Measurements of one-point statistics in 21-cm intensity maps via foreground avoidance strategy

Measurements of the one-point probability distribution function and higher-order moments (variance, skewness, kurtosis) high-redshift 21 cm fluctuations are among most direct statistical probes non-Gaussian nature structure formation evolution during reionization. However, contamination from astrophysical foregrounds instrument systematics pose significant challenges in measuring these statistics real observations. In this work, we use forward modelling to investigate feasibility through a foreground avoidance strategy. Leveraging characteristic wedge-shape k-space, apply wedge-cut filter that removes contaminated modes mock data set based on Hydrogen Epoch Reionization Array (HERA) instrument, measure image-space representation remaining non-contaminated modes. We experiment with varying degrees wedge-cutting over different frequency bandwidths find centre band is least susceptible bias wedge-cutting. Based finding, introduce rolling method allows reconstruction an optimal 21~cm intensity map full bandwidth using outputs multiple sub-bands. perform Monte Carlo simulations show HERA should be able rise skewness kurtosis near end reionization if leakage Fourier transform window can controlled.