Abstract
In the next decade, radio telescopes like 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 radiations have reionised the previously cold and neutral gas of the
Universe creating ionised bubbles that percolate at the end of the EoR (at a
redshift of approximately 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. This paper aims at measuring 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. We also compare these
measurements with analytical predictions obtained within the gaussian random
field (GRF) theory. The gaussian random fields (GRFs) theory allows us to
compute many statistics of a field: 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 and a 21cmFAST
simulations at 1 a cMpc/h resolution. We also compared our results to GRFs
generated from the fitted power spectra of the simulation maps. Both EMMA and
21cmFAST reionisation time fields (treion(r)) are close to be gaussian fields,
in contrast with the 21 cm, density or ionisation fraction that are all proven
to be non-gaussian. Only accelerating ionisation fronts at the end of the EoR
seem to be a cause of small non-gaussianities in treion(r). Overall our results
indicate that an analytical description of the reionisation percolation can be
reasonably made within the framework of GRF theory.
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