Exploring One-point Statistics in HERA Phase I Data: Effects of Foregrounds and Systematics on Measuring One-Point Statistics

Measuring one-point statistics in redshifted 21 cm intensity maps offers an opportunity to explore non-Gaussian features of the early universe. We assess the impact of instrumental effects on measurements made with the Hydrogen Epoch of Reionization Array (HERA) by forward modeling observational and simulation data. Using HERA Phase I observations over 94 nights, we examine the second (m2, variance) and third (m3) moments of images. We employ the DAYENU-filtering method for foreground removal and reduce simulated foreground residuals to 10% of the 21 cm signal residuals. In noiseless cosmological simulations, the amplitudes of one-point statistics measurements are significantly reduced by the instrument response and further reduced by wedge-filtering. Analyses with wedge-filtered observational data, along with expected noise simulations, show that systematics alter the probability distribution of the map pixels. Likelihood analysis based on the observational data shows m2 measurements disfavor the cold reionization model characterized by inefficient X-ray heating, in line with other power spectra measurements. Small signals in m3 due to the instrument response of the Phase I observation and wedge-filtering make it challenging to use these non-Gaussian statistics to explore model parameters. Forecasts with the full HERA array predict high signal-to-noise ratios for m2, m3, and S3 assuming no foregrounds, but wedge-filtering drastically reduces these ratios. This work demonstrates conclusively that a comprehensive understanding of instrumental effects on m2 and m3 is essential for their use as a cosmological probe, given their dependence on the underlying model.