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 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 of the contour Minkowski tensor. Further, we show that a size parameter constructed from the eigenvalues of this tensor provide an upper bound on the characteristic sizes of ionized bubbles at different redshifts. The shape and size parameters provide information of the characteristic time epochs when bubble mergers begin and end. Our method is expected to be useful to reconstruct the reionization history using data of the brightness temperature field.