The Evolving Power Spectrum for the light cone Epoch of Reionization (EoR) 21-cm signal

The rapid evolution of the cosmological neutral hydrogen (HI) distribution during the EoR is imprinted along the line of sight (LoS) in the redshifted 21-cm signal due to the light cone (LC) effect. The LC EoR 21-cm signal ceases to be ergodic along the LoS, and the Fourier transform-based three-dimensional power spectrum (PS) fails to capture the full two-point statistics. Several earlier studies have used the multi-frequency angular power spectrum (MAPS) $\mathcal{C}_\ell(\nu_1,\nu_2)$ to overcome this limitation. However, we do not have a simple interpretation of $\mathcal{C}_\ell(\nu_1,\nu_2)$ in terms of comoving length scale, and the data volume is large. Here we introduce the evolving power spectrum (ePS) to quantify the two-point statistics of the LC EoR 21-cm signal. This has a simple interpretation in terms of redshift evolution and comoving length scales, and the binned ePS reduces the data volume by several orders of magnitude compared to MAPS. Considering simulations, we study the first three even angular multipoles of ePS to quantify the LoS anisotropy of the signal. We find that as reionization progresses, at large $k$ ($ \ge 0.6 \, {\rm Mpc}^{-1}$), $P_{e\,0}(k,z)$ the monopole moment decreases as $\propto \bar{x}_{\rm H I}$ the mean neutral HI fraction, which, in principle, can be used to observationally determine the reionization history. Furthermore, $P_{e\,2}(k,z)$ the quadrupole moment is negative at small $k$ and positive at large $k$. We propose the binned ePS, which captures the entire information contained in MAPS, to quantify the full two-point statistics of the LC EoR 21-cm signal.