The reionization process is expected to be prolonged by the small-scale absorbers (SSAs) of ionizing photons, which have been seen as Lyman-limit systems in quasar absorption line observations. We use a set of semi-numerical simulations to investigate the effects of absorption systems on the reionization process, especially their impacts on the neutral islands during the late epoch of reionization (EoR). Three model are studied, i.e. the extreme case of no-SSA model with a high level of ionizing background, the moderate-SSA model with a relatively high level of ionizing background, and the dense-SSA model with a low level of ionizing background. We find that while the characteristic scale of neutral regions decreases during the early and middle stages of reionization, it stays nearly unchanged at about 10 comoving Mpc during the late stage for the no-SSA and moderate-SSA models. However, in the case of weak ionizing background in the dense-SSA model, the characteristic island scale shows obvious evolution, as large islands break into many small ones that are slowly ionized. The evolutionary behavior of neutral islands during the late EoR thus provides a novel way to constrain the abundance of SSAs. We discuss the 21-cm observation with the upcoming Square Kilometre Array (SKA). The different models can be distinguished by the 21-cm power spectrum measurement, and it is also possible to extract the characteristic island scale from the imaging observation with a proper choice of the 21-cm brightness threshold.
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