Testing the Topology of Reionization

The central overlap phase of cosmological hydrogen reionization is fundamentally a change in the topology of ionized regions. Before overlap, ionized bubbles grew in isolation. During overlap, they merge into a percolating ionized medium, which fills an ever-increasing volume and eventually replaces neutral gas throughout the intergalactic medium. Overlap can therefore be well studied using topological statistics, and in particular the genus number of the neutral-ionized interface. The most promising observational tools for applying such tests are (a) Lyman alpha galaxies, and (b) 21 cm tomography. Lyman alpha galaxies will be detected whenever they inhabit bubbles larger than 1 physical Mpc, and their presence can therefore be used to map such bubbles. Such large bubbles are expected during the overlap phase, and moreover, each one should contain a few detectably bright Lyman alpha galaxies. The 21cm line in principle affords better spatial resolution, but the required sensitivity and foreground subtraction may be an issue. Upcoming Lyman alpha surveys in the near-infrared could thus provide our first look at the topology of reionization.