The shape and size distribution of HII 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 x(HI) less than or similar to 0.728 (or equivalently z less than or similar to 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 x B, provides a measure of the 'cross-section' of a filament-like ionized region. We find that, near percolation, the value of T x B for the largest ionized region remains stable at similar to 7Mpc(2) (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 proportional to V-0.72, at the onset of percolation.