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