# Studying the morphology of reionisation with the triangle correlation function of phases

## TL;DR

This paper introduces the triangle correlation function (TCF), a new phase-based statistical tool derived from the three-point correlation function, to analyze ionized region scales during reionization from 21cm data, offering advantages over traditional power spectrum methods.

## Contribution

The paper presents the TCF as a novel phase-sensitive statistic for probing ionized bubble scales, demonstrating its effectiveness and robustness on simulated and semi-realistic reionization fields.

## Key findings

- TCF peaks at characteristic bubble radius in simple models
- Robustness of TCF under observational noise and resolution effects
- Ability to identify multiple characteristic scales in complex fields

## Abstract

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.