Title: Bubble size statistics during reionization from 21-cm tomography,
Abstract: The upcoming SKA1-Low radio interferometer will be sensitive enough to
produce tomographic imaging data of the redshifted 21-cm signal from the Epoch
of Reionization. Due to the non-Gaussian distribution of the signal, a power
spectrum analysis alone will not provide a complete description of its
properties. Here, we consider an additional metric which could be derived from
tomographic imaging data, namely the bubble size distribution of ionized
regions. We study three methods that have previously been used to characterize
bubble size distributions in simulation data for the hydrogen ionization
fraction - the spherical-average, mean-free-path and friends-of-friends methods
- and apply them to simulated 21-cm data cubes. Our simulated data cubes have
the (sensitivity-dictated) resolution expected for the SKA1-Low reionization
experiment and we study the impact of both the light-cone and redshift space
distortion effects. To identify ionized regions in the 21-cm data we introduce
a new, self-adjusting thresholding approach based on the K-Means algorithm. We
find that the fraction of ionized cells identified in this way consistently
falls below the mean volume-averaged ionized fraction. From a comparison of the
three bubble size methods, we conclude that all three methods are useful, but
that the mean-free-path method performs best in terms of tracking the progress
of reionization and separating different reionization scenarios. The light-cone
effect is found to affect data spanning more than about 10~MHz in frequency
($\Delta z\sim0.5$). We find that redshift space distortions only marginally
affect the bubble size distributions.