Patchy Helium and Hydrogen Reionization from the Kinetic Sunyaev-Zel'dovich Effect and Galaxies

Upcoming cosmic microwave background (CMB) experiments will measure temperature fluctuations on small angular scales with unprecedented precision, enabling improved measurements of the kinetic Sunyaev-Zel'dovich (kSZ) effect. This secondary anisotropy has emerged as a valuable probe of the distribution of ionized electrons in the post-recombination Universe. Although the sensitivity of the kSZ effect has recently been utilized to study the high-redshift epoch of hydrogen (H) reionization, its redshift-integrated nature -- combined with anticipated improvements in measurement precision -- suggests that accounting for the later epoch of helium (He) reionization will become increasingly important in the near future. Joint characterization of the epochs will allow for a more coherent understanding of early-star and -quasar formation, as these sources drive the ionization of H and He in the intergalactic medium. In this paper, we extend the kSZ higher-order statistic introduced by Smith \& Ferraro (2017) to forecast the ability of upcoming CMB surveys to probe the morphology of both H and He reionization. Moreover, given that upcoming large-scale structure surveys will trace density fluctuations at redshifts overlapping with the epoch of He reionization, we propose a novel cross-correlation between the kSZ higher-order statistic and galaxy survey measurements. Using a joint information-matrix analysis of H and He reionization, we show that next-generation CMB and galaxy surveys will have sufficient statistical power to characterize the patchy morphology of H reionization and set constraints on the redshift evolution of its He counterpart.