The shape and size distribution of H II regions near the percolation transition

Using Shapefinders, which are ratios of Minkowski functionals, we study the morphology of neutral hydrogen (H?I) density fields, simulated using seminumerical technique (inside-out), at various stages of reionization. Accompanying the Shapefinders, we also employ the ‘largest cluster statistic’ (LCS), originally proposed in Klypin & Shandarin, to study the percolation in both neutral and ionized hydrogen. We find that the largest ionized region is percolating below the neutral fraction xHI?0.728 (or equivalently z ? 9). The study of Shapefinders reveals that the largest ionized region starts to become highly filamentary with non-trivial topology near the percolation transition. During the percolation transition, the first two Shapefinders – ‘thickness’ (T) and ‘breadth’ (B) – of the largest ionized region do not vary much, while the third Shapefinder – ‘length’ (L) – abruptly increases. Consequently, the largest ionized region tends to be highly filamentary and topologically quite complex. The product of the first two Shapefinders, T × B, provides a measure of the ‘cross-section’ of a filament-like ionized region. We find that, near percolation, the value of T × B for the largest ionized region remains stable at ~7?Mpc2 (in comoving scale) while its length increases with time. Interestingly, all large ionized regions have similar cross-sections. However, their length shows a power-law dependence on their volume, L ? V0.72, at the onset of percolation.