Measuring cosmic bulk flow with kinetic Sunyaev-Zel'dovich velocity reconstruction

Technical Summary: Measuring cosmic bulk flow with kinetic Sunyaev-Zel'dovich velocity reconstruction

Problem Statement
The Cosmological Principle posits that the universe is homogeneous and isotropic on large scales. A fundamental test of this principle is the measurement of "cosmic bulk flow"—the volume-averaged peculiar velocity of matter. Historically, bulk flow measurements have been limited to scales of $R \lesssim 100 \, h^{-1}\text{Mpc}$ due to the reliance on standard distance indicators (e.g., Tully-Fisher relations, Type Ia supernovae), whose uncertainties scale proportionally with distance. While some studies have reported excess bulk velocities at distances of $\sim 100\text{--}300 \, h^{-1}\text{Mpc}$ that appear in tension with $\Lambda$CDM predictions, the origin of these discrepancies remains ambiguous (systematics, incomplete modeling, or new physics). There is a critical need for independent probes capable of mapping the velocity field out to cosmological distances ($\sim 100\text{--}1000 \, h^{-1}\text{Mpc}$) to resolve these tensions and test the Cosmological Principle on gigaparsec (Gpc) scales.

Methodology
The authors employ the kinetic Sunyaev-Zel'dovich (kSZ) effect, a distance-independent probe of peculiar velocities arising from the Doppler shifting of Cosmic Microwave Background (CMB) photons scattering off free electrons in large-scale structure. The study utilizes a kSZ velocity reconstruction pipeline based on the quadratic estimator formalism, which cross-correlates CMB temperature maps with galaxy overdensity maps across multiple tomographic redshift bins.

• Data Products:
  • Galaxy Catalogs: Two large-scale catalogs were used, split into three tomographic bins each:
    • WISE$\times$SuperCOSMOS (WxSCOS): Three bins with median redshifts $z_{\text{med}} \approx 0.11, 0.19, 0.27$.
    • unWISE: Three bins ('blue', 'green', 'red') with median redshifts $z_{\text{med}} \approx 0.6, 1.1, 1.5$.
  • CMB Maps: Planck SMICA temperature maps.
• Reconstruction and Systematics:
  • Galaxy number-count maps were corrected for survey systematics (e.g., extinction, depth variations) using empirical weights derived from high-frequency Planck maps (857 GHz), which are dominated by the Cosmic Infrared Background (CIB).
  • Velocity maps were reconstructed for each of the six subsamples.
  • Optical Depth Degeneracy: A key challenge in galaxy-based kSZ reconstruction is the degeneracy between the velocity amplitude and the uncertain optical depth of the gas (parameterized as a velocity bias, $b_v$). The authors address this by translating high signal-to-noise $b_v$ measurements from ACT$\times$DESI data into priors applicable to their Planck$\times$WxSCOS and Planck$\times$unWISE combinations, marginalizing over $b_v$ when deriving bounds.
• Theoretical Framework:
  • The authors formalize the link between the dipole ($\ell=1$) of the kSZ-reconstructed velocity field and the standard bulk flow variance.
  • They derive constraints on the full-sky dipole power spectrum ($C^{vv}_1$) from the cut-sky data, accounting for mode-mode coupling and reconstruction noise.
  • To compare with standard literature results, they map the kSZ effective window function to an idealized spherical top-hat (TH) window function. This allows the translation of their kSZ-derived constraints into upper limits on the bulk flow variance, $\sigma^2_{V_{\text{TH}}}(R_{\text{TH}})$, and the matter power spectrum amplitude, $P_{mm}(k)$.

Key Contributions

1. Scale Extension: The study extends bulk flow measurements to effective radii of $R \sim 2000 \, h^{-1}\text{Mpc}$, bridging the gap between traditional distance-limited surveys and cosmological scales.
2. Theoretical Unification: The work provides a rigorous theoretical framework connecting kSZ velocity reconstruction (specifically the dipole component) to the volume-averaged bulk flow, demonstrating that both measure the same physical quantity filtered by different window functions.
3. Novel Bias Handling: A new approach is introduced to map the optical depth bias ($b_v$) across different data combinations, allowing constraints from high-S/N deep surveys (ACT$\times$DESI) to inform analyses of wide-area, lower-resolution datasets (Planck$\times$unWISE/WxSCOS).
4. Low-k Constraints: The method yields constraints on the matter power spectrum at low wavenumbers ($k \lesssim 10^{-3} \, \text{Mpc}^{-1}$) using low-redshift ($z \sim 1$) tracers, a regime typically probed only by the CMB at high redshift.

Results

• Bulk Flow Upper Limits: The analysis finds no statistically significant detection of bulk flow; consequently, it places tight upper limits. The results are fully consistent with $\Lambda$CDM expectations.
  • At scales $200 \lesssim R [h^{-1}\text{Mpc}] \lesssim 2000$, the derived upper limits are among the tightest to date.
  • The unWISE 'blue' and 'green' constraints are particularly strong at $\sim$Gpc scales.
• Tension with CatWISE: The unWISE constraints are in strong tension with the CatWISE quasar number-count dipole measurement. If the CatWISE dipole (observed at $R \sim 1000 \, h^{-1}\text{Mpc}$) were due to a coherent bulk flow, it would imply a velocity of $\sim 370 \, \text{km s}^{-1}$. This is in significant conflict with the unWISE upper limits ($\hat{V}_{\text{TH}} < 115 \, \text{km s}^{-1}$ for 'green' and $< 72 \, \text{km s}^{-1}$ for 'blue').
• Local Scale Tension: There is a $\sim 2\sigma$ tension between the WxSCOS 1 upper limit and some previous bulk flow measurements (e.g., Watkins et al. 2009, 2023) at $R \sim 100 \, h^{-1}\text{Mpc}$. The authors note their current upper limits are conservative and that more rigorous window function matching (e.g., Minimum Variance estimators) might reveal stronger tension.
• Matter Power Spectrum: The study derives 1$\sigma$ upper limits on the matter power spectrum amplitude $P_{mm}(k)$ at low-$k$, consistent with $\Lambda$CDM but not yet stringent enough to rule out beyond-$\Lambda$CDM scenarios.

Significance and Claims
The paper claims to successfully bridge the theoretical gap between kSZ-reconstructed velocities and traditional bulk flow measurements, effectively expanding the horizon of bulk velocity measurements to Gpc scales. By finding results consistent with the large-scale statistical homogeneity and isotropy expected in $\Lambda$CDM, the work supports the Cosmological Principle on these scales.

The authors emphasize that their results do not indicate anomalous bulk motion of Large Scale Structure (LSS) tracers at Gpc scales, thereby challenging interpretations of the CatWISE quasar dipole as a kinematic effect caused by a massive bulk flow. While the current constraints are upper limits, the authors assert that kSZ velocity reconstruction is poised to transition from providing competitive upper limits to acting as a precision probe of fundamental cosmology as future surveys (e.g., SPHEREx, Euclid, LSST, Simons Observatory) provide higher galaxy number densities and CMB resolution.