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

Observations of redshifted 21cm radiation from neutral hydrogen (HI) at high redshifts is an important future probe of reionization. We consider the Multi-frequency Angular Power Spectrum (MAPS) to quantify the statistics of the HI signal as a joint function of the angular multipole l and frequency separation ∆ν. The signal at two different frequencies is expected to get decorrelated as ∆ν is increased, and quantifying this decorrelation 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 ∆ν. In this paper we develop formulae relating the MAPS to different components of the three dimensional 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 the HI traces the dark matter and (ii) PR: where the effects of patchy reionization are incorporated through two parameters which are related to the bubble size and the clustering of the bubble centers 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 fluctuations dominated, and the signal is considerably enhanced for large bubble size. For most cases of interest at l ∼ 100 the signal is uncorrelated beyond∆ν ∼ 1MHz or even less, whereas it occurs around∼ 0.1MHz at l ∼ 10. The ∆ν dependence also carries an imprint of the bubble size and the bias, and is expected to be an important probe of the reionization scenario.