Studying the morphology of H i isodensity surfaces during reionization using Shapefinders and percolation analysis

Minkowski functionals and Shapefinders shed light on the connectedness of large-scale structure by determining its topology and morphology. We use a sophisticated code, SURFGEN2, to measure the Minkowski functionals and Shapefinders of individual clusters by modelling cluster surfaces using the 'Marching Cube 33' triangulation algorithm. In this paper, we study the morphology of simulated neutral hydrogen (HI) density fields using Shapefinders at various stages of reionization from the excursion set approach. Accompanying the Shapefinders, we also employ the 'largest cluster statistic' (LCS) to understand the percolation process. Percolation curves demonstrate that the non-Gaussianity in the HI field increases as reionization progresses. The large clusters in both the HI overdense and underdense excursion sets possess similar values of "thickness" ($T$), as well as "breadth" ($B$), but their third Shapefinder - "length" ($L$) - becomes almost proportional to their volume. The large clusters in both HI overdense and underdense segments are overwhelmingly filamentary. The 'cross-section' of a filamentary cluster can be estimated using the product of the first two Shapefinders, $T \times B$. Hence the cross sections of the large clusters at the onset of percolation do not vary much with volume and their sizes only differ in terms of their lengths. This feature appears more vividly in HI overdense regions than in underdense regions and is more pronounced at lower redshifts which correspond to an advanced stage of reionization. These geometrical properties of our reionization model can be compared with that of the future observations with the upcoming low-frequency radio interferometers.