Analyzing the 21-cm forest with wavelet scattering transform: Insight into non-Gaussian features of the 21-cm forest

The 21cm forest, narrow absorption features in the spectra of high redshift radio sources caused by intervening neutral hydrogen, offers a unique probe of the intergalactic medium and small-scale structures during reionization. While traditional power spectrum methods have been widely used for analyzing the 21cm forest, these techniques are limited in capturing the non-Gaussian nature of the signal. In this work, we introduce the Wavelet Scattering Transform (WST) as a novel diagnostic tool for the 21cm forest, which allows for the extraction of higher-order statistical features that power spectrum methods cannot easily capture. By decomposing simulated brightness temperature spectra into a hierarchy of scattering coefficients, the WST isolates both local intensity fluctuations (first-order coefficients) and scale-scale correlations (second-order coefficients), revealing the complex, multi-scale non-Gaussian interactions inherent in the 21cm forest. This approach enhances the power of 21cm forest in distinguishing between different cosmological models, such as Cold Dark Matter (CDM) and Warm Dark Matter (WDM), as well as scenarios with enhanced X-ray heating. Unlike traditional methods, which focus primarily on Gaussian statistics, the WST captures richer astrophysical and cosmological information. Our analysis shows that WST can significantly improve constraints on key parameters, such as the X-ray heating efficiency and the WDM particle mass, providing deeper insights into the early stages of cosmic structure formation.