross-power spectra, or 400 cross-powers in total. Neighbouring bins overlap, so these measurements are correlated, and a method that ignores those correlations cannot weight them optimally.

QML addresses this by modelling the full covariance matrix of the binned fields and inverting it. That is normally prohibitive in cosmology, but the authors note it becomes tractable here because the signal is concentrated on the largest scales: they work at ℓmax = 60 with Healpix Nside = 32 for the QML estimators, over 2×20 binned fields. The paper describes this as the first demonstration that the QML pipeline can handle a large number of correlated binned fields, and the code is released separately.

Building a velocity map from CMB and galaxies

The velocity estimator combines CMB temperature anisotropies with redshift-binned galaxy overdensities through a quadratic combination, with weights chosen to keep the estimator unbiased and to minimise its variance. In practice the authors implement the estimator in pixel space, inverse-variance filtering the CMB map and the galaxy overdensity map and multiplying them, with a theoretically computed reconstruction noise normalising the result. The maps are prepared at Nside = 4096 so that the small-scale kSZ signal is retained, then filtered to remove modes beyond ℓ = 10000.

Two data choices matter for interpreting the result. Only the 90 GHz and 150 GHz ACT channels are used, to limit cosmic infrared background contamination, and clusters with SNR > 5 in the ACT DR5 catalogue are masked to suppress thermal SZ emission. The galaxy maps are calibrated with a regression model of 11 imaging systematic maps over the DESI footprint, which the paper shows reduces excess large-scale power in the galaxy auto-spectrum.

A low amplitude points to feedback in massive halos

The headline number is not the detection significance but the amplitude A = 0.42 ± 0.042, measured relative to a halo model prediction. A value near unity would mean the observed kSZ signal matches that prediction; the measured value is roughly 42% of it. The authors interpret this as possibly indicating strong feedback in massive halos, and note it agrees with previous studies, including the earlier 13σ ACT cross-correlation result.

That interpretation depends on a quantity the data cannot directly measure. The electron–galaxy cross-power Cτg enters the estimator through a coefficient Γ, and there is currently no direct probe of it; the authors compute it from a model. An error in its amplitude produces a linear bias on the overall velocity–galaxy cross-power, a degeneracy the paper calls the optical depth degeneracy. So A should be read as an amplitude relative to a modelled prediction, not as an independent measurement of gas depletion.

Cutting contaminated bins raises the fit quality

The 10σ figure is not computed from all 400 cross-powers. The authors find consistent outliers when the velocity and galaxy bins are the same, which they associate with thermal SZ and cosmic infrared background foregrounds entering through a three-point correlation involving large- and small-scale galaxy fields. They also find outliers for widely separated bins with |α − β| > 10, which they attribute to mismodelling the redshift window at high redshift where galaxy number density is low and photo-z errors become catastrophic.

Their final selection removes cross-powers with |α − β| < 2 or |α − β| > 10, reducing the effective set from 400 to 252. The paper reports that this greatly improves the goodness of fit, while noting that the amplitude A and the SNR are more sensitive to removing nearby bins, where most of the signal sits. Readers comparing this 10σ to other kSZ numbers should therefore check whether the same bin selection was applied.

Agreement with a parallel analysis strengthens the result

The paper compares itself with a contemporaneous analysis that also performs kSZ velocity reconstruction with ACT and DESI-LS luminous red galaxies. The two pipelines differ substantially: this one is 2+1 dimensional in redshift-binned spherical coordinates, while the other uses a 3-dimensional Cartesian representation and restricts to the northern galactic hemisphere to reduce image systematics. They nonetheless reach very similar SNR and velocity bias, with the other analysis reporting A ∼ 0.44.

The authors also cross-check the kSZ-derived velocity field against a linear velocity reconstruction built directly from the DESI-LS galaxy overdensity. For four redshift bins, the correlation coefficient between the two reconstructed velocity maps is mostly positive over multipoles from ℓ = 5 to ℓ = 44, which the paper reads as evidence of nonzero positive correlation between the two reconstruction routes. This is a consistency check on the reconstructed field, not an independent cosmological measurement.

The 20% gain is a same-data comparison

The improvement claim is narrow and should be kept that way. It compares QML and pseudo-Cℓ on identical ACT DR6 and DESI-LS DR9 inputs, with the pseudo-Cℓ covariance matrix derived from 105 simulations; the authors state that this covariance does not fully converge for weakly correlated redshift bin pairs but has negligible effect on the kSZ amplitude and its 1σ error. The 20% figure is therefore an estimator-level comparison at this resolution and scale range, not a forecast for other surveys or other summary statistics.

The paper is explicit that it reconstructs the velocity field and does not perform a cosmological parameter analysis. Its case for the method rests on the largest scales, where the signal lives and where the dense matrix inversion is affordable. That is also why the authors position the pipeline as a starting point for future high-resolution surveys, for which the introduction cites predicted kSZ signal-to-noise around 200, and for a follow-up primordial non-Gaussianity analysis.

The decisive test is a parameter analysis, not a higher SNR

For readers weighing this result, the most useful split is between what the paper establishes and what it defers. It establishes that an optimal QML estimator is computationally feasible for 20 correlated redshift bins at ℓmax = 60, that it delivers 10σ on this dataset, and that it beats pseudo-Cℓ by about 20% in SNR on the same data. It does not establish cosmological constraints, and its amplitude A inherits the modelled electron–galaxy cross-power through the optical depth degeneracy.

The paper's own priority for follow-up is a cosmological parameter inference, especially of local primordial non-Gaussianity fNL, which it argues suits this pipeline because the signal is concentrated on large scales. The practical judgement for a reader is therefore not simply that 10σ exceeds 8.3, but that the estimator advantage is demonstrated precisely in the large-scale, many-bin regime where future kSZ cosmology analyses will need it — while the amplitude interpretation still rests on a halo model prediction that the data cannot independently calibrate.

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