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In this paper we investigate the nature and distribution of large neutralregions during the late epoch of reionization. In the "bubble model" ofreionization, the mass distribution of large ionized regions ("bubbles") duringthe early stage of reionization is obtained by using the excursion set model,where the ionization of a region corresponds to the first up-crossing of abarrier by random trajectories. We generalize this idea, and develop a methodto predict the distribution of large scale neutral regions during the latestage of reionization, taking into account the ionizing background after thepercolation of HII regions. The large scale neutral regions which we call"neutral islands" are not individual galaxies or minihalos, but larger regionswhere fewer galaxies formed and hence ionized later, and they are identified inthe excursion set model with the first down-crossings of the island barrier.Assuming that the consumption rate of ionizing background photons isproportional to the surface area of the neutral islands, we obtained the sizedistribution of the neutral islands. We also take the "bubbles-in-island"effect into account by considering the conditional probability of up-crossing abubble barrier after down-crossing the island barrier. We find that this effectis very important. An additional barrier is set to avoid islands beingpercolated through. We find that there is a characteristic scale for theneutral islands, while the small islands are rapidly swallowed up by theionizing background, this characteristic scale does not change much as thereionization proceeds.

An analytical model of the large neutral regions during the late stage of reionization