First detection of the moving lens effect with ACT and DESI LS

Technical Summary: First Detection of the Moving Lens Effect with ACT and DESI LS

Problem Statement
The transverse component of the peculiar velocity field of large-scale structure has remained largely inaccessible to observation, unlike the radial component which is probed via redshift-space distortions and the kinetic Sunyaev-Zel'dovich (kSZ) effect. The "moving lens effect" offers a pathway to measure these transverse velocities. This effect arises when a gravitational potential well moves transversely to the line of sight, creating a time-varying potential along the photon path. This induces a net energy shift in Cosmic Microwave Background (CMB) photons, resulting in a temperature anisotropy proportional to the line-of-sight integral of $\nabla_\perp \Psi \cdot v_\perp$.

While theoretically well-established, detecting this signal is challenging due to its small amplitude and significant contamination from foregrounds. Previous studies identified that correlations between extragalactic foreground emission gradients (specifically the thermal Sunyaev-Zel'dovich effect, tSZ, and the Cosmic Infrared Background, CIB) and the transverse velocity field could produce signals morphologically similar to the moving lens but orders of magnitude larger on single-frequency maps. Furthermore, the signal shares a blackbody frequency spectrum with the primary CMB, making it inseparable by frequency information alone.

Methodology
The authors developed a Fourier-space cross-spectrum estimator to detect the moving lens effect, applied to CMB temperature maps from the Atacama Cosmology Telescope (ACT) DR6 and luminous red galaxy (LRG) catalogs from the DESI Legacy Imaging Surveys (DESI-LS).

1. Velocity Reconstruction: A transverse velocity template is constructed from the galaxy density field. Using a linear reconstruction filter (Wiener filter) applied to the galaxy overdensity, the authors estimate the transverse velocity field $\hat{v}_\perp$. Crucially, this reconstruction includes a hard cutoff in 3D wavenumber space ($k_{max} = 0.05 \text{ Mpc}^{-1}$) to separate large-scale bulk motions from small-scale foreground physics.
2. Cross-Spectrum Estimator: Instead of stacking CMB patches or using a quadratic estimator, the authors construct a spin-1 vector field $X_a(\theta)$ by weighting galaxies with their reconstructed transverse velocities. This field is decomposed into gradient ($X^G$) and curl ($X^C$) modes in harmonic space. The moving lens signal is predicted to produce a non-zero cross-correlation between the CMB temperature ($T$) and the gradient mode ($X^G$), denoted as $C^{TG}_\ell$, while the curl mode ($C^{TC}_\ell$) should vanish due to parity symmetry.
3. Normalization and Bias Mitigation: The pipeline utilizes "surrogate fields" (Gaussian random fields) to compute the normalization factor $N$ and account for survey geometry and selection functions without requiring full mock simulations. To mitigate foregrounds, the analysis enforces a separation of scales: the velocity reconstruction is limited to low $k$, ensuring that the cross-correlation is measured at multipoles $\ell \gg k_{max}\chi_*$, where foreground contamination is theoretically suppressed.
4. Data Sets: The analysis uses ACT DR6 NILC (foreground-cleaned) maps and single-frequency maps (90, 150, 220 GHz), cross-correlated with DESI-LS LRG samples (main and extended) in the Northern (NGC) and Southern (SGC) Galactic caps.

Key Results

• Detection Significance: Using the foreground-cleaned NILC map, the authors report a detection of the moving lens effect with a signal-to-noise ratio (SNR) of 4.8$\sigma$ for the extended DESI-LS sample ($b_{ML} = 1.24 \pm 0.26$) and 3.7$\sigma$ for the main sample ($b_{ML} = 0.93 \pm 0.25$). The measured amplitude is consistent with the fiducial halo-model prediction ($b_{ML}=1$).
• Robustness and Null Tests:
  • Curl Mode: All curl-mode cross-spectra ($C^{TC}_\ell$) are consistent with zero, with no test exceeding $2\sigma$ significance, confirming the absence of parity-asymmetric systematics.
  • Frequency Differences: Null tests using frequency-difference maps (e.g., 150-90 GHz) show no significant signal, consistent with the blackbody nature of the moving lens. While 220 GHz difference maps showed deviations up to $1.8\sigma$, these were deemed consistent with statistical fluctuations.
  • Foreground Constraints:
    • Empirical: Cross-correlations with Planck 353 and 545 GHz maps (dominated by CIB) were used to predict CIB contamination at ACT frequencies. The predicted bias was consistent with zero ($\Delta b_{ML} \approx 0.00 \pm 0.10$ at 150 GHz).
    • Simulation: A simplified pipeline using Quijote N-body simulations demonstrated that the hard $k_{max}$ cutoff in velocity reconstruction suppresses tSZ and CIB foreground biases at the multipoles used for the signal measurement ($\ell > 2500$).
• Consistency: Results are consistent across NGC and SGC footprints, between main and extended galaxy samples, and between night-only and day-night CMB co-adds.

Significance and Claims
The paper claims the first observational detection of the moving lens effect. This achievement unlocks access to the transverse velocity field of the Universe, a new cosmological probe distinct from radial velocity measurements.

The authors emphasize that this detection is significant because:

1. It validates the theoretical framework for measuring transverse velocities via CMB secondary anisotropies.
2. It demonstrates that foreground contamination (specifically tSZ and CIB) can be effectively mitigated through scale separation in the velocity reconstruction, contrary to earlier pessimistic forecasts.
3. It provides a new, independent avenue for cosmological inference. When combined with kSZ tomography (which measures radial velocities), the moving lens effect allows for the reconstruction of the full 3D velocity field. This can break degeneracies inherent in kSZ measurements (such as the optical-depth degeneracy) and provide independent constraints on the growth rate of structure ($f\sigma_8$) and primordial non-Gaussianity ($f_{NL}$).

The work establishes a pipeline that is robust against foregrounds and systematics, paving the way for future applications with higher-sensitivity CMB experiments (like the Simons Observatory and CMB-S4) and deeper galaxy surveys (like DESI spectroscopic data and LSST), which are forecasted to yield much higher signal-to-noise ratios.