A novel probe of ionized bubble shape and size statistics of the epoch of reionization using the contour Minkowski Tensor

Abstract

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.

Saturation mechanism of the fluctuation dynamo at PrM ≥ 1

“…To characterize the magnetic structures, we use the Minkowski functionals [76]. Minkowski functionals have been used in studying morphology of structures in a number of numerical simulations [34,[77][78][79][80][81][82] and observations [83][84][85][86]. The morphology of a d-dimensional structure can be described by d + 1 Minkowski functionals.…”

The impact of non-Gaussianity on the error covariance for observations of the Epoch of Reionization (EoR) 21-cm power spectrum

“…Only weak upper limits on the EoR 21-cm PS have been estimated till date (McGreer, Mesinger & Fan 2011;Parsons et al 2014;Pober, Greig & Mesinger 2016a). In addition to the PS, various other statistics such as the variance (Patil et al 2014), bispectrum (Yoshiura et al 2015;Shimabukuro et al 2017;Majumdar et al 2018), and the Minkowski Functional (Bag et al 2018;Kapahtia et al 2018) have been proposed to quantify the EoR 21-cm signal .…”

Morphology of 21cm brightness temperature during the Epoch of Reionization using Contour Minkowski Tensor

“…Therefore, their values can be important characteristic features that can discriminate different models. Note that in [44] it was found that at z 0.5 , N con = N hole . We will show this to be true for all models we have considered in our study.…”

“…5). For this choice of ν cut , N con ∼ N hole at x HI = 0.5 [44]. For the x HI field, a connected region corresponds to a neutral region and a hole corresponds to an ionized region.…”

“…In the bottom panel we find that β ch x does not show much variation with redshift z and that the connected regions are more anisotropic than holes. The morphology of the neutral hydrogen field was studied in [44] for different smoothing scales and different values of ν cut . ν cut refers to the value of threshold above (below) which a connected region (hole) is interpreted as a neutral (ionized) region.…”