Topology of reionisation times: Concepts, measurements, and comparisons to Gaussian random field predictions

Abstract

Context. In the next decade, radio telescopes, such as the Square Kilometer Array (SKA), will explore the Universe at high redshift, and particularly during the epoch of reionisation (EoR). The first structures emerged during this epoch, and their radiation reionised the previously cold and neutral gas of the Universe, creating ionised bubbles that percolate at the end of the EoR (z ∼ 6). SKA will produce 2D images of the distribution of the neutral gas at many redshifts, pushing us to develop tools and simulations to understand its properties. Aims. With this paper, we aim to measure topological statistics of the EoR in the so-called reionisation time fields from both cosmological and semi-analytical simulations. This field informs us about the time of reionisation of the gas at each position; it is used to probe the inhomogeneities of reionisation histories and can be extracted from 21 cm maps. We also compare these measurements with analytical predictions obtained within Gaussian random field (GRF) theory. Methods. The GRF theory allows us to compute many statistics of a field, namely the probability distribution functions (PDFs) of the field or its gradient, isocontour length, critical point distributions, and skeleton length. We compare these theoretical predictions to measurements made on reionisation time fields extracted from an EMMA simulation and a 21cmFAST simulation at 1 cMpc/h resolution. We also compared our results to GRFs generated from the fitted power spectra of the simulation maps. Results. Both EMMA and 21cmFAST reionisation time fields (treion(r)) are close to being Gaussian fields, in contrast with the 21 cm, density, or ionisation fraction, which have all been shown to be non-Gaussian. Only accelerating ionisation fronts at the end of the EoR seem to be the cause of small non-gaussianities in treion(r). Overall, this topological description of reionisation times provides a new quantitative and reproducible way to characterise the EoR scenario. Under the assumption of GRFs, it enables the generation of reionisation models with their propagation, percolation, or seed statistics simply from the reionisation time power spectrum. Conversely, these topological statistics provide a means to constrain the properties of the power spectrum and by extension the physics that drive the propagation of radiation.