A novel probe of bubble size statistics and time scales of the epoch of reionization using the contour Minkowski Tensor

Abstract

We employ the rank-2 {\em 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.