DESI+ACT kSZ Profile Measurements

• DESI+ACT kSZ profiles are measurements capturing Doppler shifts from free electrons, enabling precise mapping of ionized gas and cosmic velocity fields.
• They employ methodologies like pairwise momentum estimation, velocity-weighted stacking, and Fourier-space analyses to isolate the subtle kSZ signal.
• Recent analyses report 5σ to 10σ detections, providing critical constraints on baryonic feedback processes and the spatial distribution of halo gas.

The kinetic Sunyaev-Zel'dovich (kSZ) effect probes the bulk motion of ionized gas through its imprint on the cosmic microwave background (CMB) via Doppler shifting of CMB photons resulting from Thomson scattering off free electrons with peculiar velocities. In the context of modern large-scale structure surveys (such as DESI and the Dark Energy Survey) combined with high-resolution millimeter-wave CMB observations (notably ACT and SPT), measurements of kSZ effect profiles enable the direct paper of ionized gas distribution, baryonic feedback, cosmic velocity fields, and tests of gravity on cosmological scales. This article reviews the principles, methodologies, results, and implications of recent and forecasted kSZ effect measurements, particularly in the synergy between DESI and ACT-class data.

1. Theoretical Basis and Signal Formation

The kSZ effect arises from the Doppler shift of CMB photons by free electrons moving with respect to the cosmic rest frame. The observed temperature fluctuation in direction $\mathbf{n}$ is given by

$$\frac{\Delta T_{\rm kSZ}(\mathbf{n})}{T_{\rm CMB}} = -\int \frac{d\chi}{1+z}\,e^{-\tau(\chi)} n_e(\chi\mathbf{n}, z)\sigma_T \frac{\mathbf{v}_e\cdot\mathbf{n}}{c}$$

where $n_e$ is the electron density, $\sigma_T$ the Thomson cross-section, $\mathbf{v}_e$ the proper velocity, $z$ the redshift, $\tau(\chi)$ the cumulative Thomson optical depth, and $\chi$ is the comoving distance. This effect is linear in $n_e$ and $v_e$ (unlike the quadratic dependence of the thermal SZ), allowing it to trace the baryonic momentum field in halos and the surrounding large-scale structure.

For clusters or galaxy groups, the kSZ signal can be expressed in terms of a mean optical depth $\tau$ and the mean peculiar velocity $v_{\rm los}$: $$\Delta T_{\rm kSZ} = -\tau T_{\rm CMB} (v_{\rm los}/c)$$. The signal is frequency-independent and typically sub-dominant to the primary CMB and tSZ except in optimal stacking or pairwise velocity measurements.

2. Observational Strategies and Statistical Estimators

Several statistical techniques have been developed and validated for extracting kSZ signals from noisy CMB data:

• Pairwise Momentum Estimator: Measures the mean pairwise velocity between halos/groups by considering the temperature differences in the CMB at the positions of galaxy/cluster pairs, weighted by their line-of-sight separation. This estimator is robust to uncorrelated foregrounds and allows for direct inference of the gas momentum and its cosmological correlations (Keisler et al., 2012, Calafut et al., 2021, Chen et al., 2021).
• Velocity-Weighted Stacking: Stacks CMB temperature decrements at galaxy locations weighted by reconstructed line-of-sight velocities (obtained via continuity equation inversion or BAO-based reconstruction), maximizing the kSZ signal while suppressing non-velocity-correlated contaminants (Schaan et al., 2015, Mallaby-Kay et al., 2023, Hadzhiyska et al., 9 Jul 2024, Guachalla et al., 25 Mar 2025).
• Fourier-Space Pairwise Power Spectra: Constructs the density-weighted pairwise kSZ power spectrum in harmonic space, leveraging the statistical isotropy of the field and suppressing configuration-space systematics. This approach naturally incorporates survey window functions and redshift-space distortions (Sugiyama et al., 2017, Li et al., 7 Jan 2024).
• Bispectrum and Quadratic Estimators: Uses the kSZ-induced non-zero density-density-temperature bispectrum to reconstruct the large-scale cosmic velocity field using quadratic estimators, particularly in synergistic ACT+DESI analyses (McCarthy et al., 8 Oct 2024, Lai et al., 26 Jun 2025).
• Compensated Aperture Photometry (CAP): Mitigates primary CMB and foregrounds by subtracting the mean temperature in an annulus around the object, thus isolating the small-scale kSZ feature (Calafut et al., 2021, Hadzhiyska et al., 4 Dec 2024, Guachalla et al., 25 Mar 2025).

Instrumental systematics and foregrounds, notably the tSZ and CMB lensing signals, are controlled via multi-frequency cleaning, component separation, and template subtraction. Calibration is typically carried out with hydrodynamical simulations and mock CMB skies (Gong et al., 2023).

3. Empirical Results from DESI+ACT and Related Pipelines

Recent analyses employing DESI, ACT, Planck, SDSS, and related datasets have robustly detected the kSZ effect in the low- and intermediate-redshift universe ($z < 1$):

