Detecting the non-Gaussianity of the 21-cm signal during reionization with the wavelet scattering transform

Detecting the 21-cm hyperfine transition from neutral hydrogen in the intergalactic medium is our best probe for understanding the astrophysical processes driving the Epoch of Reionization (EoR). The primary means for a detection of this 21-cm signal is through a statistical measurement of the spatial fluctuations using the 21-cm power spectrum (PS). However, the 21-cm signal is non-Gaussian meaning the PS, which only measures the Gaussian fluctuations, is suboptimal for characterizing all of the available information. The upcoming Square Kilometre Array (SKA) will perform a deep, 1000 h observation over 100 deg2 specifically designed to recover direct images of the 21-cm signal. In this work, we use the Wavelet Scattering Transform (WST) to extract the non-Gaussian information directly from these 2D images of the 21-cm signal. The key advantage of the WST is its stability with respect to statistical noise for measuring non-Gaussian information, unlike the bispectrum whose statistical noise diverges. In this work, we specifically focus on introducing a novel method to isolate non-Gaussian information from an image and apply this methodology to individual mock 21-cm images to quantify the strength of the non-Gaussian information contained within a single image. For example, at 150 (177) MHz (z ∼8.5 and ∼7) for a fiducial reionization model we recover a signal to noise of ∼5 (8) for the non-Gaussian information assuming perfect foreground removal and ∼2 (3) assuming foreground wedge avoidance.