The multifrequency angular power spectrum of the epoch of reionization 21-cm signal

Observations of redshifted 21-cm radiation from neutral hydrogen (HI) at high redshifts is an important future probe of reionization. We consider the multifrequency angular power spectrum (MAPS) to quantify the statistics of the HI signal as a joint function of the angular multipole l and frequency separation Delta nu. The signal at two different frequencies is expected to decorrelate as Delta nu is increased, and quantifying this is particularly important in deciding the frequency resolution for future HI observations. This is also expected to play a very crucial role in extracting the signal from foregrounds as the signal is expected to decorrelate much faster than the foregrounds (which are largely continuum sources) with increasing Delta nu. In this paper, we develop formulae relating MAPS to different components of the 3D HI power spectrum taking into account HI peculiar velocities. We show that the flat-sky approximation provides a very good representation over the angular scales of interest, and a final expression which is very simple to calculate and interpret. We present results for z=10 assuming a neutral hydrogen fraction of 0.6 considering two models for the HI distribution, namely, (i) DM: where HI traces the dark matter and (ii) PR: where the effects of patchy reionization are incorporated through two parameters which are the bubble size and the clustering of the bubble centres relative to the dark matter (bias), respectively. We find that while the DM signal is largely featureless, the PR signal peaks at the angular scales of the individual bubbles where it is Poisson fluctuation dominated, and the signal is considerably enhanced for large bubble size. For most cases of interest at l similar to 100 the signal is uncorrelated beyond Delta nu 1MHz or even less, whereas this occurs around similar to 0.1MHz at l similar to 10(3). The Delta nu dependence also carries an imprint of the bubble size and the bias, and is expected to be an important probe of the reionization scenario. Finally, we find that the l range 10(3) - 10(4) is optimum for separating out the cosmological HI signal from the foregrounds, while this will be extremely demanding at l < 100 where it is necessary to characterize the Delta nu dependence of the foreground MAPS to an accuracy better than 1 per cent.