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

TL;DR

This paper demonstrates that morphological descriptors like Minkowski tensors and Betti numbers derived from 21cm maps can effectively constrain parameters of the Epoch of Reionization, improving understanding of the universe's ionization history.

Contribution

The study introduces a novel combination of morphological descriptors and Bayesian analysis to recover EoR model parameters from simulated 21cm maps, showing their potential for future observations.

Findings

Structures are smaller in regions with lower neutral hydrogen fraction.

Smoothing at scales >9.5 Mpc is necessary for accurate parameter recovery.

Descriptors provide tight constraints on ionization fraction, with low coefficient of variation.

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 $n_{con}$ and holes $n_{hole}$) and the area of structures in the excursion set of the field. We use a three parameter model of EoR simulated using 21\textrm{cmFAST}, namely the ionizing efficiency of sources $\zeta$, the minimum virial temperature $T_{vir}$ required for collapse into a halo and the maximum radius for ionizing radiation described by $R_{mfp}$. 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 $\mathrm{\bar x}_{HI} \simeq 0.5$. We find that in the absence of noise the average size of structures in the field with $x_{HI} \lesssim 0.5$ is smaller than regions with $x_{HI} \gtrsim 0.5$ and the structures are equally isotropic when $\mathrm{\bar x}_{HI}=0.5$ . We also find that in order to recover the input model to within $1-\sigma$ accuracy for a mock noisy image at a single frequency channel of $1~\mathrm{MHz}$, for an observation time $t_{obs}<2000~\mathrm{hrs}$, the noisy $\delta T_b$ map needs to be smoothed at a scale $R_s>9.5~\mathrm{Mpc}$. Finally we show that the systematic behaviour of the statistic as ionization progresses, enables us to obtain stringent constraints on $\mathrm{\bar x}_{HI}$ (with a coefficient of variation $\sim 0.05$ as compared to $\sim 0.1-0.2$ for model parameter constraints), thereby making these descriptors a promising statistic for constraining EoR model parameters and the ionization history of the universe.