Scintillation noise power spectrum and its impact on high redshift 21-cm observations

Visibility scintillation resulting from wave propagation through the turbulent ionosphere can be an important sources of noise at low radio frequencies ($\nu\lesssim 200$ MHz). Many low frequency experiments are underway to detect the power spectrum of brightness temperature fluctuations of the neutral-hydrogen $21$-cm signal from the Epoch of Reionization (EOR: $12\gtrsim z\gtrsim 7$, $100\lesssim \nu \lesssim 175$ MHz). In this paper, we derive scintillation noise power-spectra in such experiments while taking into account the effects of typical data processing operations such as self-calibration and Fourier synthesis. We find that for minimally redundant arrays such as LOFAR and MWA, scintillation noise is of the same order of magnitude as thermal noise, has a spectral coherence dictated by stretching of the snapshot $uv$-coverage with frequency, and thus is confined to the well known wedge-like structure in the cylindrical ($2$-dimensional) power spectrum space. Compact, fully redundant ($d_{\rm core}\lesssim r_{\rm F} \approx 300$ m at $150$ MHz) arrays such as HERA and SKA-LOW (core) will be scintillation noise dominated at all baselines, but the spatial and frequency coherence of this noise will allow it to be removed along with spectrally smooth foregrounds.