A Halo Model Approach to the 21 cm and Lyα Cross-correlation

We present a halo-model-based approach to calculate the cross-correlation between 21 {cm} H I intensity fluctuations and {Ly}α emitters (LAE) during the epoch of reionization (EoR). Ionizing radiation around dark matter halos are modeled as bubbles with the size and growth determined based on the reionization photon production, among other physical parameters. The cross-correlation shows a clear negative-to-positive transition, associated with transition from ionized to neutral hydrogen in the intergalactic medium during EoR. The cross-correlation is subject to several foreground contaminants, including foreground radio point sources important for 21 {cm} experiments and low-z interloper emission lines, such as {{H}}α , O III, and O II, for {Ly}α experiments. Our calculations show that by masking out high fluxes in the {Ly}α measurement, the correlated foreground contamination on the 21 {cm}-{Ly}α cross-correlation can be dramatically reduced. We forecast the detectability of 21 {cm}-{Ly}α cross-correlation at different redshifts and adopt a Fisher matrix approach to estimate uncertainties on the key EoR parameters that have not been well constrained by other observations of reionization. This halo-model-based approach enables us to explore the EoR parameter space rapidly for different 21 {cm} and {Ly}α experiments.