The re-markable 21-cm power spectrum I: Probing the HI distribution in the post-reionization era using marked statistics

The neutral hydrogen (HI) power spectrum, measured from intensity fluctuations in the 21-cm background, offers insights into the large-scale structures (LSS) of our Universe in the post-reionization era (redshift $z<6$). A significant amount of HI is expected to reside in low- and intermediate-density environments, but the power spectrum mainly captures information from high-density regions. To more fully extract the information contained in the HI field, we investigate the use of a marked power spectrum statistic. Here, the power spectrum is effectively re-weighted using a non-linear mark function which depends on the smoothed local density, such that low- or high-density regions are up- or down-weighted. This approach may also capture information on some higher-order statistical moments of the field. We model the HI distribution using semi-numerical simulations and for the first time study the marked HI power spectrum, across $1 \leq z \leq 5$. Our analysis indicates that there is considerable evolution of the HI field during the post-reionization era. Over a wide range of length scales (comoving wave numbers $0.05\leq k \leq 1.0$ Mpc$^{-1}$) we expectedly find that the HI evolves slowly at early times, but more rapidly at late times. This evolution is not well-captured by the power spectrum of the standard (unmarked) HI field. We also study how the evolution of the HI field depends on the chosen smoothing scale for the mark, and how this affects the marked power spectrum. We conclude that the information about the HI content at low and intermediate densities is important for a correct and consistent analysis of HI content and evolution based on the 21-cm background. The marked power spectrum can thus provide a less biased statistic for parameter constraints than the normal power spectrum.