Probing Reionization up to the Mark: The Marked Power Spectrum to unveil the HI 21-cm signal from the EoR

The redshifted 21-cm signal from neutral hydrogen (HI) in the intergalactic medium (IGM) is a powerful probe of the Epoch of Reionization (EoR). Owing to the complex growth and morphology of ionized regions, the 21-cm brightness-temperature field becomes strongly non-Gaussian during the EoR, limiting the information captured by the standard power spectrum alone. While higher-order statistics such as the bispectrum can recover part of this information, they are computationally expensive and often less straightforward to interpret. In this work, we investigate marked statistics as an alternative framework for characterizing the EoR 21-cm signal. Using semi-numerical 21-cm simulations, we introduce a set of EoR-tailored mark functions, inspired by and extending existing marked-statistics ideas, and study both the power spectrum of the mark and that of the marked field. We show that suitably chosen marks can selectively enhance contributions from different IGM environments, capture additional non-Gaussian information beyond the standard power spectrum, and improve the statistical constraining power on EoR model parameters in a Fisher-matrix analysis. These results demonstrate that Fourier-space marked statistics, including both the power spectrum of the mark and that of the marked field, provide a computationally simple and flexible extension of standard two-point statistics for extracting astrophysical information from the EoR 21-cm signal.