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Scientists propose a new statistical tool, called the shear–kSZ estimator, to measure how ionized gas traces the total matter in the universe. The method combines three things: maps of tiny temperature shifts in the cosmic microwave background caused by moving electrons (the kinematic Sunyaev–Zel’dovich, or kSZ, effect), a template for the line-of-sight velocity field built from galaxy redshifts, and a weak‑lensing convergence map that traces projected matter. The estimator isolates the matter–electron cross‑power spectrum P_me(k), which tells how free electrons follow the total matter on different spatial scales.
At a high level the estimator works because the kSZ signal is proportional to electron density times velocity, while weak lensing traces matter without needing a model for how galaxies sit in halos. By correlating the kSZ temperature map with the product of a reconstructed velocity template and the lensing convergence, the observable factorizes into a calibratable velocity kernel times P_me(k). That factorization is analogous to the standard “stacked kSZ” approach, but the key difference is that shear–kSZ probes the full matter distribution rather than the electron distribution only around a particular galaxy sample. This allows a more direct measurement of the baryonic suppression S(k) — the scale‑dependent reduction of the matter power spectrum caused by gas physics — which is a main uncertainty for upcoming weak‑lensing surveys.
The authors derive the estimator from first principles and test it with simulations. They use N‑body output from the AbacusSummit simulations and construct a smoothed velocity template from tracer halos in thin radial bins to mimic real velocity reconstruction. Their analytic prediction matches the simulation measurement at the percent level, and they report agreement at better than about 5% over the scales where the signal dominates. The velocity dependence of the estimator is captured in a single kernel per radial bin, which can be calibrated from the data or simulations in the same way reconstruction transfer functions are calibrated in current kSZ analyses.
They also forecast detectability with realistic noise. Using a Simons Observatory–like CMB temperature map, a DESI‑like spectroscopic sample of luminous red galaxies for velocity reconstruction, and LSST‑like lensing sources, they find a signal‑to‑noise ratio around 16 for a sky fraction f_sky = 0.2. In their setup this corresponds to roughly a 1% measurement of S(k). Because the forecast is limited mainly by CMB instrument noise rather than lensing depth, they expect a detection already at roughly 10σ with early LSST data releases and estimate about a twofold improvement with an Advanced Simons Observatory.
This measurement matters because S(k) — the baryonic suppression of the matter power spectrum — is a dominant astrophysical systematic for future cosmic shear (weak‑lensing) surveys such as LSST and Euclid. A direct, calibrated measurement of how free electrons follow matter would reduce the need to extrapolate galaxy‑halo connections across mass scales. The shear–kSZ approach also benefits from a parity structure that cancels many CMB foreground contributions, reducing a common source of contamination.
There are important caveats. The method needs overlapping sky coverage between CMB maps, the spectroscopic tracer sample, and lensing sources. The forecast depends on assumptions about velocity reconstruction fidelity and about CMB noise and beam; the authors used the true halo velocities in the simulation to build the template and note that in real data the template must be produced and calibrated via reconstruction. The derivation uses approximations such as thin radial bins and the Limber approximation, and it neglects some connected non‑Gaussian terms that are expected to be subdominant for the multipole range of interest. Small theoretical corrections — a sub‑percent dark‑matter backreaction term and a bounded baryon auto‑spectrum correction — are identified but do not negate the estimator’s main promise. Overall, the paper presents a concrete, testable pathway to measure the matter–electron relation and hence the baryonic impact on matter clustering with current and near‑term surveys.