Shear-kSZ: A New Estimator for the Matter-Electron Power Spectrum from kSZ Tomography and Weak Lensing

Abstract

We propose a new estimator for the ionized gas--matter power spectrum, which correlates the kinematic Sunyaev--Zel'dovich (kSZ) field with the line-of-sight velocity field and the weak-lensing convergence map. Analogously to the standard stacked kSZ estimator, this estimator factorizes into a calibratable velocity kernel multiplying the matter--electron cross-power spectrum, $P_{me}(k)$. Because the estimator accesses $P_{me}(k)$ for the full matter distribution rather than around a specific biased tracer as is the case with the standard stacked kSZ estimator, it allows us to determine the baryonic suppression of the matter power spectrum, $S(k)$, one of the dominant astrophysical systematics for Stage-IV cosmic shear. We derive and validate an analytical expression for the estimator against simulations, finding percent-level agreement. Due to its parity structure, contributions from cosmic microwave background (CMB) foregrounds cancel. Using a realistic CMB temperature map with Simons Observatory-like noise and beam, a smoothed velocity field as obtained via linear velocity reconstruction applied to DESI-like luminous red galaxies (LRGs), and LSST-like sources at high redshifts, which suppresses the effect of intrinsic alignments and boost factors, we forecast a $16\sigma$ measurement over $f_{\rm sky}=0.2$ (corresponding to 1\% measurement of $S(k)$), establishing our estimator as a readily measurable target for current surveys, e.g., LSST and \textit{Euclid}. Because the signal-to-noise is dominated by CMB noise rather than lensing depth, we expect a detection already at $\sim10\sigma$ with early LSST data releases. Substantial (factor of 2) gains in signal-to-noise are expected with Advanced Simons Observatory. While here we focus on DESI-like LRGs as the foreground sample, lower-redshift samples provide an even wider array of source samples in the background.