Shear-kSZ: A New Estimator for the Matter-Electron Power Spectrum from kSZ Tomography and Weak Lensing
We propose a new estimator of the electron--matter power spectrum, $P_{me}(k)$, which correlates the kinematic Sunyaev--Zel'dovich (kSZ) temperature with the product of the line-of-sight velocity field and the weak-lensing convergence. Like the stacked kSZ estimator, it factorizes into a calibratable velocity kernel times $P_{me}(k)$, but it probes the full matter distribution rather than the gas around a biased tracer. It therefore measures the baryonic suppression of the matter power spectrum, $S(k)$, one of the dominant astrophysical systematics for Stage-IV cosmic shear. We derive an analytic expression for the estimator, validate it against simulations at the per-cent level, and show that its parity structure cancels cosmic microwave background (CMB) foregrounds. We forecast the detectability with a realistic pipeline: velocities reconstructed from the simulated tracers, with and without photometric-redshift errors; the kSZ signal of all the ionized gas along the line of sight; a CMB map with Simons Observatory (SO) noise; and LSST source samples free of intrinsic alignments. A DESI-like spectroscopic sample at $0.5<z<1$ over the $20\%$ of the sky that DESI, LSST and SO share gives a $4$--$7σ$ detection. Photometric redshifts cost only $5$--$10\%$ of the significance, so LSST can supply its own velocity tracers over its full overlap with SO: with tracers at $0.1<z<1.3$ and five source samples we find $10σ$ in an end-to-end simulation, and $13σ$ with Advanced SO (16$σ$ if extending to $z < 1.5$). This corresponds to a few-per-cent measurement of $S(k)$ at $k\simeq1$--$4\,h\,{\rm Mpc}^{-1}$, the scales that matter most for cosmic shear.