kSZ for everyone: the pseudo-Cl approach to stacking

TL;DR

The paper introduces a harmonic-space cross-correlation estimator, $C_l^{\pi T}$, between a galaxy momentum density proxy and CMB temperature to measure the kSZ signal around galaxies. By leveraging pseudo-$C_l$ techniques and masking, the method recovers all information contained in traditional kSZ stacking while offering improved computational efficiency and straightforward uncertainty propagation, including cross-covariances with other probes. Validation with toy models and simulations shows unbiased cross-spectra and a faithful reconstruction of stacking signals, and application to ACT DR6 with DESI Y1 LRG data yields a significant detection in agreement with stacking within errors. The approach facilitates seamless multi-tracer analyses and robust baryonic physics constraints, while highlighting the need for deeper covariance studies and potential extensions to other stacking schemes.

Abstract

We present a harmonic-space estimator for the cross-correlation between the kinematic Sunyaev-Zel'dovich effect and the reconstructed galaxy momentum field that offers several practical advantages over the traditional stacking approach. The estimator is easy to deploy using relatively modest computational resources and recovers all information available in the galaxy-kSZ cross-correlation. In particular, by using well-understood power spectrum estimation techniques, its statistical uncertainties, including potential correlated uncertainties with other large-scale structure observables, can be easily and accurately estimated. Moreover, standard kSZ stacking measurements can be reconstructed exactly from the estimator at a lower computational cost, employing harmonic-space, catalog-level techniques to recover all small-scale information.

Figures (12)

• Figure 1: Harmonic transform of the compensated aperture photometry filter for different apertures $\theta_d$. The solid lines show the calculation using the flat-sky approximation (Eq. \ref{['eq:cap_fourier']}), with the points showing the exact calculation (Eq. \ref{['eq:cap_harm']}). The flat-sky estimate is accurate enough on all relevant scales, and significantly faster to calculate. The CAP filters peak at a scale $\ell_{\rm CAP}\sim2.5/\theta_d$, with an amplitude proportional to $\theta_d^2$.
• Figure 2: Completeness mask used for the mock survey described in Section \ref{['ssec:res.val']}.
• Figure 3: Coupled cross-spectrum between a momentum field computed from a simulated source catalog and its smooth map-based counterpart at $N_{\rm side}=128$, for catalog sizes of $10^5$, $10^4$, $10^3$. We compare against the theoretical input computed from the ground truth coupled with the catalog-based mode-coupling matrix. Upper panel: mean over 1000 simulations with bars showing the expected standard error on the mean. Lower panel: relative bias, in units of the error on the mean.
• Figure 4: Mode-decoupled catalog$\times$map cross-spectrum for a simulated source catalog and its smooth map-based counterpart at $N_{\rm side}=128$, for catalog sizes of $10^5$, $10^4$, $10^3$. Upper panel: mean over 1000 simulations with bars showing the expected standard error on the mean. Lower panel: relative bias, in units of the error on the mean.
• Figure 5: Redshift distribution of the galaxy samples used here. The simulated photometric LRG galaxy sample of 2001.06018, used in Section \ref{['ssec:res.stack']}, is shown in purple. The spectroscopic DESI Y1 LRG sample 2208.08515, used in Section \ref{['ssec:res.data']}, is shown in green.