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