Abstract
The bubble size distribution of ionized hydrogen regions, which could be
derived from the tomographic imaging data of the redshifted 21~cm signal from
the epoch of reionization, probes the information about the morphology of \HII\
bubbles during the reionization. However, 21~cm imaging is observationally very
challenging even for the upcoming large radio interferometers. Given that these
interferometers promise to measure the 21~cm power spectrum accurately, we
propose a new method, which is based on the artificial neural networks (ANN),
to reconstruct the \HII\ bubble size distribution from the 21~cm power
spectrum. We demonstrate that the reconstruction from the 21~cm power spectrum
can be almost as accurate as directly measured from the imaging data with the
fractional error $10\%$, even with thermal noise at the sensitivity
level of the Square Kilometre Array. Nevertheless, systematic errors might
arise from approximations made in reionization simulations used for training
the ANN. This paper, as the first in a series, exemplifies the possibility of
recovering from the 21~cm power spectrum with ANN additional statistics of
cosmic reionization that could not otherwise be inferred from the power
spectrum analysis directly in the conventional methods.
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