LAUSR

We use morphological descriptors, Betti numbers and Contour Minkowski Tensor (CMT) on 21cm brightness temperature excursion sets, to study the ionization and heating history of the intergalactic medium (IGM) during and before the Epoch of Reionization (EoR). The ratio of eigenvalues of the CMT denoted by $\beta$, gives shape information while it's trace gives the contour length of holes and connected regions. We simulate the matter density, neutral hydrogen fraction, spin temperature and brightness temperature field using the publicly available code 21cmFAST in a redshift range of $z=20.22$ to $z=6$. We study the redshift evolution of three quantities - the Betti number counts $N_{con,hole}$, the characteristic size $r^{ch}_{con,hole}$ and shape anisotropy parameter $\beta^{ch}_{con,hole}$ of connected regions and holes for these fields and investigate the different physical origins of their evolution. We make a qualitative comparison of different models of heating and ionization during the EoR. We obtain different regimes of morphological evolution of brightness temperature, depending upon how the shapes and sizes of connected regions and holes change with redshift for different astrophysical settings affecting the ionization and heating history of the IGM during and before the EoR. We find that the morphology of the brightness temperature field traces the morphology of ionized regions below a certain redshift value depending upon the model, where $\Delta r^{ch}_{hole}<10 \%$ and $\Delta \beta^{ch}_{hole}<1 \%$ relative to the $x_{HI}$ field. This difference decreases with redshift. Therefore, the ionization history of the IGM can be reconstructed using the morphological description of $\delta T_b$ in real space.