The ‘marked’-statistics to unveil EoR 21-cm signal

Abstract

The 21-cm signal from neutral hydrogen in the intergalactic medium (IGM) serves as a powerful probe of the Epoch of Reionization (EoR), the period during which the first luminous sources were formed and Universe went through a phase transition from being neutral to ionized. The 21-cm signal, arising from the spin-flip transition in neutral hydrogen, traces the distribution and evolution of large-scale structures during this critical phase of cosmic history. The EoR 21-cm brightness temperature field exhibits significant non-Gaussianity due to the complex distribution and growth of ionized regions, which is tied to the various astrophysical processes in the IGM and within the sources. As a result, the standard 21-cm power spectrum fails to capture all the relevant statistical information hidden in this field. While higher-order statistics, such as the bispectrum, can provide additional insights, they are computationally intensive and often difficult to interpret. This project investigates the application of marked statistics as an alternative approach to characterize the 21-cm field. By employing non-linear transformations to the original field, the contributions from distinct types of fluctuations can be modified independently, allowing for targeted analysis of specific features. In particular, enhancing specific field properties amplifies their corresponding fluctuations, improving the ability of the marked power spectrum to capture non-Gaussian signatures. Through this project, we demonstrated that it is possible to construct transformations that render the power spectrum a more optimal summary statistic for the transformed field. Marked statistics assign weights or "marks" to each spatial location based on local field properties, effectively emphasizing targeted structures. We show that this approach provides a computationally efficient framework for extracting non- Gaussian information and enables a more detailed statistical description of the 21-cm signal. The project further explores different forms of mark functions and their impact on the resulting statistics, with the broader goal of improving our understanding of the EoR.