Morphology of the secondary cosmic microwave background anisotropies: the key to 'smouldering' reionization

We show how the morphological analysis of the maps of the secondary cosmic microwave background anisotropies can detect an extended period of 'smouldering' reionization, during which the Universe remains partially ionized. Neither radio observations of the redshifted 21-cm line nor infrared observations of the redshifted Lyman-alpha forest will be able to detect such a period. The most sensitive parameters to this kind of non-Gaussianity are the number of regions in the excursion set, N-cl, the perimeter of the excursion set, P-g, and the genus (i.e. '1 - number of holes') of the largest (by area) region. For example, if the Universe reionized fully at z = 6, but maintained about 1/3 mean ionized fraction as z = 20, then a 2-arcmin map with 500(2) pixel resolution and a signal-to-noise ratio S/N = 1/2 allows us to detect the non-Gaussianity due to reionization with better than 99 per cent confidence level.