Studying the morphology of reionisation with the triangle correlation
  function of phases
  We present a new statistical tool, called the triangle correlation function
(TCF), inspired by the earlier work of Obreschkow et al. It is derived from the
three-point correlation function and aims to probe the characteristic scale of
ionized regions during the epoch of reionization from 21cm interferometric
observations. Unlike most works, which focus on power spectrum, i.e. amplitude
information, our statistic is based on the information we can extract from the
phases of the Fourier transform of the ionization field. In this perspective,
it may benefit from the well-known interferometric concept of closure phases.
We find that this statistical estimator performs very well on simple ionization
fields. For example, with well-defined fully ionized discs, there is a peaking
scale, which we can relate to the radius of the ionized bubbles. We explore the
robustness of the TCF when observational effects such as angular resolution and
noise are considered. We also get interesting results on fields generated by
more elaborate simulations such as 21CMFAST. Although the variety of sources
and ionized morphologies in the early stages of the process make its
interpretation more challenging, the nature of the signal can tell us about the
stage of reionization. Finally, and in contrast to other bubble size
distribution algorithms, we show that the TCF can resolve two different
characteristic scales in a given map.
