Prospects for kSZ$^2$-Galaxy Cross-Correlations during Reionization

We explore a new approach for extracting reionization-era contributions to the kinetic Sunyaev-Zel'dovich (kSZ) effect. Our method utilizes the cross-power spectrum between filtered and squared maps of the cosmic microwave background (CMB) and photometric galaxy surveys during the Epoch of Reionization (EoR). This kSZ$^2$-galaxy cross-power spectrum statistic has been successfully detected at lower redshifts ($z \lesssim 1.5$). Here we extend this method to $z \gtrsim 6$ as a potential means to extract signatures of patchy reionization. We model the expected signal across multiple photometric redshift bins using semi-numeric simulations of the reionization process. In principle, the cross-correlation statistic robustly extracts reionization-era contributions to the kSZ signal, while its redshift evolution yields valuable information regarding the timing of reionization. Specifically, the model cross-correlation signal near $\ell \sim 1,000$ peaks during the early stages of the EoR, when about 20% of the volume of the universe is ionized. Detectible $\ell$ modes mainly reflect squeezed triangle configurations of the related bispectrum, quantifying correlations between the galaxy overdensity field on large scales and the smaller-scale kSZ power. We forecast the prospects for detecting this signal using future wide-field samples of Lyman-break galaxies from the Roman Space Telescope and next-generation CMB surveys including the Simons Observatory, CMB-S4, and CMB-HD. We find that a roughly 13$\sigma$ detection is possible for CMB-HD and Roman after summing over all $\ell$ modes. We discuss the possibilities for improving this approach and related statistics, with the aim of moving beyond simple detections to measure the scale and redshift dependence of the cross-correlation signals.