The escape fraction of ionizing photons during the Epoch of Reionization: observability with the Square Kilometre Array

One of the most important parameters in characterizing the Epoch of Reionization, the escape fraction of ionizing photons, f_esc, remains unconstrained both observationally and theoretically. With recent work highlighting the impact of galaxy-scale feedback on the instantaneous value of f_esc, it is important to develop a model in which reionization is self-consistently coupled to galaxy evolution. In this work, we present such a model and explore how physically motivated functional forms of f_esc affect the evolution of ionized hydrogen within the intergalactic medium. Using the 21 cm power spectrum evolution, we investigate the likelihood of observationally distinguishing between a constant f_esc and other models that depend upon different forms of galaxy feedback. We find that changing the underlying connection between f_esc and galaxy feedback drastically alters the large-scale 21 cm power. The upcoming Square Kilometre Array Low Frequency instrument possesses the sensitivity to differentiate between our models at a fixed optical depth, requiring only 200 h of integration time focused on redshifts z = 7.5-8.5. Generalizing these results to account for a varying optical depth will require multiple 800 h observations spanning redshifts z = 7-10. This presents an exciting opportunity to observationally constrain one of the most elusive parameters during the Epoch of Reionization.