Prospects of constraining reionization model parameters using Minkowski tensors and Betti numbers

Abstract

We explore the possibility of constraining model parameters of the Epoch of Reionization (EoR) from 21cm brightness temperature maps, using a combination of morphological descriptors constructed from the eigenvalues of the Contour Minkowski Tensor (CMT), Betti numbers (count of connected regions ncon and holes nhole) and the area of structures in the excursion set of the field. We use a three parameter model of EoR simulated using 21cmFAST, namely the ionizing efficiency of sources ζ, the minimum virial temperature Tvir required for collapse into a halo and the maximum radius for ionizing radiation described by Rmfp. We performed a Bayesian analysis to recover model parameters for a mock 21cm image from SKA phase I at a redshift of z=7.4 corresponding to a mean neutral hydrogen fraction of x̅HI≃ 0.5. We find that in the absence of noise the average size of structures in the field with xHI≲ 0.5 is smaller than regions with xHI≳ 0.5 and the structures are equally isotropic when x̅HI=0.5 . We also find that in order to recover the input model to within 1-σ accuracy for a mock noisy image at a single frequency channel of 1 MHz, for an observation time t_obs<2000 hrs, the noisy δ Tb map needs to be smoothed at a scale R_s>9.5 Mpc. Finally we show that the systematic behaviour of the statistic as ionization progresses, enables us to obtain stringent constraints on x̅HI (with a coefficient of variation ∼ 0.05 as compared to ∼ 0.1–0.2 for model parameter constraints), thereby making these descriptors a promising statistic for constraining EoR model parameters and the ionization history of the universe.