Cross-correlating Squared kSZ and HI Intensity Fields: A Map-level ACT--MeerKAT Forecast

The kinetic Sunyaev–Zel’dovich (kSZ) effect probes the line-of-sight momentum of free electrons, but its blackbody spectrum and velocity-dependent sign make it difficult to isolate and cause conventional cross-correlations with density tracers to vanish. In this work, we investigate the cross-correlation of the squared kSZ field with the projected squared HI intensity field using mock ACT and MeerKAT observations constructed from a Jiutian-1G simulation lightcone. We generate halo-based kSZ maps and MeerKAT-like HI brightness-temperature cubes over a ${13.5}^{\circ }\times {13.5}^{\circ }$ field. The simulations incorporate ACT beam smoothing and effective internal-linear-combination noise, together with the frequency-dependent MeerKAT beam, scanning strategy, map-making, and inhomogeneous thermal noise. We analyze signal-only, idealized amplitude-reconstructed, and Wiener-filtered kSZ maps. The resulting squared-field cross-correlations have diagnostic cumulative signal-to-noise ratios of approximately $3$-$4$. Our map-level results demonstrate the detectability of the ${\mathrm{k}\mathrm{S}\mathrm{Z}}^2\times {\mathrm{H}\mathrm{I}}^2$ correlation in future joint ACT–MeerKAT observations.