Prospects of constraining reionization model parameters using Minkowski tensors and Betti numbers. Issue 5 (12th May 2021) - Kapahtia, Akanksha
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.