Predictions for measuring the 21-cm multi-frequency angular power spectrum using SKA-Low.

The light-cone (LC) effect causes the mean as well as the statistical properties of the redshifted 21-cm signal $T_{\rm b}(\hat{\bf n},\nu)$ to change with frequency $\nu$ (or cosmic time). Consequently, the statistical homogeneity (ergodicity) of the signal along the line of sight (LoS) direction is broken. This is a severe problem particularly during the Epoch of Reionization (EoR) when the mean neutral hydrogen fraction ($\bar{x}_{\rm HI}$) changes rapidly as the universe evolves. This will also pose complications for large bandwidth observations. These effects imply that the 3D power spectrum $P(k)$ fails to quantify the entire second-order statistics of the signal as it assumes the signal to be ergodic and periodic along the LoS. As a proper alternative to $P(k)$, we use the multi-frequency angular power spectrum (MAPS) ${\mathcal C}_{\ell}(\nu_1,\nu_2)$ which does not assume the signal to be ergodic and periodic along the LoS. Here, we study the prospects for measuring the EoR 21-cm MAPS using future observations with the upcoming SKA-Low. We find that the EoR 21-cm MAPS can be measured at a confidence level $\ge 5\sigma$ at angular scales $\ell \sim 1300$ for total observation time $t_{\rm obs} \ge 128\,{\rm hrs}$ across $\sim 44\,{\rm MHz}$ observational bandwidth. These results are very relevant for the upcoming large bandwidth EoR experiments as previous predictions were all restricted to individually analyzing the signal over small frequency (or equivalently redshift) intervals.