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

Abstract

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 × 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.

Saturation mechanism of the fluctuation dynamo at PrM ≥ 1

“…To characterize the magnetic structures, we use the Minkowski functionals [76]. Minkowski functionals have been used in studying morphology of structures in a number of numerical simulations [34,[77][78][79][80][81][82] and observations [83][84][85][86]. The morphology of a d-dimensional structure can be described by d + 1 Minkowski functionals.…”

Inference from the 21cm signal

“…An extension to Minkowski functionals, shape-finders ( [185]) are a way to characterise the shapes of compact surfaces. Applied to reionisation ( [6,5]), these shape-finders can provide a means to characterise how the ionised regions grow. For example, they are useful in being able to distinguish between whether the topology is planar or filamentary.…”

“…[55]). When describing the largest singly connected ionised region, [6,5] find that both T and B evolve slowly whereas L increases rapidly. Thus, this large ionised region grows only along its 'length' implying a highly filamentary structure.…”

Distinguishing reionization models using the largest cluster statistics of the 21-cm maps

“…There are a number of complementary methods which deal with the signal in real space and have been employed directly on the simulated tomographic images to probe the morphology of the 21-cm field and its evolution during the EoR through the analysis of topology and geometry of this field. Among them, the widely used methods are the Minkowski Functionals (MFs) (Friedrich et al 2011;Hong et al 2014;Yoshiura et al 2017;Bag et al 2018Bag et al , 2019 which have been used to track the reionization history, the Minkowski tensors (Kapahtia et al 2019) which are the generalized tensorial form of MFs and can encapsulate the direction information. These are also methods based on percolation theory (Iliev et al 2006;Iliev et al 2014;Furlanetto & Oh 2016;Bag et al 2018Bag et al , 2019, granulometry (Kakiichi et al 2017) and persistence theory (Elbers & van de Weygaert 2019) which have been used for the theoretical study of the topological phases of H regions during EoR.…”