Studying the morphology of HI 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.
