Probing the Intergalactic Medium with Ly$\alpha$ and 21 cm Fluctuations

We study 21cm and Ly$\alpha$ fluctuations, as well as H$\alpha$, while distinguishing between Ly$\alpha$ emission of galactic, diffuse, and scattered intergalactic medium (IGM) origin. Cross-correlation information about the state of the IGM is obtained, testing neutral versus ionized medium cases with different tracers in a seminumerical simulation setup. In order to pave the way toward constraints on reionization history and modeling beyond power spectrum information, we explore parameter dependencies of the cross-power signal between 21$$cm and Ly$\alpha$, which displays a characteristic morphology and a turnover from negative to positive correlation at scales of a couple Mpc${}^{-1}$. In a proof of concept for the extraction of further information on the state of the IGM using different tracers, we demonstrate the use of the 21$$cm and H$\alpha$ cross-correlation signal to determine the relative strength of galactic and IGM emission in Ly$\alpha$. We conclude by showing the detectability of the 21$$cm and Ly$\alpha$ cross-correlation signal over more than one decade in scale at high signal-to-noise ratio for upcoming probes like SKA and the proposed all-sky intensity mapping satellites SPHEREx and CDIM, while also including the Ly$\alpha$ damping tail and 21cm foreground avoidance in the modeling.