We employ the rank-2 contour Minkowski Tensor in two dimensions to probe length and time scales of ionized bubbles during the epoch of reionization. We demonstrate that the eigenvalues of this tensor provide excellent probes of the distribution of the sizes of ionized bubbles, and from it the characteristic bubble sizes, at different redshifts. We show that ionized bubbles are not circular, and hence not spherical in three dimensions, as is often assumed for simplified analytic arguments. We quantify their shape anisotropy by using the ratio of the two eigenvalues. The shape parameter provides the characteristic time epochs when bubble mergers begin and end. Our method will be very useful to reconstruct the reionization history using data of the brightness temperature field.

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 β, 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

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.