Recovering the HII region size statistics from 21-cm tomography

We introduce a novel technique, called "granulometry", to characterize and recover the mean size and the size distribution of HII regions from 21-cm tomography. The technique is easy to implement, but places the previously not very well defined concept of morphology on a firm mathematical foundation. The size distribution of the cold spots in 21-cm tomography can be used as a direct tracer of the underlying probability distribution of HII region sizes. We explore the capability of the method using large-scale reionization simulations and mock observational data cubes while considering capabilities of SKA1-low and a future extension to SKA2. We show that the technique allows the recovery of the HII region size distribution with a moderate signal-to-noise ratio from wide-field imaging ($\rm SNR\lesssim3$), for which the statistical uncertainty is sample variance dominated. We address the observational requirements on the angular resolution, the field-of-view, and the thermal noise limit for a successful measurement. To achieve a full scientific return from 21-cm tomography and to exploit a synergy with 21-cm power spectra, we suggest an observing strategy using wide-field imaging (several tens of square degrees) by an interferometric mosaicking/multi-beam observation with additional intermediate baselines (~2-4 km).