Quantiles as Robust Probes of Non-Gaussianity in 21-cm Images
  The early epoch in which the first stars and galaxies formed is among the
most exciting unexplored eras of the Universe. A major research effort focuses
on probing this era with the 21-cm spectral line of hydrogen. While most
research focused on statistics like the 21-cm power spectrum or the
sky-averaged global signal, there are other ways to analyze tomographic 21-cm
maps, which may lead to novel insights. We suggest statistics based on
quantiles as a method to probe non-Gaussianities of the 21-cm signal. We show
that they can be used in particular to probe the variance, skewness, and
kurtosis of the temperature distribution, but are more flexible and robust than
these standard statistics. We test these statistics on a range of possible
astrophysical models, including different galactic halo masses, star-formation
efficiencies, and spectra of the X-ray heating sources, plus an exotic model
with an excess early radio background. Simulating data with angular resolution
and thermal noise as expected for the Square Kilometre Array (SKA), we conclude
that these statistics can be measured out to redshifts above 20 and offer a
promising statistical method for probing early cosmic history.
