Topology of neutral hydrogen distribution with the Square Kilometer Array

Abstract

Morphology of the complex HI gas distribution can be quantified by statistics like the Minkowski functionals, and can provide a way to statistically study the large scale structure in the HI maps both at low redshifts, and during the epoch of reionization (EoR). At low redshifts, the 21cm emission traces the underlying matter distribution. Topology of the HI gas distribution, as measured by the genus, could be used as a "standard ruler". This enables the determination of distance-redshift relation and also the discrimination of various models of dark energy and of modified gravity. The topological analysis is also sensitive to certain primordial non-Gaussian features. Compared with two-point statistics, the topological statistics are more robust against the nonlinear gravitational evolution, bias, and redshift-space distortion. The HI intensity map observation naturally avoids the sparse sampling distortion, which is an important systematic in optical galaxy survey. The large cosmic volume accessible to SKA would provide unprecedented accuracy using such a measurement. During the EoR, topology can be a powerful and intuitive tool to distinguish among the different evolutionary stages of reionization, where the ionized regions make up a significant fraction of the volume. Furthermore, it can also discriminate among various reionization models. The genus curves evolve during cosmological reionization, and for different reionization scenarios, the topology of the HI gas distribution can be significantly different even if the global ionization fractions are the same. It can provide clear and intuitive diagnostics for how the reionization takes place, and indirectly probes the properties of radiation-sources. In this brief chapter we will describe the scientific background of the topology study, and forecast the potential of the SKA for measuring cosmological parameters and constraining structure formation mechanism through the study of topology of HI gas distribution.