http://arxiv.org/abs/1801.01116
It is well known that the Minkowski functionals, and the associated Shapefinders, shed light on the connectedness of large scale structure by determining its topology and morphology. These geometrical tools therefore play a role which is complementary to that of traditional N-point correlation functions. Using Shapefinders we study the morphology of neutral hydrogen (HI) density fields, simulated using semi-numerical technique (inside-out), at various stages of reionization. Accompanying the Shapefinders, we also employ the ‘largest cluster statistic’ (LCS), originally proposed in Klypin and Shandarin (1993), to study the percolation in both neutral and ionized hydrogen. We find that the percolation transition in the ionized segment takes place below the neutral fraction $x_{HI} \lesssim 0.728$ (or $z \lesssim 9$). 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, $T\times B$, provides a measure of the ‘cross-section’ of a filament-like ionized region. We find that, near percolation, the value of $T\times B$ for the largest ionized region remains stable at $\sim 7$ Mpc$^2$ (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, $L\propto V^{0.72}$, at the onset of percolation.
S. Bag, R. Mondal, P. Sarkar, et. al.
Thu, 4 Jan 2018
21/44
Comments: 19 pages, 9 figures