• Detection Significance: Pairwise and stacking analyses have achieved $\gtrsim5\sigma$ detections for DESI-based cluster/group catalogs and $\sim10\sigma$ for large spectroscopic samples (DESI LRG, BGS) cross-correlated with ACT DR6 maps (Guachalla et al., 25 Mar 2025, Chen et al., 2021, Li et al., 7 Jan 2024, Hadzhiyska et al., 9 Jul 2024).
• Profile Extensions: Stacked kSZ profiles extended to multiple virial radii demonstrate that hot gas is more spatially extended than dark matter, a result systematically observed in DESI+ACT analyses (Hadzhiyska et al., 9 Jul 2024, Guachalla et al., 25 Mar 2025). The measured profiles are more consistent with high-feedback hydrodynamical simulations (Illustris) than with low-feedback models (IllustrisTNG).
• Optical Depth Scaling: The optical depth $\bar{\tau}$ inferred from kSZ measurements scales linearly with halo/group mass in log space: $$\log\bar{\tau} = \gamma (\log \tilde{M} - 14) + \log \beta$$, with typical slope $\gamma \approx 0.55\pm 0.1$ (Li et al., 7 Jan 2024).
• Tomographic and Anisotropic Probing: Tomographic (redshift-binned) reconstruction recovers the cosmic velocity field at high significance ($11.7\sigma$, $A=0.39\pm0.04$ relative to fiducial models) (Lai et al., 26 Jun 2025). Oriented stacking and multipole decomposition have isolated anisotropic (quadrupole) kSZ signatures, indicating gas density alignment with cosmic web filaments (Hadzhiyska et al., 4 Dec 2024).
• Calibration with CMB Lensing: Joint analyses with ACT CMB lensing maps have provided independent mass calibration of the host halos, enabling direct calculation of the baryon fraction and demonstrating that nearly all baryons are recovered at large aperture ($>2$–$3$ virial radii), resolving the "missing baryon" problem for group/cluster-mass halos (Hadzhiyska et al., 18 Jul 2025).

4. Methodological Advances and Robustness

The development and intercomparison of multiple estimators have improved the robustness and interpretation of kSZ results:

Method	Noise/Foreground Control	Unique Aspect
Pairwise Momentum	Velocity-weighted pairs	Direct measurement of mean flows
CAP Stacking	Annulus subtraction	Insensitivity to primary CMB
Fourier-space Power	Multipole suppression	Natural treatment of RSDs, window fxn
Bispectrum/QML	Optimal covariance usage	Tomographic, redshift-bin sensitivity

Correction factors are essential:

• CAP filtering requires an attenuation correction (calibrated in simulation) to recover unbiased amplitudes due to annulus subtraction (Gong et al., 2023).
• The matched filter approach relies on tuning the spatial template for the gas profile and instrument beam.
• Systematics from line-of-sight projection, cluster miscentering, and photo-z uncertainties (photo-z error suppresses small-scale signal) are modeled via simulations; spectroscopic redshifts minimize this effect (Chen et al., 2021, Guachalla et al., 25 Mar 2025).

Comparison between tSZ-derived and kSZ-derived optical depths yield consistent results, strengthening the reliability of measured baryonic gas content (Calafut et al., 2021).

5. Scientific Impact and Cosmological Implications

DESI + ACT kSZ measurements have enabled:

• Direct Baryon Census: At large radii ($\gtrsim$2–3 $R_{\rm vir}$) the cumulative gas fraction approaches the cosmological ratio $\Omega_b/\Omega_m$, indicating that the missing baryons reside in the outskirts of halos, consistent with a scenario where feedback expels or redistributes hot gas to the periphery (Hadzhiyska et al., 18 Jul 2025).
• Feedback Constraints: Observed gas distributions and cumulative gas fractions at fixed radius are systematically lower than in "standard" simulations (TNG300), presenting $>4\sigma$ evidence for stronger baryonic feedback in real halos (Hadzhiyska et al., 18 Jul 2025, Hadzhiyska et al., 9 Jul 2024, Guachalla et al., 25 Mar 2025).
• Velocity Field Reconstruction: Quadratic and QML-based velocity field reconstruction achieves high signal-to-noise, paving the way for stringent constraints on gravity, dark energy, and possibly primordial non-Gaussianity (McCarthy et al., 8 Oct 2024, Lai et al., 26 Jun 2025).
• Cosmic Web and Filamentary Flows: The detection of anisotropic kSZ signatures along filaments reveals the alignment and flow of baryons within the cosmic web—evidence for accretion and directed feedback (e.g., AGN) processes (Hadzhiyska et al., 4 Dec 2024).
• De-kSZing and CMB Analytics: kSZ serves both as a signal and a source of confusion noise for other CMB probes (e.g., lensing, moving-lens effect). Template subtraction using DESI-based velocity/density tracers (de-kSZing) can remove ≈10–20% of the kSZ power from CMB maps, improving cosmological parameter estimation and lensing precision (Foreman et al., 2022).

6. Future Prospects and Methodological Challenges

Forecasts indicate substantial gains as survey depth, area, and CMB resolution increase:

• Signal-to-noise for velocity-stacked kSZ measurements is anticipated to reach $S/N \sim 50$ with DESI Year 3, ACT, and Rubin LSST data sets (Guachalla et al., 25 Mar 2025).
• Optimal quadratic and QML estimators implemented in tomographic redshift bins will exploit the full information available in forthcoming surveys, incorporating realistic masks, noise, and mode-coupling (Lai et al., 26 Jun 2025).
• Continued development in hydrodynamical modeling, mass calibration via lensing, and multi-wavelength approaches (combining kSZ, tSZ, X-rays, and FRBs) will further constrain baryonic feedback models and the gas-dark matter connection.
• Accurate modeling and subtraction of systematic contributions, such as CMB lensing contamination to patchy screening signals, remains critical to unbiased measurements (Hadzhiyska et al., 20 Jun 2025).

7. Concluding Perspectives

The DESI+ACT kSZ profile measurements have transformed the field’s ability to measure baryonic gas distributions, constrain feedback mechanisms, and reconstruct cosmic velocity fields with high precision. These results strongly support the scenario of extended hot gas in halos driven by robust feedback processes and provide a direct resolution to the missing baryons on galaxy group and cluster scales. The combined power of future photometric and spectroscopic galaxy surveys with next-generation CMB observatories will enable precision kSZ cosmology, providing crucial insight into galaxy formation, cosmic flows, and the fundamental physics of structure formation.